bibliography.bib

@misc{abbottMcabbottTullioJl2022,
  title = {Mcabbott/{{Tullio}}.Jl: V0.3.5},
  shorttitle = {Mcabbott/{{Tullio}}.Jl},
  author = {Abbott, Michael and {Dilum Aluthge} and {N3N5} and Schaub, Simeon and Elrod, Chris and Lucibello, Carlo and Chen, Johnny},
  year = {2022},
  month = sep,
  doi = {10.5281/ZENODO.7106192},
  url = {https://zenodo.org/record/7106192},
  urldate = {2023-07-12},
  abstract = {Tullio v0.3.5 Diff since v0.3.4 {$<$}strong{$>$}Closed issues:{$<$}/strong{$>$} Using Tullio within generated functions (\#149) poor performance for simple GPU loop (\#152) Symbolic gradient producing surprising results (\#153) {$<$}strong{$>$}Merged pull requests:{$<$}/strong{$>$} Don't call {$<$}code{$>$}parent{$<$}/code{$>$} before {$<$}code{$>$}similar{$<$}/code{$>$} (\#159) (@mcabbott)},
  copyright = {Open Access},
  howpublished = {Zenodo}
}

@article{AlnaesEtal2015,
  title = {The {{FEniCS}} Project Version 1.5},
  author = {Alnaes, M. S. and Blechta, J. and Hake, J. and Johansson, A. and Kehlet, B. and Logg, A. and Richardson, C. and Ring, J. and Rognes, M. E. and Wells, G. N.},
  year = {2015},
  journal = {Archive of Numerical Software},
  volume = {3},
  doi = {10.11588/ans.2015.100.20553}
}

@article{andersonMFEMModularFinite2021a,
  title = {{{MFEM}}: {{A}} Modular Finite Element Methods Library},
  shorttitle = {{{MFEM}}},
  author = {Anderson, Robert and Andrej, Julian and Barker, Andrew and Bramwell, Jamie and Camier, Jean-Sylvain and Cerveny, Jakub and Dobrev, Veselin and Dudouit, Yohann and Fisher, Aaron and Kolev, Tzanio and Pazner, Will and Stowell, Mark and Tomov, Vladimir and Akkerman, Ido and Dahm, Johann and Medina, David and Zampini, Stefano},
  year = {2021},
  month = jan,
  journal = {Computers \& Mathematics with Applications},
  series = {Development and {{Application}} of {{Open-source Software}} for {{Problems}} with {{Numerical PDEs}}},
  volume = {81},
  pages = {42--74},
  issn = {0898-1221},
  doi = {10.1016/j.camwa.2020.06.009},
  url = {https://www.sciencedirect.com/science/article/pii/S0898122120302583},
  urldate = {2024-02-01},
  abstract = {MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM's goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library.},
  keywords = {Finite element methods,High-order methods,High-performance computing,Matrix-free algorithms,Numerical PDEs,Open-source scientific software},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/P8YG34V6/Anderson et al. - 2021 - MFEM A modular finite element methods library.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/GTUDF8S5/S0898122120302583.html}
}

@incollection{arndtExaDGHighOrderDiscontinuous2020,
  title = {{{ExaDG}}: {{High-Order Discontinuous Galerkin}} for the {{Exa-Scale}}},
  shorttitle = {{{ExaDG}}},
  booktitle = {Software for {{Exascale Computing}} - {{SPPEXA}} 2016-2019},
  author = {Arndt, Daniel and Fehn, Niklas and Kanschat, Guido and Kormann, Katharina and Kronbichler, Martin and Munch, Peter and Wall, Wolfgang A. and Witte, Julius},
  editor = {Bungartz, Hans-Joachim and Reiz, Severin and Uekermann, Benjamin and Neumann, Philipp and Nagel, Wolfgang E.},
  year = {2020},
  volume = {136},
  pages = {189--224},
  publisher = {{Springer International Publishing}},
  address = {{Cham}},
  doi = {10.1007/978-3-030-47956-5_8},
  url = {http://link.springer.com/10.1007/978-3-030-47956-5_8},
  urldate = {2023-07-10},
  abstract = {This text presents contributions to efficient high-order finite element solvers in the context of the project ExaDG, part of the DFG priority program 1648 Software for Exascale Computing (SPPEXA). The main algorithmic components are the matrix-free evaluation of finite element and discontinuous Galerkin operators with sum factorization to reach a high node-level performance and parallel scalability, a massively parallel multigrid framework, and efficient multigrid smoothers. The algorithms have been applied in a computational fluid dynamics context. The software contributions of the project have led to a speedup by a factor 3 - 4 depending on the hardware. Our implementations are available via the deal.II finite element library.},
  isbn = {978-3-030-47955-8 978-3-030-47956-5},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/YFXL2BZT/Arndt et al. - 2020 - ExaDG High-Order Discontinuous Galerkin for the E.pdf}
}

@article{arnoldUnifiedAnalysisDiscontinuous2002,
  title = {Unified {{Analysis}} of {{Discontinuous Galerkin Methods}} for {{Elliptic Problems}}},
  author = {Arnold, Douglas N. and Brezzi, Franco and Cockburn, Bernardo and Marini, L. Donatella},
  year = {2002},
  month = jan,
  journal = {SIAM Journal on Numerical Analysis},
  volume = {39},
  number = {5},
  pages = {1749--1779},
  issn = {0036-1429, 1095-7170},
  doi = {10.1137/S0036142901384162},
  url = {http://epubs.siam.org/doi/10.1137/S0036142901384162},
  urldate = {2022-12-20},
  abstract = {We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.},
  langid = {english},
  annotation = {2071 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/28SVLGZN/Arnold et al. - 2002 - Unified Analysis of Discontinuous Galerkin Methods.pdf}
}

@article{badiaGenericFiniteElement2020,
  title = {A {{Generic Finite Element Framework}} on {{Parallel Tree-Based Adaptive Meshes}}},
  author = {Badia, Santiago and Mart{\'i}n, Alberto F. and Neiva, Eric and Verdugo, Francesc},
  year = {2020},
  month = jan,
  journal = {SIAM Journal on Scientific Computing},
  volume = {42},
  number = {6},
  pages = {C436-C468},
  issn = {1064-8275, 1095-7197},
  doi = {10.1137/20M1328786},
  url = {https://epubs.siam.org/doi/10.1137/20M1328786},
  urldate = {2023-07-10},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/PFJRRGFN/Badia et al. - 2020 - A Generic Finite Element Framework on Parallel Tre.pdf}
}

@article{bangerthDataStructuresRequirements2009,
  title = {Data Structures and Requirements for {\emph{Hp}} Finite Element Software},
  author = {Bangerth, W. and {Kayser-Herold}, O.},
  year = {2009},
  month = mar,
  journal = {ACM Transactions on Mathematical Software},
  volume = {36},
  number = {1},
  pages = {1--31},
  issn = {0098-3500, 1557-7295},
  doi = {10.1145/1486525.1486529},
  url = {https://dl.acm.org/doi/10.1145/1486525.1486529},
  urldate = {2023-03-29},
  abstract = {Finite element methods approximate solutions of partial differential equations by restricting the problem to a finite dimensional function space. In               hp               adaptive finite element methods, one defines these discrete spaces by choosing different polynomial degrees for the shape functions defined on a locally refined mesh.                          Although this basic idea is quite simple, its implementation in algorithms and data structures is challenging. It has apparently not been documented in the literature in its most general form. Rather, most existing implementations appear to be for special combinations of finite elements, or for discontinuous Galerkin methods.                            In this article, we discuss generic data structures and algorithms used in the implementation of               hp               methods for arbitrary elements, and the complications and pitfalls one encounters. As a consequence, we list the information a description of a finite element has to provide to the generic algorithms for it to be used in an               hp               context. We support our claim that our reference implementation is efficient using numerical examples in two dimensions and three dimensions, and demonstrate that the               hp               -specific parts of the program do not dominate the total computing time. This reference implementation is also made available as part of the Open Source deal.II finite element library.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/LGB6443K/Bangerth und Kayser-Herold - 2009 - Data structures and requirements for hp fin.pdf}
}

@article{bangerthDealIIGeneralpurpose2007,
  title = {Deal.{{II}} - {{A}} General-Purpose Object-Oriented Finite Element Library},
  author = {Bangerth, W. and Hartmann, R. and Kanschat, G.},
  year = {2007},
  month = aug,
  journal = {ACM Transactions on Mathematical Software},
  volume = {33},
  number = {4},
  pages = {24--es},
  issn = {0098-3500},
  doi = {10.1145/1268776.1268779},
  url = {https://doi.org/10.1145/1268776.1268779},
  urldate = {2022-05-13},
  abstract = {An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced object-oriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through this approach, deal.II supports a large number of different applications covering a wide range of scientific areas, programming methodologies, and application-specific algorithms, without imposing a rigid framework into which they have to fit. A judicious use of programming techniques allows us to avoid the computational costs frequently associated with abstract object-oriented class libraries. The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools. Finally, some results obtained with applications built atop deal.II are shown to demonstrate the powerful capabilities of this toolbox.},
  keywords = {Object-orientation,software design},
  annotation = {856 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/8AJA2XAC/Bangerth et al. - 2007 - deal.II&#x2014;A general-purpose object-oriented f.pdf}
}

@article{barangerConnectionFiniteVolume1996,
  title = {Connection between Finite Volume and Mixed Finite Element Methods},
  author = {Baranger, Jacques and Maitre, Jean-Fran{\c c}ois and Oudin, Fabienne},
  year = {1996},
  journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
  volume = {30},
  number = {4},
  pages = {445--465},
  issn = {0764-583X, 1290-3841},
  doi = {10.1051/m2an/1996300404451},
  url = {http://www.esaim-m2an.org/10.1051/m2an/1996300404451},
  urldate = {2022-10-21},
  langid = {english},
  annotation = {60 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/VTXDLYKB/Baranger et al. - 1996 - Connection between finite volume and mixed finite .pdf}
}

@article{besardEffectiveExtensibleProgramming2018,
  title = {Effective Extensible Programming: {{Unleashing Julia}} on {{GPUs}}},
  author = {Besard, Tim and Foket, Christophe and De Sutter, Bjorn},
  year = {2018},
  journal = {IEEE Transactions on Parallel and Distributed Systems},
  eprint = {1712.03112},
  primaryclass = {cs.PL},
  issn = {1045-9219},
  doi = {10.1109/TPDS.2018.2872064},
  archiveprefix = {arxiv},
  annotation = {66 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/BRJKWEBQ/Besard et al. - 2018 - Effective extensible programming Unleashing Julia.pdf}
}

@article{bezansonJuliaFreshApproach2017,
  title = {Julia: {{A Fresh Approach}} to {{Numerical Computing}}},
  shorttitle = {Julia},
  author = {Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B.},
  year = {2017},
  month = jan,
  journal = {SIAM Review},
  volume = {59},
  number = {1},
  pages = {65--98},
  publisher = {{Society for Industrial and Applied Mathematics}},
  issn = {0036-1445},
  doi = {10.1137/141000671},
  url = {https://epubs.siam.org/doi/abs/10.1137/141000671},
  urldate = {2023-03-21},
  abstract = {This is the third in a series of papers on aspects of modern computing environments that are relevant to statistical data analysis. In this paper, we discuss programming environments. In particular, we argue that integrated programming environments (for example, Lisp and Smalltalk environments) are more appropriate as a base for data analysis than conventional operating systems (for example, Unix).},
  annotation = {2244 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/MQQ6HM4G/Bezanson et al. - 2017 - Julia A Fresh Approach to Numerical Computing.pdf}
}

@book{bitsadze1988some,
  title = {Some Classes of Partial Differential Equations},
  author = {Bitsadze, Andrei Vasilevich},
  year = {1988},
  volume = {4},
  publisher = {{CRC Press}}
}

@article{brackbillContinuumMethodModeling1992,
  ids = {brackbillContinuumMethodModeling1992a},
  title = {A Continuum Method for Modeling Surface Tension},
  author = {Brackbill, J.U and Kothe, D.B and Zemach, C},
  year = {1992},
  month = jun,
  journal = {Journal of Computational Physics},
  volume = {100},
  number = {2},
  pages = {335--354},
  issn = {0021-9991},
  doi = {10.1016/0021-9991(92)90240-Y},
  url = {http://www.sciencedirect.com/science/article/pii/002199919290240Y},
  abstract = {A new method for modeling surface tension effects on fluid motion has been developed. Interfaces between fluids of different properties, or ``colors,'' are represented as transition regions of finite thickness, across which the color variable varies continuously. At each point in the transition region, a force density is defined which is proportional to the curvature of the surface of constant color at that point. It is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero. The continuum method eliminates the need for interface reconstruction, simplifies the calculation of surface tension, enables accurate modeling of two- and three-dimensional fluid flows driven by surface forces, and does not impose any modeling restrictions on the number, complexity, or dynamic evolution of fluid interfaces having surface tension. Computational results for two-dimensional flows are given to illustrate the properties of the method.},
  keywords = {marangoni},
  annotation = {6102 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/Y5IZYGKN/Brackbill et al. - 1992 - A continuum method for modeling surface tension.pdf;C\:\\Users\\zimbropa\\Downloads\\1-s2.0-002199919290240Y-main.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/T5667NVA/002199919290240Y.html}
}

@article{brezziDiscourseStabilityConditions1990,
  title = {A Discourse on the Stability Conditions for Mixed Finite Element Formulations},
  author = {Brezzi, Franco and Bathe, Klaus-J{\"u}rgen},
  year = {1990},
  month = sep,
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {82},
  number = {1-3},
  pages = {27--57},
  issn = {00457825},
  doi = {10.1016/0045-7825(90)90157-H},
  url = {https://linkinghub.elsevier.com/retrieve/pii/004578259090157H},
  urldate = {2024-02-02},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/VTJDMAKZ/Brezzi und Bathe - 1990 - A discourse on the stability conditions for mixed .pdf}
}

@article{brooksStreamlineUpwindPetrovGalerkin1982,
  title = {Streamline Upwind/{{Petrov-Galerkin}} Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible {{Navier-Stokes}} Equations},
  author = {Brooks, Alexander N. and Hughes, Thomas J. R.},
  year = {1982},
  month = sep,
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {32},
  number = {1},
  pages = {199--259},
  issn = {0045-7825},
  doi = {10.1016/0045-7825(82)90071-8},
  url = {https://www.sciencedirect.com/science/article/pii/0045782582900718},
  urldate = {2023-06-30},
  abstract = {A new finite element formulation for convection dominated flows is developed. The basis of the formulation is the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes. When implemented as a consistent Petrov-Galerkin weighted residual method, it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods. The accuracy of the streamline upwind/Petrov-Galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples. The formulation is extended to the incompressible Navier-Stokes equations. An efficient implicit pressure/explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step. The effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a Reynolds number of 100.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/GMD5KZGT/Brooks und Hughes - 1982 - Streamline upwindPetrov-Galerkin formulations for.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/L4CP8SDB/0045782582900718.html}
}

@article{bui-thanhGodunovUnifiedHybridized2015,
  title = {From {{Godunov}} to a Unified Hybridized Discontinuous {{Galerkin}} Framework for Partial Differential Equations},
  author = {{Bui-Thanh}, Tan},
  year = {2015},
  month = aug,
  journal = {Journal of Computational Physics},
  volume = {295},
  pages = {114--146},
  issn = {00219991},
  doi = {10.1016/j.jcp.2015.04.009},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0021999115002557},
  urldate = {2023-07-10},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/QG8VYLEI/Bui-Thanh - 2015 - From Godunov to a unified hybridized discontinuous.pdf}
}

@article{caboussatNumericalSimulationTemperaturedriven2023,
  title = {Numerical Simulation of Temperature-Driven Free Surface Flows, with Application to Laser Melting and Polishing},
  author = {Caboussat, Alexandre and Hess, Julien and Masserey, Alexandre and Picasso, Marco},
  year = {2023},
  month = jun,
  journal = {Journal of Computational Physics: X},
  pages = {100127},
  issn = {25900552},
  doi = {10.1016/j.jcpx.2023.100127},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S2590055223000057},
  urldate = {2023-06-06},
  abstract = {We present a multi-physics model for the approximation of the coupled system formed by the heat equation and the Navier-Stokes equations with solidification and free surfaces. The computational domain is the union of two overlapping regions: a larger domain to account for thermal effects, and a smaller region to account for the fluid flow. Temperature-dependent surface effects are accounted for via surface tension and Marangoni forces. The volume-of-fluid approach is used to track the free surfaces between the metal (liquid or solidified) and the ambient air. The numerical method incorporates all the physical phenomena within an operator splitting strategy. The discretization relies on a two-grid approach that uses an unstructured finite element mesh for diffusion phenomena and a structured Cartesian grid for advection phenomena. The model is validated through numerical experiments, the main application being laser melting and polishing.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/54TG5UH2/Caboussat et al. - 2023 - Numerical simulation of temperature-driven free su.pdf}
}

@article{cahnFreeEnergyNonuniform1958,
  title = {Free {{Energy}} of a {{Nonuniform System}}. {{I}}. {{Interfacial Free Energy}}},
  author = {Cahn, John W. and Hilliard, John E.},
  year = {1958},
  month = feb,
  journal = {The Journal of Chemical Physics},
  volume = {28},
  number = {2},
  pages = {258--267},
  publisher = {{American Institute of Physics}},
  issn = {0021-9606},
  doi = {10.1063/1.1744102},
  url = {https://aip.scitation.org/doi/10.1063/1.1744102},
  urldate = {2021-03-03},
  annotation = {7359 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/4BAUM2QI/1.html}
}

@inproceedings{Chaco95,
  title = {A Multilevel Algorithm for Partitioning Graphs},
  booktitle = {Supercomputing '95: {{Proceedings}} of the 1995 {{ACM}}/{{IEEE}} Conference on Supercomputing ({{CDROM}})},
  author = {Hendrickson, Bruce and Leland, Robert},
  year = {1995},
  pages = {28},
  publisher = {{ACM Press}},
  address = {{New York}},
  doi = {https://doi.acm.org/10.1145/224170.224228},
  isbn = {0-89791-816-9}
}

@article{chowdhuryLaserPowderBed2022,
  title = {Laser {{Powder Bed Fusion}}: {{A State-of-the-Art Review}} of the {{Technology}}, {{Materials}}, {{Properties}} \& {{Defects}}, and {{Numerical Modelling}}},
  shorttitle = {Laser {{Powder Bed Fusion}}},
  author = {Chowdhury, Sohini and Yadaiah, N. and Prakash, Chander and Ramakrishna, Seeram and Dixit, Saurav and Gulta, Lovi Raj and Buddhi, Dharam},
  year = {2022},
  month = aug,
  journal = {Journal of Materials Research and Technology},
  issn = {2238-7854},
  doi = {10.1016/j.jmrt.2022.07.121},
  url = {https://www.sciencedirect.com/science/article/pii/S2238785422011607},
  urldate = {2022-08-16},
  abstract = {Additive Manufacturing (AM) has revolutionized the manufacturing industry in several directions. Laser powder bed fusion (LPBF), a powder bed fusion AM process, has been dramatically accepted in various industries due to its versatility with several materials, including alloys. This comprehensive review article primarily explains the basic principle of the LPBF process, scientific and technological progress of several inter-related parameters, feedstock materials, produced properties/defects, and insights of numerical modelling to virtually understand the process behavior. Specific attention has been given to selective laser-meted (LPBFed) properties, driven through the microstructure formations and, thereby, concerning defects. The scope of the post-processing techniques to refine microstructure has also been discussed in this review paper. It has been identified that the defects are vital in LPBF process and are primarily governed by the process parameters. Therefore, a wisely chosen, optimized set of parameters can play a crucial role in minimizing defects considerably. Finally, the numerical modeling discussed in this review paper will help the researchers understand the LPBF process.},
  langid = {english},
  keywords = {Additive Manufacturing,Defects,Feedstock Materials,Numerical Modeling,Properties,Selective Laser Melting},
  annotation = {13 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/6GAIRWB3/Chowdhury et al. - 2022 - Laser Powder Bed Fusion A State-of-the-Art Review.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/P8A74WBC/S2238785422011607.html}
}

@book{ciarletFiniteElementMethod2002,
  title = {The Finite Element Method for Elliptic Problems},
  author = {Ciarlet, Philippe G.},
  year = {2002},
  series = {Classics in Applied Mathematics},
  number = {40},
  publisher = {{Society for Industrial and Applied Mathematics}},
  address = {{Philadelphia, PA}},
  isbn = {978-0-89871-514-9},
  langid = {english},
  lccn = {QA377 .C53 2002},
  keywords = {Boundary value problems,Differential equations Elliptic,Finite element method,Numerical solutions},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/2YCXUWYD/Preface_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/3SPIT289/Copyright-page_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/4KXEDEP5/Studies-in-Mathematics-and-its-Appl_1978_Studies-in-Mathematics-and-Its-Appl.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/63D75GDQ/General-Plan-and-Interdependence-_1978_Studies-in-Mathematics-and-Its-Applic.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/6YQUT3QK/Chapter-4---Other-Finite-Element-Methods-Fo_1978_Studies-in-Mathematics-and-.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/82QUJH6R/Dedication_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/9QSGK7DW/Bibliography_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/F4VNL779/Chapter-2---Introduction-to-the-Finite-_1978_Studies-in-Mathematics-and-Its-.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/HYW4D8W4/Chapter-1---Elliptic-Boundary-Value-_1978_Studies-in-Mathematics-and-Its-App.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/IYLK2ALF/Chapter-3---Conforming-Finite-Element-Method_1978_Studies-in-Mathematics-and.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/NBKI4YNJ/Index_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/PNZXQEN3/Ciarlet - 2002 - The finite element method for elliptic problems.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/THCKSWCZ/Epilogue----Some--real-life--finite-eleme_1978_Studies-in-Mathematics-and-It.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/V39H7JZ3/Chapter-6---Finite-Element-Methods-for-T_1978_Studies-in-Mathematics-and-Its.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/XNCG74MP/Glossary-of-Symbols_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/YYVG5VZC/Chapter-5---Application-of-the-finite-Element-_1978_Studies-in-Mathematics-a.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/ZDGUL9BT/Front-Matter_1978_Studies-in-Mathematics-and-Its-Applications.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/ZDHC2XRL/Chapter-7---A-Mixed-Finite-Element-_1978_Studies-in-Mathematics-and-Its-Appl.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/ZSTELMIQ/Chapter-8---Finite-Element-Methods-f_1978_Studies-in-Mathematics-and-Its-App.pdf}
}

@book{cockburnDiscontinuousGalerkinMethods2000,
  title = {Discontinuous {{Galerkin Methods}}: {{Theory}}, {{Computation}} and {{Applications}}},
  shorttitle = {Discontinuous {{Galerkin Methods}}},
  editor = {Cockburn, Bernardo and Karniadakis, George E. and Shu, Chi-Wang},
  year = {2000},
  series = {Lecture {{Notes}} in {{Computational Science}} and {{Engineering}}},
  publisher = {{Springer-Verlag}},
  address = {{Berlin Heidelberg}},
  doi = {10.1007/978-3-642-59721-3},
  url = {https://www.springer.com/gp/book/9783642640988},
  urldate = {2021-03-19},
  abstract = {This volume contains current progress of a new class of finite element method, the Discontinuous Galerkin Method (DGM), which has been under rapid developments recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simulation, turbomachinery, turbulent flows, materials processing, Magneto-hydro-dynamics, plasma simulations and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effect in organizing and publishing the existing volume of knowledge on this subject. The current volume organizes this knowledge and it covers both theoretical as well as practical issues of the Discontinuous Galerkin method.},
  isbn = {978-3-642-64098-8},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/JPNLXCEZ/Cockburn et al. - 2000 - Discontinuous Galerkin Methods Theory, Computatio.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/XB2YCWD2/2000_Book_DiscontinuousGalerkinMethods.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/CHJXBB84/9783642640988.html}
}

@article{cockburnHybridizableDiscontinuousGalerkin2009,
  title = {A {{Hybridizable Discontinuous Galerkin Method}} for {{Steady-State Convection-Diffusion-Reaction Problems}}},
  author = {Cockburn, Bernardo and Dong, Bo and Guzm{\'a}n, Johnny and Restelli, Marco and Sacco, Riccardo},
  year = {2009},
  month = jan,
  journal = {SIAM Journal on Scientific Computing},
  volume = {31},
  number = {5},
  pages = {3827--3846},
  issn = {1064-8275, 1095-7197},
  doi = {10.1137/080728810},
  url = {http://epubs.siam.org/doi/10.1137/080728810},
  urldate = {2023-03-27},
  abstract = {In this article, we propose a novel discontinuous Galerkin method for convectiondiffusion-reaction problems, characterized by three main properties. The first is that the method is hybridizable; this renders it efficiently implementable and competitive with the main existing methods for these problems. The second is that, when the method uses polynomial approximations of the same degree for both the total flux and the scalar variable, optimal convergence properties are obtained for both variables; this is in sharp contrast with all other discontinuous methods for this problem. The third is that the method exhibits superconvergence properties of the approximation to the scalar variable; this allows us to postprocess the approximation in an element-by-element fashion to obtain another approximation to the scalar variable which converges faster than the original one. In this paper, we focus on the efficient implementation of the method and on the validation of its computational performance. With this aim, extensive numerical tests are devoted to explore the convergence properties of the novel scheme, to compare it with other methods in the diffusiondominated regime, and to display its stability and accuracy in the convection-dominated case.},
  langid = {english},
  annotation = {120 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/YY6QY54W/Cockburn et al. - 2009 - A Hybridizable Discontinuous Galerkin Method for S.pdf}
}

@article{cockburnLocalDiscontinuousGalerkin1998,
  title = {The {{Local Discontinuous Galerkin Method}} for {{Time-Dependent Convection-Diffusion Systems}}},
  author = {Cockburn, Bernardo and Shu, Chi-Wang},
  year = {1998},
  month = dec,
  journal = {SIAM Journal on Numerical Analysis},
  volume = {35},
  number = {6},
  pages = {2440--2463},
  issn = {0036-1429, 1095-7170},
  doi = {10.1137/S0036142997316712},
  url = {http://epubs.siam.org/doi/10.1137/S0036142997316712},
  urldate = {2022-04-13},
  abstract = {In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge{\textendash}Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling of complicated geometries for convection-dominated problems. It is proven that for scalar equations, the LDG methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are kth order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.},
  langid = {english},
  annotation = {1559 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/9B5TJJG3/S0036142997316712.pdf}
}

@article{cockburnLocallyDivergencefreeDiscontinuous2004,
  title = {Locally Divergence-Free Discontinuous {{Galerkin}} Methods for the {{Maxwell}} Equations},
  author = {Cockburn, Bernardo and Li, Fengyan and Shu, Chi-Wang},
  year = {2004},
  month = mar,
  journal = {Journal of Computational Physics},
  volume = {194},
  number = {2},
  pages = {588--610},
  issn = {0021-9991},
  doi = {10.1016/j.jcp.2003.09.007},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999103004960},
  urldate = {2024-02-15},
  abstract = {In this paper, we develop the locally divergence-free discontinuous Galerkin method for numerically solving the Maxwell equations. The distinctive feature of the method is the use of approximate solutions that are exactly divergence-free inside each element. As a consequence, this method has a smaller computational cost than that of the discontinuous Galerkin method with standard piecewise polynomial spaces. We show that, in spite of this fact, it produces approximations of the same accuracy. We also show that this method is more efficient than the discontinuous Galerkin method using globally divergence-free piecewise polynomial bases. Finally, a post-processing technique is used to recover (2k+1)th order of accuracy when piecewise polynomials of degree k are used.},
  keywords = {Discontinuous Galerkin method,Divergence-free solutions,Maxwell equations},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/3KZCCTAQ/S0021999103004960.html}
}

@article{cockburnRungeKuttaDiscontinuous2001,
  title = {Runge{\textendash}{{Kutta Discontinuous Galerkin Methods}} for {{Convection-Dominated Problems}}},
  author = {Cockburn, Bernardo and Shu, Chi-Wang},
  year = {2001},
  month = sep,
  journal = {Journal of Scientific Computing},
  volume = {16},
  number = {3},
  pages = {173--261},
  issn = {1573-7691},
  doi = {10.1023/A:1012873910884},
  url = {https://doi.org/10.1023/A:1012873910884},
  urldate = {2022-01-18},
  abstract = {In this paper, we review the development of the Runge{\textendash}Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge{\textendash}Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier{\textendash}Stokes equations, and Hamilton{\textendash}Jacobi-like equations.},
  langid = {english},
  keywords = {convection-diffusion equations,discontinuous Galerkin methods,non-linear conservation laws},
  annotation = {1257 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/TJHNISQ2/Cockburn und Shu - 2001 - Runge–Kutta Discontinuous Galerkin Methods for Con.pdf}
}

@article{cockburnUnifiedHybridizationDiscontinuous2009,
  title = {Unified {{Hybridization}} of {{Discontinuous Galerkin}}, {{Mixed}}, and {{Continuous Galerkin Methods}} for {{Second Order Elliptic Problems}}},
  author = {Cockburn, Bernardo and Gopalakrishnan, Jayadeep and Lazarov, Raytcho},
  year = {2009},
  month = jan,
  journal = {SIAM Journal on Numerical Analysis},
  volume = {47},
  number = {2},
  pages = {1319--1365},
  issn = {0036-1429, 1095-7170},
  doi = {10.1137/070706616},
  url = {http://epubs.siam.org/doi/10.1137/070706616},
  urldate = {2023-03-27},
  abstract = {We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continuous Galerkin, nonconforming, and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements. Since the associated matrix is sparse, symmetric, and positive definite, these methods can be efficiently implemented. Moreover, the framework allows, in a single implementation, the use of different methods in different elements or subdomains of the computational domain, which are then automatically coupled. Finally, the framework brings about a new point of view, thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques, as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom.},
  langid = {english},
  annotation = {661 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/IM5BHIQ6/Cockburn et al. - 2009 - Unified Hybridization of Discontinuous Galerkin, M.pdf}
}

@article{dalcinParallelDistributedComputing2011,
  title = {Parallel Distributed Computing Using {{Python}}},
  author = {Dalcin, Lisandro D. and Paz, Rodrigo R. and Kler, Pablo A. and Cosimo, Alejandro},
  year = {2011},
  month = sep,
  journal = {Advances in Water Resources},
  volume = {34},
  number = {9},
  pages = {1124--1139},
  issn = {03091708},
  doi = {10.1016/j.advwatres.2011.04.013},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0309170811000777},
  urldate = {2021-05-11},
  langid = {english},
  annotation = {306 citations (Crossref) [2023-03-27]}
}

@article{debroyAdditiveManufacturingMetallic2018,
  title = {Additive Manufacturing of Metallic Components {\textendash} {{Process}}, Structure and Properties},
  author = {DebRoy, T. and Wei, H. L. and Zuback, J. S. and Mukherjee, T. and Elmer, J. W. and Milewski, J. O. and Beese, A. M. and {Wilson-Heid}, A. and De, A. and Zhang, W.},
  year = {2018},
  month = mar,
  journal = {Progress in Materials Science},
  volume = {92},
  pages = {112--224},
  issn = {0079-6425},
  doi = {10.1016/j.pmatsci.2017.10.001},
  url = {https://www.sciencedirect.com/science/article/pii/S0079642517301172},
  urldate = {2021-02-16},
  abstract = {Since its inception, significant progress has been made in understanding additive manufacturing (AM) processes and the structure and properties of the fabricated metallic components. Because the field is rapidly evolving, a periodic critical assessment of our understanding is useful and this paper seeks to address this need. It covers the emerging research on AM of metallic materials and provides a comprehensive overview of the physical processes and the underlying science of metallurgical structure and properties of the deposited parts. The uniqueness of this review includes substantive discussions on refractory alloys, precious metals and compositionally graded alloys, a succinct comparison of AM with welding and a critical examination of the printability of various engineering alloys based on experiments and theory. An assessment of the status of the field, the gaps in the scientific understanding and the research needs for the expansion of AM of metallic components are provided.},
  langid = {english},
  keywords = {3D printing,Additive manufacturing,Directed energy deposition,Laser deposition,Powder bed fusion,Printability},
  annotation = {3528 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/B5RY5Y3B/DebRoy et al. - 2018 - Additive manufacturing of metallic components – Pr.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/GSKY6E58/S0079642517301172.html}
}

@article{dugastPartscaleThermalProcess2021,
  title = {Part-Scale Thermal Process Modeling for Laser Powder Bed Fusion with Matrix-Free Method and {{GPU}} Computing},
  author = {Dugast, Florian and Apostolou, Petros and Fernandez, Alfonso and Dong, Wen and Chen, Qian and Strayer, Seth and Wicker, Ryan and To, Albert C.},
  year = {2021},
  month = jan,
  journal = {Additive Manufacturing},
  volume = {37},
  pages = {101732},
  issn = {2214-8604},
  doi = {10.1016/j.addma.2020.101732},
  url = {https://www.sciencedirect.com/science/article/pii/S2214860420311040},
  urldate = {2022-05-09},
  abstract = {This paper presents an efficient GPU-based part-scale thermal process simulator for laser powder bed fusion (L-PBF) additive manufacturing (AM). To take full advantage of modern GPU computing, a matrix-free preconditioned conjugate gradient (PCG) finite element algorithm with voxel mesh is proposed to solve the transient heat transfer problem involved in the L-PBF process. The accuracy of the developed simulator is demonstrated by comparing with a commercial software (ANSYS) using representative L-PBF process parameters and temperature-dependent thermal properties for Ti6Al4V. For efficiency, it is found that the process simulation has a significant speedup going from a single CPU to a single GPU implementation. A speedup is also observed with the matrix-free method compared to a linear solver using a sparse matrix, both on a single GPU. In addition, several schemes devised to gain higher efficiency are discussed in details, which include exclusion of inactive elements from the memory, adaptive meshing in the build direction, preconditioner, and layer lumping. Using these schemes, the adaptability and scalability of the developed simulator are demonstrated on a complex geometry. A calibration of the model is also performed in realistic conditions with a thermocouple measurement coming from experimental data.},
  langid = {english},
  keywords = {Additive manufacturing,Finite element analysis,GPU computing,Heat transfer modeling,Laser powder bed fusion,Matrix-free method,Process simulation},
  annotation = {1 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/PANS2WXW/S2214860420311040.html}
}

@article{dumbserUnifiedFrameworkConstruction2008a,
  title = {A Unified Framework for the Construction of One-Step Finite Volume and Discontinuous {{Galerkin}} Schemes on Unstructured Meshes},
  author = {Dumbser, Michael and Balsara, Dinshaw S. and Toro, Eleuterio F. and Munz, Claus-Dieter},
  year = {2008},
  month = sep,
  journal = {Journal of Computational Physics},
  volume = {227},
  number = {18},
  pages = {8209--8253},
  issn = {0021-9991},
  doi = {10.1016/j.jcp.2008.05.025},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999108002829},
  urldate = {2024-02-13},
  abstract = {In this article, a conservative least-squares polynomial reconstruction operator is applied to the discontinuous Galerkin method. In a first instance, piecewise polynomials of degree N are used as test functions as well as to represent the data in each element at the beginning of a time step. The time evolution of these data and the flux computation, however, are then done with a different set of piecewise polynomials of degree M⩾N, which are reconstructed from the underlying polynomials of degree N. This approach yields a general, unified framework that contains as two special cases classical high order finite volume (FV) schemes (N=0) as well as the usual discontinuous Galerkin (DG) method (N=M). In the first case, the polynomial is reconstructed from cell averages, for the latter, the reconstruction reduces to the identity operator. A completely new class of numerical schemes is generated by choosing N{$\neq$}0 and M{$>$}N. The reconstruction operator is implemented for arbitrary polynomial degrees N and M on unstructured triangular and tetrahedral meshes in two and three space dimensions. To provide a high order accurate one-step time integration of the same formal order of accuracy as the spatial discretization operator, the (reconstructed) polynomial data of degree M are evolved in time locally inside each element using a new local continuous space{\textendash}time Galerkin method. As a result of this approach, we obtain, as a high order accurate predictor, space{\textendash}time polynomials for the vector of conserved variables and for the physical fluxes and source terms, which then can be used in a natural way to construct very efficient fully-discrete and quadrature-free one-step schemes. This feature is particularly important for DG schemes in three space dimensions, where the cost of numerical quadrature may become prohibitively expensive for very high orders of accuracy. Numerical convergence studies of all members of the new general class of proposed schemes are shown up to sixth-order of accuracy in space and time on unstructured two- and three-dimensional meshes for two very prominent nonlinear hyperbolic systems, namely for the Euler equations of compressible gas dynamics and the equations of ideal magnetohydrodynamics (MHD). The results indicate that the new class of intermediate schemes (N{$\neq$}0,M{$>$}N) is computationally more efficient than classical finite volume or DG schemes. Finally, a large set of interesting test cases is solved on unstructured meshes, where the proposed new time stepping approach is applied to the equations of ideal and relativistic MHD as well as to nonlinear elasticity, using a standard high order WENO finite volume discretization in space to cope with discontinuous solutions.},
  keywords = {-exact  least squares reconstruction,Discontinuous Galerkin,Euler equations,Finite volume,Hyperbolic PDE,Ideal and relativistic MHD equations,Local continuous space-time Galerkin method,Nonlinear elasticity,One-step time discretization,Unstructured meshes,WENO},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/DYVBTIKQ/S0021999108002829.html}
}

@article{eMultiscaleModeling2011,
  title = {Multiscale Modeling},
  author = {E, Weinan and Lu, Jianfeng},
  year = {2011},
  journal = {Scholarpedia},
  volume = {6},
  number = {10},
  pages = {11527},
  issn = {1941-6016},
  doi = {10.4249/scholarpedia.11527},
  url = {http://www.scholarpedia.org/article/Multiscale_modeling},
  urldate = {2021-02-15},
  langid = {english},
  annotation = {14 citations (Crossref) [2023-03-27]}
}

@book{ePrinciplesMultiscaleModeling2011,
  title = {Principles of Multiscale Modeling},
  author = {E, Weinan},
  year = {2011},
  publisher = {{Cambridge University Press}},
  address = {{Cambridge ; New York}},
  isbn = {978-1-107-09654-7},
  lccn = {TA342 .E13 2011},
  keywords = {Multiscale modeling},
  annotation = {OCLC: ocn721888752},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/WX9GXANS/E - 2011 - Principles of multiscale modeling.pdf}
}

@article{epshteynSymmetricInteriorPenalty,
  title = {Symmetric {{Interior Penalty Galerkin Method}} for {{Elliptic Problems}}},
  author = {Epshteyn, Yekaterina and Riviere, Beatrice},
  abstract = {This paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods. In particular, we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements. Numerical examples in all dimensions and for different polynomial degrees are presented. We investigate the numerical effects of loss of coercivity.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/GMC8UQ8I/Epshteyn und Riviere - Symmetric Interior Penalty Galerkin Method for Ell.pdf}
}

@book{ernTheoryPracticeFinite2004,
  title = {Theory and {{Practice}} of {{Finite Elements}}},
  author = {Ern, Alexandre and Guermond, Jean-Luc},
  year = {2004},
  series = {Applied {{Mathematical Sciences}}},
  publisher = {{Springer-Verlag}},
  address = {{New York}},
  doi = {10.1007/978-1-4757-4355-5},
  url = {https://www.springer.com/gp/book/9780387205748},
  urldate = {2021-03-17},
  abstract = {This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.},
  isbn = {978-0-387-20574-8},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/65R33WRK/Ern und Guermond - 2004 - Theory and Practice of Finite Elements.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/LZQ4AEUC/9780387205748.html}
}

@book{evansPartialDifferentialEquations2010,
  title = {Partial Differential Equations},
  author = {Evans, Lawrence C.},
  year = {2010},
  series = {Graduate Studies in Mathematics},
  edition = {2nd ed},
  number = {v. 19},
  publisher = {{American Mathematical Society}},
  address = {{Providence, R.I}},
  abstract = {"This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including: a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, and a significantly expanded bibliography."--Publisher's description},
  isbn = {978-0-8218-4974-3},
  lccn = {QA377 .E95 2010},
  keywords = {Differential equations Partial},
  annotation = {OCLC: ocn465190110},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/5V9NYTZB/Evans - 2010 - Partial differential equations.pdf}
}

@incollection{eymardFiniteVolumeMethods2000,
  title = {Finite Volume Methods},
  booktitle = {Handbook of {{Numerical Analysis}}},
  author = {Eymard, Robert and Gallou{\"e}t, Thierry and Herbin, Rapha{\`e}le},
  year = {2000},
  month = jan,
  series = {Solution of {{Equation}} in {{$\mathbb{R}$}} ({{Part}} 3), {{Techniques}} of {{Scientific Computing}} ({{Part}} 3)},
  volume = {7},
  pages = {713--1018},
  publisher = {{Elsevier}},
  doi = {10.1016/S1570-8659(00)07005-8},
  url = {https://www.sciencedirect.com/science/article/pii/S1570865900070058},
  urldate = {2021-09-23},
  abstract = {This chapter focuses on finite volume methods. The finite volume method is a discretization method that is well suited for the numerical simulation of various types (for instance, elliptic, parabolic, or hyperbolic) of conservation laws; it has been extensively used in several engineering fields, such as fluid mechanics, heat and mass transfer, or petroleum engineering. Some of the important features of the finite volume method are similar to those of the finite element method: it may be used on arbitrary geometries, using structured or unstructured meshes, and it leads to robust schemes. The finite volume method is locally conservative because it is based on a ``balance" approach: a local balance is written on each discretization cell that is often called ``control volume;'' by the divergence formula, an integral formulation of the fluxes over the boundary of the control volume is then obtained. The fluxes on the boundary are discretized with respect to the discrete unknowns.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/ADA7HTCR/bookevol.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/UV4NNXSD/Eymard et al. - 2000 - Finite volume methods.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/AMG5IP4I/S1570865900070058.html}
}

@manual{FiredrakeUserManual,
  type = {Manual},
  title = {Firedrake User Manual},
  author = {Ham, David A. and Kelly, Paul H. J. and Mitchell, Lawrence and Cotter, Colin J. and Kirby, Robert C. and Sagiyama, Koki and Bouziani, Nacime and Vorderwuelbecke, Sophia and Gregory, Thomas J. and Betteridge, Jack and Shapero, Daniel R. and {Nixon-Hill}, Reuben W. and Ward, Connor J. and Farrell, Patrick E. and Brubeck, Pablo D. and Marsden, India and Gibson, Thomas H. and Homolya, Mikl{\'o}s and Sun, Tianjiao and McRae, Andrew T. T. and Luporini, Fabio and Gregory, Alastair and Lange, Michael and Funke, Simon W. and Rathgeber, Florian and Bercea, Gheorghe-Teodor and Markall, Graham R.},
  year = {2023},
  month = may,
  edition = {First edition},
  institution = {{Imperial College London and University of Oxford and Baylor University and University of Washington}},
  doi = {10.25561/104839}
}

@article{FleckFedermannPogorelov2018,
  title = {Phase-Field Modeling of {{Li-insertion}} Kinetics in Single {{LiFePO4-nano-particles}} for Rechargeable {{Li-ion}} Battery Application},
  author = {Fleck, Michael and Federmann, Holger and Pogorelov, Evgeny},
  year = {2018},
  month = oct,
  journal = {Computational Materials Science},
  volume = {153},
  pages = {288--296},
  issn = {0927-0256},
  doi = {10.1016/j.commatsci.2018.06.049},
  url = {https://www.sciencedirect.com/science/article/pii/S0927025618304282},
  urldate = {2023-09-25},
  abstract = {We develop a continuum phase-field model for the simulation of diffusion limited solid-solid phase transformations during lithium insertion in LiFePO4-nano-particles. The solid-solid phase boundary between the LiFePO4 (LFP)-phase and the FePO4 (FP)-phase is modeled as a diffuse interface of finite width. The model-description explicitly resolves a single LiFePO4-particle, which is embedded in an elastically soft electrolyte-phase. Furthermore, we explicitly include anisotropic (orthorhombic) and inhomogeneous elastic effects, resulting from the coherency strain, as well as anisotropic (1D) Li-diffusion inside the nano-particle. In contrast to other related research work, we employ an Allen-Cahn-type phase-field approach for the diffuse interface modeling of the solid-solid phase boundary. The model contains an extra non-conserved order parameter field to distinguish the two different phases. The evolution of this order parameter field is controlled by an extra kinetic parameter independent from the Li-diffusion. Further, the effect of the nano-particle's size on the kinetics of FP to LFP phase transformations is investigated by means of both model. Both models predict a substantial increase in the steady state transformation velocity as the particle-size decreases down to dimensions that are comparable with the width of the interface between the FP and the LFP-phase. However, the extra kinetic parameter of the Allen-Cahn-type description may be used to reduce the strength of the velocity-increase with the decreasing particle size. Further, we consider the influence of anisotropic and inhomogeneous elasticity on the lithiation-kinetics within a rectangularly shaped LiFePO4-particle embedded in an elastically soft electrolyte. Finally, the simulation of equilibrium shapes of LiFePO4-particles is discussed. Within a respective feasibility study, we demonstrate that also the simulation of strongly anisotropic particles with aspect ratios up to 1/5 is possible.},
  keywords = {Anisotropic elasticity,Anisotropic surface energy,LiFePO-Cathod material,Phase-field modeling,Solid-solid phase transformations},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/N4LS46K5/Fleck et al. - 2018 - Phase-field modeling of Li-insertion kinetics in s.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/VSFM36LZ/S0927025618304282.html}
}

@article{fleckFrictionlessMotionDiffuse2022,
  title = {Frictionless {{Motion}} of {{Diffuse Interfaces}} by {{Sharp Phase-Field Modeling}}},
  author = {Fleck, Michael and Schleifer, Felix and Zimbrod, Patrick},
  year = {2022},
  month = oct,
  journal = {Crystals},
  volume = {12},
  number = {10},
  pages = {1496},
  publisher = {{Multidisciplinary Digital Publishing Institute}},
  issn = {2073-4352},
  doi = {10.3390/cryst12101496},
  url = {https://www.mdpi.com/2073-4352/12/10/1496},
  urldate = {2023-07-10},
  abstract = {Diffuse interface descriptions offer many advantages for the modeling of microstructure evolution. However, the numerical representation of moving diffuse interfaces on discrete numerical grids involves spurious grid friction, which limits the overall performance of the model in many respects. Interestingly, this intricate and detrimental effect can be overcome in finite difference (FD) and fast Fourier transformation (FFT)-based implementations by employing the so-called sharp phase-field method (SPFM). The key idea is to restore the discretization-induced broken translational invariance (TI) in the discrete phase-field equation by using analytic properties of the equilibrium interface profile. We prove that this method can indeed eliminate spurious grid friction in the three-dimensional space. Focusing on homogeneous driving forces, we quantitatively evaluate the impact of spurious grid friction on the overall operational performance of different phase-field models. We show that the SPFM provides superior degrees of interface isotropy with respect to energy and kinetics. The latter property enables the frictionless motion of arbitrarily oriented diffuse interfaces on a fixed 3D grid.},
  copyright = {http://creativecommons.org/licenses/by/3.0/},
  langid = {english},
  keywords = {finite differences,grid anisotropy,grid pinning,microstructure evolution,phase-field modeling},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/YSATK4T3/Fleck et al. - 2022 - Frictionless Motion of Diffuse Interfaces by Sharp.pdf}
}

@article{FleckPilipenSpatsch122010,
  title = {Brittle Fracture in Viscoelastic Materials as a Pattern-Formation Process},
  author = {Fleck, M. and Pilipenko, D. and Spatschek, R. and Brener, E. A.},
  year = {2011},
  journal = {Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
  volume = {83},
  pages = {046213},
  doi = {10.1103/PhysRevE.83.046213},
  url = {http://link.aps.org/doi/10.1103/PhysRevE.83.046213},
  abstract = {A continuum model of crack propagation in brittle viscoelastic materials is presented and discussed. Thereby, the phenomenon of fracture is understood as an elastically induced nonequilibrium interfacial pattern formation process. In this spirit, a full description of a propagating crack provides the determination of the entire time dependent shape of the crack surface, which is assumed to be extended over a finite and self-consistently selected length scale. The mechanism of crack propagation, that is, the motion of the crack surface, is then determined through linear nonequilibrium transport equations. Here we consider two different mechanisms, a first-order phase transformation and surface diffusion. We give scaling arguments showing that steady-state solutions with a self-consistently selected propagation velocity and crack shape can exist provided that elastodynamic or viscoelastic effects are taken into account, whereas static elasticity alone is not sufficient. In this respect, inertial effects as well as viscous damping are identified to be sufficient crack tip selection mechanisms. Exploring the arising description of brittle fracture numerically, we study steady-state crack propagation in the viscoelastic and inertia limit as well as in an intermediate regime, where both effects are important. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique. Different types of loading, mode I, mode III fracture, as well as mixtures of them, are discussed.},
  bdsk-url-2 = {http://arxiv.org/abs/1012.3945},
  date-added = {2023-09-02 11:24:25 +0200},
  date-modified = {2023-09-02 11:24:25 +0200},
  keywords = {crack propagation,fracture,pattern formation}
}

@article{fleckSharpPhasefieldModeling2023,
  title = {Sharp Phase-Field Modeling of Isotropic Solidification with a Super Efficient Spatial Resolution},
  author = {Fleck, Michael and Schleifer, Felix},
  year = {2023},
  month = jun,
  journal = {Engineering with Computers},
  volume = {39},
  number = {3},
  pages = {1699--1709},
  issn = {1435-5663},
  doi = {10.1007/s00366-022-01729-z},
  url = {https://doi.org/10.1007/s00366-022-01729-z},
  urldate = {2023-07-10},
  abstract = {The phase-field method provides a powerful framework for microstructure evolution modeling in complex systems, as often required within the framework of integrated computational materials engineering. However, spurious grid friction, pinning and grid anisotropy seriously limit the resolution efficiency and accuracy of these models. The energetic resolution limit is determined by the maximum dimensionless driving force at which reasonable model operation is still ensured. This limit turns out to be on the order of 1 for conventional phase-field models. In 1D, grid friction and pinning can be eliminated by a global restoration of Translational Invariance (TI) in the discretized phase-field equation. This is called the sharp phase-field method, which allows to choose substantially coarser numerical resolutions of the diffuse interface without the appearance of pinning. In 3D, global TI restricts the beneficial properties to a few specific interface orientations. We propose an accurate scheme to restore TI locally in the local interface normal direction. The new sharp phase-field model overcomes grid friction and pinning in three-dimensional simulations, and can accurately operate at dimensionless driving forces up to the order of \$\$10\^\{4\}\$\$. At one-grid-point interface resolutions, exceptional degrees of isotropy can be achieved, if further the largely inhomogeneous latent heat release at the advancing solid-liquid interface is mitigated. Imposing a newly proposed source term regularization, the new model captures the formation of isotropic seaweed structures without spurious dendritic selection by grid anisotropy, even at one-grid-point interface resolutions.},
  langid = {english},
  keywords = {Finite differences,Nonlinear preconditioning,Phase-field modeling,Solidification},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/TF85JN8M/Fleck und Schleifer - 2023 - Sharp phase-field modeling of isotropic solidifica.pdf}
}

@article{fornbergGenerationFiniteDifference1988,
  title = {Generation of Finite Difference Formulas on Arbitrarily Spaced Grids},
  author = {Fornberg, Bengt},
  year = {1988},
  journal = {Mathematics of Computation},
  volume = {51},
  number = {184},
  pages = {699--706},
  issn = {0025-5718, 1088-6842},
  doi = {10.1090/S0025-5718-1988-0935077-0},
  url = {https://www.ams.org/mcom/1988-51-184/S0025-5718-1988-0935077-0/},
  urldate = {2022-05-02},
  abstract = {Simple recursions are derived for calculating the weights in compact finite difference formulas for any order of derivative and to any order of accuracy on one-dimensional grids with arbitrary spacing. Tables are included for some special cases (of equispaced grids).},
  langid = {english},
  keywords = {Finite difference coefficients,high-order accuracy},
  annotation = {556 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/WBDVSRL7/Fornberg - 1988 - Generation of finite difference formulas on arbitr.pdf}
}

@article{fringerUnstructuredgridFinitevolumeNonhydrostatic2006,
  title = {An Unstructured-Grid, Finite-Volume, Nonhydrostatic, Parallel Coastal Ocean Simulator},
  author = {Fringer, O.B. and Gerritsen, M. and Street, R.L.},
  year = {2006},
  month = jan,
  journal = {Ocean Modelling},
  volume = {14},
  number = {3-4},
  pages = {139--173},
  issn = {14635003},
  doi = {10.1016/j.ocemod.2006.03.006},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S1463500306000394},
  urldate = {2023-08-28},
  abstract = {A finite-volume formulation is presented that solves the three-dimensional, nonhydrostatic Navier{\textendash}Stokes equations with the Boussinesq approximation on an unstructured, staggered, z-level grid, with the goal of simulating nonhydrostatic processes in the coastal ocean with grid resolutions of tens of meters. In particular, the code has been developed to simulate the nonlinear, nonhydrostatic internal wave field in the littoral ocean. The method is based on the formulation developed by Casulli, in that the free-surface and vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly with the second-order Adams{\textendash}Bashforth method, while the pressure-correction method is employed for the nonhydrostatic pressure in order to achieve overall second-order temporal accuracy. Advection of momentum is accomplished with an Eulerian discretization which conserves momentum in cells that do not contain the free surface, and scalar advection is discretized in a way that ensures consistency with continuity, thereby ensuring local and global mass conservation using a velocity field that conserves volume on a local and global basis. The nonhydrostatic pressure field is solved efficiently using a block-Jacobi preconditioner, and while stability is limited by the internal gravity wave speed and vertical advection of momentum, applications requiring relatively small time steps due to accuracy or stability constraints are run efficiently on parallel computers, since the present formulation is written entirely with the message-passing interface (MPI). The ParMETIS libraries are employed in order to achieve a load-balanced parallel partitioning that minimizes interprocessor communication, and the grid is reordered to optimize per-processor performance by limiting cache misses while accessing arrays in memory. Test cases demonstrate the ability of the code to efficiently and accurately compute the nonhydrostatic lock exchange and internal waves in idealized as well as real domains, and we evaluate the parallel efficiency of the code using up to 32 processors.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/FM3KRICN/Fringer et al. - 2006 - An unstructured-grid, finite-volume, nonhydrostati.pdf}
}

@article{gaburroUnifiedFrameworkSolution2021,
  title = {A {{Unified Framework}} for the {{Solution}} of {{Hyperbolic PDE Systems Using High Order Direct Arbitrary-Lagrangian}}{\textendash}{{Eulerian Schemes}} on {{Moving Unstructured Meshes}} with {{Topology Change}}},
  author = {Gaburro, Elena},
  year = {2021},
  month = may,
  journal = {Archives of Computational Methods in Engineering},
  volume = {28},
  number = {3},
  pages = {1249--1321},
  issn = {1886-1784},
  doi = {10.1007/s11831-020-09411-7},
  url = {https://doi.org/10.1007/s11831-020-09411-7},
  urldate = {2023-07-06},
  abstract = {In this work, we review the family of direct Arbitrary-Lagrangian{\textendash}Eulerian (ALE) finite vlume (FV) and discontinuous Galerkin (DG) schemes on moving meshes that at each time step are rearranged by explicitly allowing topology changes, in order to guarantee a robust mesh evolution even for high shear flow and very long evolution times. Two different techniques are presented: a local nonconforming approach for dealing with sliding lines, and a global regeneration of Voronoi tessellations for treating general unpredicted movements. Corresponding elements at consecutive times are connected in space-time to construct closed space-time control volumes, whose bottom and top faces may be polygons with a different number of nodes, with different neighbors, and even degenerate space-time sliver elements. Our final ALE FV-DG scheme is obtained by integrating, over these arbitrary shaped space-time control volumes, the space-time conservation formulation of the governing hyperbolic PDE system: so, we directly evolve the solution in time avoiding any remapping stage, being conservative and satisfying the GCL by construction. Arbitrary high order of accuracy in space and time is achieved through a fully discrete one-step predictor{\textendash}corrector ADER approach, also integrated with well balancing techniques to further improve the accuracy and to maintain exactly even at discrete level many physical invariants of the studied system. A large set of different numerical tests has been carried out in order to check the accuracy and the robustness of our methods for both smooth and discontinuous problems, in particular in the case of vortical flows.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/YXUDN2N5/Gaburro - 2021 - A Unified Framework for the Solution of Hyperbolic.pdf}
}

@article{ghanbariAdaptiveLocalglobalMultiscale2020,
  title = {Adaptive Local-Global Multiscale Approach for Thermal Simulation of the Selective Laser Melting Process},
  author = {Ghanbari, P. Gh and Mazza, E. and Hosseini, E.},
  year = {2020},
  month = jan,
  journal = {Additive Manufacturing},
  pages = {101518},
  issn = {2214-8604},
  doi = {10.1016/j.addma.2020.101518},
  abstract = {Additive Manufacturing, Journal Pre-proof, 101518. doi:10.1016/j.addma.2020.101518},
  keywords = {Adaptive local-global simulation,additive manufacturing,Computational efficiency,Multiscale thermal modeling,selective laser melting},
  annotation = {3 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/LMKR2UWE/1-s2.0-S2214860420308903-main.pdf}
}

@article{hartmannOptimalOrderInterior2008,
  title = {An Optimal Order Interior Penalty Discontinuous {{Galerkin}} Discretization of the Compressible {{Navier}}{\textendash}{{Stokes}} Equations},
  author = {Hartmann, Ralf and Houston, Paul},
  year = {2008},
  month = nov,
  journal = {Journal of Computational Physics},
  volume = {227},
  number = {22},
  pages = {9670--9685},
  issn = {0021-9991},
  doi = {10.1016/j.jcp.2008.07.015},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999108003975},
  urldate = {2023-03-27},
  abstract = {In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier{\textendash}Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) an adjoint consistent imposition of the boundary conditions; (ii) an adjoint consistent reformulation of the underlying target functional of practical interest; (iii) design of appropriate interior penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L2-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi and Rebay, cf. [F. Bassi, S. Rebay, GMRES discontinuous Galerkin solution of the compressible Navier{\textendash}Stokes equations, in: B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods, Lecture Notes in Comput. Sci. Engrg., vol. 11, Springer, Berlin, 2000, pp. 197{\textendash}208; F. Bassi, S. Rebay, Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier{\textendash}Stokes equations, Int. J. Numer. Methods Fluids 40 (2002) 197{\textendash}207], the standard SIPG method outlined in [R. Hartmann, P. Houston, Symmetric interior penalty DG methods for the compressible Navier{\textendash}Stokes equations. I: Method formulation, Int. J. Numer. Anal. Model. 3(1) (2006) 1{\textendash}20], and an NIPG variant of the new scheme will be undertaken.},
  langid = {english},
  keywords = {Adjoint consistency,Compressible Navier-Stokes equations,Discontinuous Galerkin methods,Finite element methods},
  annotation = {124 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/5D2FFC2S/Hartmann und Houston - 2008 - An optimal order interior penalty discontinuous Ga.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/NEY4VVPY/S0021999108003975.html}
}

@book{hesthavenNodalDiscontinuousGalerkin2008,
  title = {Nodal {{Discontinuous Galerkin Methods}}},
  author = {Hesthaven, Jan S. and Warburton, Tim},
  editor = {Marsden, J. E. and Sirovich, L. and Antman, S. S.},
  year = {2008},
  series = {Texts in {{Applied Mathematics}}},
  volume = {54},
  publisher = {{Springer New York}},
  address = {{New York, NY}},
  doi = {10.1007/978-0-387-72067-8},
  url = {http://link.springer.com/10.1007/978-0-387-72067-8},
  urldate = {2021-03-19},
  isbn = {978-0-387-72065-4 978-0-387-72067-8},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/SVR9HMTP/Hesthaven und Warburton - 2008 - Nodal Discontinuous Galerkin Methods.pdf}
}

@article{Homolya2016,
  title = {A Parallel Edge Orientation Algorithm for Quadrilateral Meshes},
  author = {Homolya, Mikl'os and Ham, David A.},
  year = {2016},
  journal = {SIAM Journal on Scientific Computing},
  volume = {38},
  number = {5},
  eprint = {1505.03357},
  primaryclass = {cs.MS},
  pages = {S48--S61},
  doi = {10.1137/15M1021325},
  url = {http://arxiv.org/abs/1505.03357},
  archiveprefix = {arxiv}
}

@article{hughesStabilizedMixedDiscontinuous2006,
  title = {A Stabilized Mixed Discontinuous {{Galerkin}} Method for {{Darcy}} Flow},
  author = {Hughes, Thomas J. R. and Masud, Arif and Wan, Jing},
  year = {2006},
  month = may,
  journal = {Computer Methods in Applied Mechanics and Engineering},
  series = {Discontinuous {{Galerkin Methods}}},
  volume = {195},
  number = {25},
  pages = {3347--3381},
  issn = {0045-7825},
  doi = {10.1016/j.cma.2005.06.018},
  url = {https://www.sciencedirect.com/science/article/pii/S0045782505002732},
  urldate = {2024-02-15},
  abstract = {A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes two- and three-dimensional constant-flow ``patch tests'' for distorted element geometries. The key ingredient in the formulation is a volumetric, residual-based, stabilization term that does not involve any mesh-dependent parameters.},
  keywords = {Darcy flow,Discontinuous Galerkin method,Error estimates,Finite elements,Mass balance,Mixed method,Patch test,Stabilized method},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/MYJU362W/S0045782505002732.html}
}

@article{idelsohnFiniteVolumesFinite1994,
  title = {Finite Volumes and Finite Elements: {{Two}} `Good Friends'},
  shorttitle = {Finite Volumes and Finite Elements},
  author = {Idelsohn, S. R. and O{\~n}ate, E.},
  year = {1994},
  month = oct,
  journal = {International Journal for Numerical Methods in Engineering},
  volume = {37},
  number = {19},
  pages = {3323--3341},
  issn = {0029-5981, 1097-0207},
  doi = {10.1002/nme.1620371908},
  url = {https://onlinelibrary.wiley.com/doi/10.1002/nme.1620371908},
  urldate = {2022-10-21},
  langid = {english},
  annotation = {73 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/XD3BU3UU/Idelsohn und Oñate - 1994 - Finite volumes and finite elements Two ‘good frie.pdf}
}

@article{johnDivergenceConstraintMixed2017,
  title = {On the {{Divergence Constraint}} in {{Mixed Finite Element Methods}} for {{Incompressible Flows}}},
  author = {John, Volker and Linke, Alexander and Merdon, Christian and Neilan, Michael and Rebholz, Leo G.},
  year = {2017},
  month = jan,
  journal = {SIAM Review},
  volume = {59},
  number = {3},
  pages = {492--544},
  issn = {0036-1445, 1095-7200},
  doi = {10.1137/15M1047696},
  url = {https://epubs.siam.org/doi/10.1137/15M1047696},
  urldate = {2024-02-01},
  abstract = {The divergence constraint of the incompressible Navier-Stokes equations is revisite the mixed finite element framework. While many stable and convergent mixed eleme have been developed throughout the past four decades, most classical methods relax t divergence constraint and only enforce the condition discretely. As a result, these m ods introduce a pressure-dependent consistency error which can potentially pollute t computed velocity. These methods are not robust in the sense that a contribution fro the right-hand side, which influences only the pressure in the continuous equations, pacts both velocity and pressure in the discrete equations. This article reviews the the and practical implications of relaxing the divergence constraint. Several approaches f improving the discrete mass balance or even for computing divergence-free solutions be discussed: grad-div stabilization, higher order mixed methods derived on the basis an exact de Rham complex, //(div)-conforming finite elements, and mixed methods w an appropriate reconstruction of the test functions. Numerical examples illustrate bot the potential effects of using nonrobust discretizations and the improvements obtained utilizing pressure-robust discretizations.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/QQBMI49B/John et al. - 2017 - On the Divergence Constraint in Mixed Finite Eleme.pdf}
}

@incollection{keyComparisonFiniteElementFiniteDifference1973,
  title = {Comparison of {{Finite-Element}} and {{Finite-Difference Methods}}},
  booktitle = {Numerical and {{Computer Methods}} in {{Structural Mechanics}}},
  author = {Key, Samuel W. and Krieg, Raymond D.},
  year = {1973},
  pages = {337--352},
  publisher = {{Elsevier}},
  doi = {10.1016/B978-0-12-253250-4.50019-1},
  url = {https://linkinghub.elsevier.com/retrieve/pii/B9780122532504500191},
  urldate = {2024-02-13},
  isbn = {978-0-12-253250-4},
  langid = {english}
}

@article{kirbyCGHDGComparative2012,
  title = {To {{CG}} or to {{HDG}}: {{A Comparative Study}}},
  shorttitle = {To {{CG}} or to {{HDG}}},
  author = {Kirby, Robert M. and Sherwin, Spencer J. and Cockburn, Bernardo},
  year = {2012},
  month = apr,
  journal = {Journal of Scientific Computing},
  volume = {51},
  number = {1},
  pages = {183--212},
  issn = {1573-7691},
  doi = {10.1007/s10915-011-9501-7},
  url = {https://doi.org/10.1007/s10915-011-9501-7},
  urldate = {2023-03-30},
  abstract = {Hybridization through the border of the elements (hybrid unknowns) combined with a Schur complement procedure (often called static condensation in the context of continuous Galerkin linear elasticity computations) has in various forms been advocated in the mathematical and engineering literature as a means of accomplishing domain decomposition, of obtaining increased accuracy and convergence results, and of algorithm optimization. Recent work on the hybridization of mixed methods, and in particular of the discontinuous Galerkin (DG) method, holds the promise of capitalizing on the three aforementioned properties; in particular, of generating a numerical scheme that is discontinuous in both the primary and flux variables, is locally conservative, and is computationally competitive with traditional continuous Galerkin (CG) approaches. In this paper we present both implementation and optimization strategies for the Hybridizable Discontinuous Galerkin (HDG) method applied to two dimensional elliptic operators. We implement our HDG approach within a spectral/hp element framework so that comparisons can be done between HDG and the traditional CG approach.},
  langid = {english},
  keywords = {Discontinuous Galerkin method,Domain decomposition,High-order finite elements,Hybridization,Spectral/hp elements},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/4EK6M49J/Kirby et al. - 2012 - To CG or to HDG A Comparative Study.pdf}
}

@misc{kolevModularFiniteElement2010,
  title = {Modular {{Finite Element Methods}} ({{MFEM}})},
  author = {Kolev, Tzanio and Dobrev, Veselin},
  year = {2010},
  doi = {10.11578/DC.20171025.1248},
  url = {https://www.osti.gov/doecode/biblio/35738},
  urldate = {2024-02-01},
  abstract = {MFEM is a modular parallel C++ library for finite element methods. Its goal is to enable high-performance scalable finite element discretization research and application development on a wide variety of platforms, ranging from laptops to supercomputers.},
  howpublished = {Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)},
  langid = {english}
}

@article{koppSpacetimeHpfiniteElements2022,
  title = {Space-Time Hp-Finite Elements for Heat Evolution in Laser Powder Bed Fusion Additive Manufacturing},
  author = {Kopp, Philipp and Calo, Victor and Rank, Ernst and Kollmannsberger, Stefan},
  year = {2022},
  month = sep,
  journal = {Engineering with Computers},
  issn = {1435-5663},
  doi = {10.1007/s00366-022-01719-1},
  url = {https://doi.org/10.1007/s00366-022-01719-1},
  urldate = {2022-10-07},
  abstract = {The direct numerical simulation of metal additive manufacturing processes such as laser powder bed fusion is challenging due to the vast differences in spatial and temporal scales. Classical approaches based on locally refined finite elements combined with time-stepping schemes can only address the spatial multi-scale nature and provide only limited scaling potential for massively parallel computations. We address these shortcomings in a space-time Galerkin framework where the finite element interpolation also includes the temporal dimension. In this setting, we construct four-dimensional meshes that are locally refined towards the laser spot and allow for varying temporal accuracy depending on the position in space. By splitting the mesh into conforming time-slabs, we recover a stepwise solution to solve the space-time problem locally in time at this slab; additionally, we can choose time-slab sizes significantly larger than classical time-stepping schemes. As a result, we believe this setting to be well suited for large-scale parallelization. In our work, we use a continuous Galerkin{\textendash}Petrov formulation of the nonlinear heat equation with an apparent heat capacity model to account for the phase change. We validate our approach by computing the AMB2018-02 benchmark, where we obtain an excellent agreement with the measured melt pool shape. Using the same setup, we demonstrate the performance potential of our approach by hatching a square area with a laser path length of about one meter.},
  langid = {english},
  keywords = {Laser powder bed fusion,Local hp-refinement,Metal additive manufacturing,Parallel in time,Space-time finite elements},
  annotation = {2 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/56WJ6K57/Kopp et al. - 2022 - Space-time hp-finite elements for heat evolution i.pdf}
}

@article{kronbichlerFastMassivelyParallel2018,
  title = {A Fast Massively Parallel Two-Phase Flow Solver for Microfluidic Chip Simulation},
  author = {Kronbichler, Martin and Diagne, Ababacar and Holmgren, Hanna},
  year = {2018},
  journal = {The International Journal of High Performance Computing Applications},
  volume = {32},
  number = {2},
  pages = {266--287},
  publisher = {{SAGE Publications Sage UK: London, England}},
  doi = {10.1177/1094342016671790},
  annotation = {20 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/CH9LGBXC/Kronbichler et al. - 2018 - A fast massively parallel two-phase flow solver fo.pdf}
}

@article{kronbichlerPerformanceComparisonContinuous2018,
  title = {A Performance Comparison of Continuous and Discontinuous {{Galerkin}} Methods with Fast Multigrid Solvers},
  author = {Kronbichler, Martin and Wall, Wolfgang A.},
  year = {2018},
  month = jan,
  journal = {SIAM Journal on Scientific Computing},
  volume = {40},
  number = {5},
  eprint = {1611.03029},
  pages = {A3423-A3448},
  issn = {1064-8275, 1095-7197},
  doi = {10.1137/16M110455X},
  url = {http://arxiv.org/abs/1611.03029},
  urldate = {2021-03-25},
  abstract = {This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method. Modern implementations of high-order methods with state-of-the-art multigrid solvers for the Poisson equation are considered, including fast matrix-free implementations with sum factorization on quadrilateral and hexahedral elements. For the hybridized discontinuous Galerkin method, a multigrid approach that combines a grid transfer from the trace space to the space of linear finite elements with algebraic multigrid on further levels is developed. Despite similar solver complexity of the matrix-based HDG solver and matrix-free geometric multigrid schemes with continuous and discontinuous Galerkin finite elements, the latter offer up to order of magnitude faster time to solution, even after including the superconvergence effects. This difference is because of vastly better performance of matrix-free operator evaluation as compared to sparse matrix-vector products. A roofline performance model confirms the advantage of the matrix-free implementation.},
  archiveprefix = {arxiv},
  keywords = {G.1.8,Mathematics - Numerical Analysis},
  annotation = {50 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/WYTFHA6P/Kronbichler und Wall - 2018 - A performance comparison of continuous and discont.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/KF8U32XX/1611.html}
}

@article{lagrange-0,
  title = {Periodic Table of the Finite Elements},
  author = {Arnold, Douglas N. and Logg, Anders},
  year = {2014},
  journal = {SIAM News},
  volume = {47}
}

@article{lagrange-1,
  title = {A Systematic Construction of Finite Element Commuting Exact Sequences},
  author = {Cockburn, Bernardo and Fu, Guosheng},
  year = {2017},
  journal = {SIAM journal on numerical analysis},
  volume = {55},
  pages = {1650--1688},
  doi = {10.1137/16M1073352}
}

@article{landauTheoryPhaseTransitions1937,
  title = {On the {{Theory}} of {{Phase Transitions}}},
  author = {Landau, Lev},
  year = {1937},
  journal = {Zh. Eksp. Teor. Fiz.},
  volume = {7},
  pages = {19--32},
  issn = {2071-019},
  url = {http://archive.ujp.bitp.kiev.ua/files/journals/53/si/53SI08p.pdf},
  urldate = {2023-09-11},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/PMCLGUH8/53SI08p.pdf}
}

@article{levequeHighResolutionConservativeAlgorithms1996,
  title = {High-{{Resolution Conservative Algorithms}} for {{Advection}} in {{Incompressible Flow}}},
  author = {LeVeque, Randall J.},
  year = {1996},
  month = apr,
  journal = {SIAM Journal on Numerical Analysis},
  volume = {33},
  number = {2},
  pages = {627--665},
  issn = {0036-1429, 1095-7170},
  doi = {10.1137/0733033},
  url = {http://epubs.siam.org/doi/10.1137/0733033},
  urldate = {2023-04-24},
  abstract = {A class of high-resolution algorithms is developed for advection of a scalar quantity in a given incompressible flow field in one, two, or three space dimensions. Multidimensional transport is modeled using a wave-propagation approach in which the flux at each cell interface is built up on the basis of information propagating in the direction of this interface from neighboring cells. A high-resolution second-order method using slope limiters is quite easy to implement. For constant flow, a minor modification gives a third-order accurate method. These methods are stable for Courant numbers up to 1. Fortran implementations are available by anonymous ftp.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/4WEK8EHQ/LeVeque - 1996 - High-Resolution Conservative Algorithms for Advect.pdf}
}

@book{levequeNumericalMethodsConservation1992,
  title = {Numerical {{Methods}} for {{Conservation Laws}}},
  author = {LeVeque, Randall J.},
  year = {1992},
  publisher = {{Birkh{\"a}user Basel}},
  address = {{Basel}},
  doi = {10.1007/978-3-0348-8629-1},
  url = {http://link.springer.com/10.1007/978-3-0348-8629-1},
  urldate = {2022-01-27},
  isbn = {978-3-7643-2723-1 978-3-0348-8629-1},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/V5U45EU6/LeVeque - 1992 - Numerical Methods for Conservation Laws.pdf}
}

@article{linComparativeStudyWeak2015a,
  title = {A Comparative Study on the Weak {{Galerkin}}, Discontinuous {{Galerkin}}, and Mixed Finite Element Methods},
  author = {Lin, Guang and Liu, Jiangguo and {Sadre-Marandi}, Farrah},
  year = {2015},
  month = jan,
  journal = {Journal of Computational and Applied Mathematics},
  volume = {273},
  pages = {346--362},
  issn = {03770427},
  doi = {10.1016/j.cam.2014.06.024},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0377042714003057},
  urldate = {2024-02-13},
  abstract = {This paper presents a comparative study on the newly introduced weak Galerkin finite element methods (WGFEMs) with the widely accepted discontinuous Galerkin finite element methods (DGFEMs) and the classical mixed finite element methods (MFEMs) for solving second-order elliptic boundary value problems. We examine the differences, similarities, and connection among these methods in scheme formulations, implementation strategies, accuracy, and computational cost. The comparison and numerical experiments demonstrate that WGFEMs are viable alternatives to MFEMs and hold some advantages over DGFEMs, due to their properties of local conservation, normal flux continuity, no need for penalty factor, and definiteness of discrete linear systems.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/N827AB8M/Lin et al. - 2015 - A comparative study on the weak Galerkin, disconti.pdf}
}

@article{liuEightyYearsFinite2022,
  title = {Eighty {{Years}} of the {{Finite Element Method}}: {{Birth}}, {{Evolution}}, and {{Future}}},
  shorttitle = {Eighty {{Years}} of the {{Finite Element Method}}},
  author = {Liu, Wing Kam and Li, Shaofan and Park, Harold S.},
  year = {2022},
  month = oct,
  journal = {Archives of Computational Methods in Engineering},
  volume = {29},
  number = {6},
  pages = {4431--4453},
  issn = {1134-3060, 1886-1784},
  doi = {10.1007/s11831-022-09740-9},
  url = {https://link.springer.com/10.1007/s11831-022-09740-9},
  urldate = {2022-12-01},
  abstract = {This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis on developments related to solid mechanics. We present a historical overview beginning with the theoretical formulations and origins of the FEM, while discussing important developments that have enabled the FEM to become the numerical method of choice for so many problems rooted in solid mechanics.},
  langid = {english},
  annotation = {7 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/KUIMQZNJ/Liu et al. - 2022 - Eighty Years of the Finite Element Method Birth, .pdf}
}

@article{liuRobustReconstructionUnstructured2013,
  title = {A {{Robust Reconstruction}} for {{Unstructured WENO Schemes}}},
  author = {Liu, Yuan and Zhang, Yong-Tao},
  year = {2013},
  month = feb,
  journal = {Journal of Scientific Computing},
  volume = {54},
  number = {2-3},
  pages = {603--621},
  issn = {0885-7474, 1573-7691},
  doi = {10.1007/s10915-012-9598-3},
  url = {http://link.springer.com/10.1007/s10915-012-9598-3},
  urldate = {2023-06-26},
  abstract = {The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order numerical methods for hyperbolic partial differential equations (PDEs). While WENO schemes on structured meshes are quite mature, the development of finite volume WENO schemes on unstructured meshes is more difficult. A major difficulty is how to design a robust WENO reconstruction procedure to deal with distorted local mesh geometries or degenerate cases when the mesh quality varies for complex domain geometry. In this paper, we combine two different WENO reconstruction approaches to achieve a robust unstructured finite volume WENO reconstruction on complex mesh geometries. Numerical examples including both scalar and system cases are given to demonstrate stability and accuracy of the scheme.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/24PH72QW/Liu und Zhang - 2013 - A Robust Reconstruction for Unstructured WENO Sche.pdf}
}

@article{liuSimulationPowderPacking2020,
  title = {Simulation of {{Powder Packing}} and {{Thermo-Fluid Dynamic}} of {{316L Stainless Steel}} by {{Selective Laser Melting}}},
  author = {Liu, L. and Huang, M. and Ma, Y. H. and Qin, M. L. and Liu, T. T.},
  year = {2020},
  month = nov,
  journal = {Journal of Materials Engineering and Performance},
  issn = {1544-1024},
  doi = {10.1007/s11665-020-05230-w},
  url = {https://doi.org/10.1007/s11665-020-05230-w},
  urldate = {2020-11-12},
  abstract = {A mesoscopic model was established to investigate thermo-fluid dynamic behavior in selective laser melting of 316L stainless steel. A powder packing model, including particle size distribution based on the discrete element method, was developed to describe the relative density variation of the powder bed with different layer thicknesses. A finite element method model with Gaussian laser beam was established to predict the dynamic thermal behavior and flow mechanism of the particles for a single-line scanning. The level-set method was used to trace the free surface of the molten metal with temperature-dependent surface tension. A function to describe the relative density of the powder bed with its thickness was obtained. An evaporation model considering the influence of mass, energy loss, and evaporation on the surface morphology of the molten pool was established. According to the temperature and velocity field in the molten pool, a vortex formed by the Marangoni effect might decrease the depth and increase the width of the molten pool. The molten pool was not disconnected by Plateau{\textendash}Rayleigh instability due to the small length/diameter ratio at low scanning speeds. The model assuming regularly arranged powder bed underestimates the maximum temperature as compared to the model considering a randomly packed powder bed because a higher relative density of the former facilitates heat conduction. The simulated results are consistent with experimental results, including porosity, material loss, and surface defects.},
  langid = {english},
  annotation = {4 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/8R36IDU9/Liu et al. - 2020 - Simulation of Powder Packing and Thermo-Fluid Dyna.pdf}
}

@article{maltsevHybridDiscontinuousGalerkinfinite2023,
  title = {Hybrid Discontinuous {{Galerkin-finite}} Volume Techniques for Compressible Flows on Unstructured Meshes},
  author = {Maltsev, Vadim and Yuan, Dean and Jenkins, Karl W. and Skote, Martin and Tsoutsanis, Panagiotis},
  year = {2023},
  month = jan,
  journal = {Journal of Computational Physics},
  volume = {473},
  pages = {111755},
  issn = {00219991},
  doi = {10.1016/j.jcp.2022.111755},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S002199912200818X},
  urldate = {2023-07-10},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/UA5V6VA7/Maltsev et al. - 2023 - Hybrid discontinuous Galerkin-finite volume techni.pdf}
}

@article{marshallFinitevolumeIncompressibleNavier1997,
  title = {A Finite-Volume, Incompressible {{Navier Stokes}} Model for Studies of the Ocean on Parallel Computers},
  author = {Marshall, John and Adcroft, Alistair and Hill, Chris and Perelman, Lev and Heisey, Curt},
  year = {1997},
  month = mar,
  journal = {Journal of Geophysical Research: Oceans},
  volume = {102},
  number = {C3},
  pages = {5753--5766},
  issn = {01480227},
  doi = {10.1029/96JC02775},
  url = {http://doi.wiley.com/10.1029/96JC02775},
  urldate = {2023-08-28},
  abstract = {The numericalimplementationof an oceanmodel basedon the incompressible Navier Stokesequationswhichis designedfor studiesof the oceancirculationon horizontalscaleslessthan the depth of the oceanright up to globalscaleis described.A "pressurecorrection"methodis usedwhichis solvedas a Poissonequationfor the pressurefieldwith Neumannboundaryconditionsin a geometryascomplicatedasthat of the oceanbasins.A major objectiveof the studyis to make this inversion,and hence nonhydrostaticoceanmodeling,efficienton parallel computers.The pressurefield is separatedinto surface,hydrostatica, nd nonhydrostaticomponentsF. irst, asin hydrostatic models,a two-dimensionaplroblemis invertedfor the surfacepressurewhichis thenmade useof in the three-dimensionailnversionfor the nonhydrostaticpressure.Preconditioned conjugate-gradieniterationis usedto invert symmetricellipticoperatorsin both two and three dimensionsP. hysicallymotivatedpreconditionersare designedwhichare efficientat reducingcomputationand minimizingcommunicationbetweenprocessorsO. ur method exploitsthe fact that asthe horizontalscaleof the motionbecomesvery muchlargerthan the vertical scale,the motion becomesmore and more hydrostaticand the threedimensionalPoissonoperatorbecomesincreasinglyanisotropicand dominatedby the verticalaxis.Accordingly,a preconditioneris usedwhich,in the hydrostaticlimit, is an exactintegralof the Poissonoperatorand so leadsto a singlealgorithmthat seamlessly movesfrom nonhydrostaticto hydrostaticlimits.Thus in the hydrostaticlimit the model is "fast,"competitivewith the fastestoceanclimatemodelsin usetodaybasedon the hydrostaticprimitiveequationsB. ut asthe resolutionis increased,the model dynamics asymptotesmoothlyto the Navier Stokesequationsand so can be usedto addresssmallscaleprocessesA. "finite-volume"approachis employedto discretizethe model in space in whichpropertyfluxesare definednormal to facesthat delineatethe volumes.The methodmakespossiblea noveltreatment of the boundaryin which cellsabuttingthe bottom or coastmay take on irregular shapesand be "shaved"to fit the boundary.The algorithmcan convenientlyexploitmassivelyparallel computersand suggestsa domain decompositionwhich allocatesverticalcolumnsof oceanto eachprocessingunit. The resultingmodel,whichcanhandlearbitrarilycomplexgeometry,is efficientand scalable and hasbeen mappedon to massivelyparallel multiprocessorsuchas the Connection Machine (CM5) usingdata-parallelFORTRAN and the MassachusettIsnstituteof Technologydata-flowmachineMONSOON usingthe implicitlyparallel languageId.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/KSXZEVWG/Marshall et al. - 1997 - A finite-volume, incompressible Navier Stokes mode.pdf}
}

@article{mayiTransientDynamicsStability2021,
  title = {Transient Dynamics and Stability of Keyhole at Threshold in Laser Powder Bed Fusion Regime Investigated by Finite Element Modeling},
  author = {Mayi, Yaasin A. and Dal, Morgan and Peyre, Patrice and Bellet, Michel and Metton, Charlotte and Moriconi, Clara and Fabbro, Remy},
  year = {2021},
  month = feb,
  journal = {Journal of Laser Applications},
  volume = {33},
  number = {1},
  pages = {012024},
  issn = {1042-346X, 1938-1387},
  doi = {10.2351/7.0000330},
  url = {http://lia.scitation.org/doi/10.2351/7.0000330},
  urldate = {2021-01-07},
  abstract = {A Finite element model is developed with a commercial code to investigate the keyhole dynamics and stability at keyhole threshold, a fusion regime characteristic to laser microwelding or to Laser Powder Bed Fusion. The model includes relevant physics to treat the hydrodynamic problems{\textemdash}surface tension, Marangoni stress, and recoil pressure{\textemdash}as well as a self-consistent ray-tracing algorithm to account for the ``beam-trapping'' effect. Implemented in both static and scanning laser configurations, the model successfully reproduces some key features that most recent x-ray images have exhibited. The dynamics of the liquid/gas interface is analyzed, in line with the distribution of the absorbed intensity as well as with the increase of the keyhole energy coupling. Based on these results, new elements are provided to discuss our current understanding of the keyhole formation and stability at threshold.},
  langid = {english},
  annotation = {9 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/ZD724MDS/Mayi et al. - 2021 - Transient dynamics and stability of keyhole at thr.pdf}
}

@incollection{mckeeMemoryWall2011,
  title = {Memory {{Wall}}},
  booktitle = {Encyclopedia of {{Parallel Computing}}},
  author = {McKee, Sally A. and Wisniewski, Robert W.},
  editor = {Padua, David},
  year = {2011},
  pages = {1110--1116},
  publisher = {{Springer US}},
  address = {{Boston, MA}},
  doi = {10.1007/978-0-387-09766-4_234},
  url = {https://doi.org/10.1007/978-0-387-09766-4_234},
  urldate = {2023-07-10},
  isbn = {978-0-387-09766-4},
  langid = {english}
}

@article{McRae2016,
  title = {Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements},
  author = {McRae, Andrew T. T. and Bercea, Gheorghe-Teodor and Mitchell, Lawrence and Ham, David A. and Cotter, Colin J.},
  year = {2016},
  journal = {SIAM Journal on Scientific Computing},
  volume = {38},
  number = {5},
  eprint = {1411.2940},
  primaryclass = {math.NA},
  pages = {S25--S47},
  doi = {10.1137/15M1021167},
  url = {http://arxiv.org/abs/1411.2940},
  archiveprefix = {arxiv}
}

@article{meierPhysicsBasedModelingPredictive2021,
  title = {Physics-{{Based Modeling}} and {{Predictive Simulation}} of {{Powder Bed Fusion Additive Manufacturing Across Length Scales}}},
  author = {Meier, Christoph and Fuchs, Sebastian L. and Much, Nils and Nitzler, Jonas and Penny, Ryan W. and Praegla, Patrick M. and Pr{\"o}ll, Sebastian D. and Sun, Yushen and Weissbach, Reimar and Schreter, Magdalena and Hodge, Neil E. and Hart, A. John and Wall, Wolfgang A.},
  year = {2021},
  month = mar,
  journal = {arXiv:2103.16982 [cs]},
  eprint = {2103.16982},
  primaryclass = {cs},
  url = {http://arxiv.org/abs/2103.16982},
  urldate = {2021-04-06},
  abstract = {Powder bed fusion additive manufacturing (PBFAM) of metals has the potential to enable new paradigms of product design, manufacturing and supply chains while accelerating the realization of new technologies in the medical, aerospace, and other industries. Currently, wider adoption of PBFAM is held back by difficulty in part qualification, high production costs and low production rates, as extensive process tuning, post-processing, and inspection are required before a final part can be produced and deployed. Physics-based modeling and predictive simulation of PBFAM offers the potential to advance fundamental understanding of physical mechanisms that initiate process instabilities and cause defects. In turn, these insights can help link process and feedstock parameters with resulting part and material properties, thereby predicting optimal processing conditions and inspiring the development of improved processing hardware, strategies and materials. This work presents recent developments of our research team in the modeling of metal PBFAM processes spanning length scales, namely mesoscale powder modeling, mesoscale melt pool modeling, macroscale thermo-solid-mechanical modeling and microstructure modeling. Ongoing work in experimental validation of these models is also summarized. In conclusion, we discuss the interplay of these individual submodels within an integrated overall modeling approach, along with future research directions.},
  archiveprefix = {arxiv},
  keywords = {Computer Science - Computational Engineering Finance and Science},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/HTGA22VG/Meier et al. - 2021 - Physics-Based Modeling and Predictive Simulation o.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/JFTRP58Y/Meier et al. - 2021 - Physics-based modeling and predictive simulation o.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/SCK8EUKQ/Meier et al. - 2021 - Physics-Based Modeling and Predictive Simulation o.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/GYALT53U/2103.html}
}

@book{moukalledFiniteVolumeMethod2016,
  title = {The {{Finite Volume Method}} in {{Computational Fluid Dynamics}}: {{An Advanced Introduction}} with {{OpenFOAM}}{\textregistered} and {{Matlab}}},
  shorttitle = {The {{Finite Volume Method}} in {{Computational Fluid Dynamics}}},
  author = {Moukalled, F. and Mangani, L. and Darwish, M.},
  year = {2016},
  series = {Fluid {{Mechanics}} and {{Its Applications}}},
  volume = {113},
  publisher = {{Springer International Publishing}},
  address = {{Cham}},
  doi = {10.1007/978-3-319-16874-6},
  url = {https://link.springer.com/10.1007/978-3-319-16874-6},
  urldate = {2024-02-15},
  isbn = {978-3-319-16873-9 978-3-319-16874-6},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/IGDIV23I/Moukalled et al. - 2016 - The Finite Volume Method in Computational Fluid Dy.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/TKFKP9Y6/978-3-319-16874-6.pdf}
}

@incollection{nguyenHybridizableDiscontinuousGalerkin2011,
  title = {Hybridizable {{Discontinuous Galerkin Methods}}},
  booktitle = {Spectral and {{High Order Methods}} for {{Partial Differential Equations}}},
  author = {Nguyen, N. C. and Peraire, J. and Cockburn, B.},
  editor = {Hesthaven, Jan S. and R{\o}nquist, Einar M.},
  year = {2011},
  volume = {76},
  pages = {63--84},
  publisher = {{Springer Berlin Heidelberg}},
  address = {{Berlin, Heidelberg}},
  doi = {10.1007/978-3-642-15337-2_4},
  url = {http://link.springer.com/10.1007/978-3-642-15337-2_4},
  urldate = {2022-05-25},
  isbn = {978-3-642-15336-5 978-3-642-15337-2},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/LGFY23RV/Nguyen et al. - 2011 - Hybridizable Discontinuous Galerkin Methods.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/WGJHET7Q/Nguyen et al. - 2011 - Hybridizable Discontinuous Galerkin Methods.pdf}
}

@article{nguyenImplicitHighorderHybridizable2009,
  title = {An Implicit High-Order Hybridizable Discontinuous {{Galerkin}} Method for Linear Convection{\textendash}Diffusion Equations},
  author = {Nguyen, N. C. and Peraire, J. and Cockburn, B.},
  year = {2009},
  month = may,
  journal = {Journal of Computational Physics},
  volume = {228},
  number = {9},
  pages = {3232--3254},
  issn = {0021-9991},
  doi = {10.1016/j.jcp.2009.01.030},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999109000308},
  urldate = {2023-03-27},
  abstract = {We present a hybridizable discontinuous Galerkin method for the numerical solution of steady and time-dependent linear convection{\textendash}diffusion equations. We devise the method as follows. First, we express the approximate scalar variable and corresponding flux within each element in terms of an approximate trace of the scalar variable along the element boundary. We then define a unique value for the approximate trace by enforcing the continuity of the normal component of the flux across the element boundary; a global equation system solely in terms of the approximate trace is thus obtained. The high number of globally coupled degrees of freedom in the discontinuous Galerkin approximation is therefore significantly reduced. If the problem is time-dependent, we discretize the time derivative by means of backward difference formulae. This results in efficient schemes capable of producing high-order accurate solutions in space and time. Indeed, when the time-marching method is (p+1)th order accurate and when polynomials of degree p⩾0 are used to represent the scalar variable, the flux and the approximate trace, we observe that the approximations for the scalar variable, the flux and the trace of the scalar variable converge with the optimal order of p+1 in the L2-norm. Finally, we introduce a simple element-by-element postprocessing scheme to obtain new approximations of the flux and the scalar variable. The new approximate flux, which has a continuous inter-element normal component, is shown to converge with order p+1 in the L2-norm. The new approximate scalar variable is shown to converge with order p+2 in the L2-norm. For the time-dependent case, the postprocessing does not need to be applied at each time-step but only at the times for which an enhanced solution is required. Moreover, the postprocessing procedure is less expensive than the solution procedure, since it is performed at the element level. Extensive numerical results are presented to demonstrate the convergence properties of the method.},
  langid = {english},
  keywords = {Convection-diffusion equations,Discontinuous Galerkin methods,Finite element methods,Hybrid/mixed methods},
  annotation = {215 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/MKBZKHGU/Nguyen et al. - 2009 - An implicit high-order hybridizable discontinuous .pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/PB7QWN6T/S0021999109000308.html}
}

@article{olleakEnablingPartScaleScanwise2022,
  title = {Enabling {{Part-Scale Scanwise}} Process Simulation for Predicting Melt Pool Variation in {{LPBF}} by Combining {{GPU-based Matrix-free FEM}} and Adaptive {{Remeshing}}},
  author = {Olleak, Alaa and Dugast, Florian and Bharadwaj, Prajwal and Strayer, Seth and Hinnebusch, Shawn and Narra, Sneha and To, Albert C.},
  year = {2022},
  month = dec,
  journal = {Additive Manufacturing Letters},
  volume = {3},
  pages = {100051},
  issn = {2772-3690},
  doi = {10.1016/j.addlet.2022.100051},
  url = {https://www.sciencedirect.com/science/article/pii/S2772369022000251},
  urldate = {2022-05-09},
  abstract = {This work proposes to combine matrix-free finite element modeling (FEM), adaptive remeshing, and graphical processing unit (GPU) computing to enable, for the first time, scanwise process simulation of the Laser Powder Bed Fusion (L-PBF) process with temperature-dependent thermophysical properties at the part scale. Compared to the conventional FEM using the global stiffness approach and a uniform mesh running on 10 CPU cores, l-PBF process simulation based on the proposed methodology running on a GPU card with 5,120 Compute Unified Device Architecture (CUDA) cores enables a speedup of over 10,000x. This significant speedup facilitates detailed thermal history and melt pool geometry predictions at high resolution for centimeter-scale parts within days of computation time. Two parts consisting of various geometric features are simulated to reveal the effects of scan strategy and local geometry on melt pool size variation, which correlate well with melt pool and lack-of-fusion porosity measurements obtained via experiment.},
  langid = {english},
  keywords = {Adaptive remeshing,Defects,Geometry effects,GPU Computing,Laser Powder Bed Fusion (L-PBF),Process simulation,Thermal history},
  annotation = {1 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/EJV6VN85/Olleak et al. - 2022 - Enabling Part-Scale Scanwise process simulation fo.pdf}
}

@article{olleakPartscaleFiniteElement2020,
  title = {Part-Scale {{Finite Element Modeling}} of the {{SLM Process}} with {{Layer-wise Adaptive Remeshing}} for {{Thermal History}} and {{Porosity Prediction}}},
  author = {Olleak, Alaaeldin and Xi, Zhimin},
  year = {2020},
  month = jan,
  journal = {Journal of Manufacturing Science and Engineering},
  pages = {1--26},
  issn = {1087-1357},
  doi = {10.1115/1.4047733},
  abstract = {Predicting the part thermal history during the selective laser melting (SLM) process is critical to understand how SLM process parameters influence parts quality. Existing thermal finite element approaches are mainly associated with simplifications in the mesh configuration, heat source model, and domain size, e.g., limited to multiple scanning tracks. The proposed work presents an efficient adaptive remeshing technique that enables part-scale SLM process simulations and helps reduce model size without sacrificing accuracy with the purpose of making the part-scale simulation computationally efficient. In particular, the SLM process simulation for an entire part was developed with the capability of considering different process parameters. The model predicts the influence of process parameters on part thermal history, melt pool statistics, and porosity. The simulation results agree well with the experimental results in literature. In addition, the remeshing technique was demonstrated to be more computationally efficient than the existing element death and birth approach.},
  annotation = {8 citations (Crossref) [2023-03-27]}
}

@article{olleakScanwiseAdaptiveRemeshing2020a,
  title = {Scan-Wise Adaptive Remeshing for Efficient {{LPBF}} Process Simulation: {{The}} Thermal Problem},
  author = {Olleak, Alaa and Xi, Zhimin},
  year = {2020},
  month = jan,
  journal = {Manufacturing Letters},
  volume = {23},
  pages = {75--78},
  issn = {2213-8463},
  doi = {10.1016/j.mfglet.2020.01.003},
  url = {http://www.sciencedirect.com/science/article/pii/S2213846319301270},
  abstract = {Understanding parts thermal history during the laser powder bed fusion (LPBF) process is crucial since it can help avoiding manufacturing defects, identifying hotspots, saving time and cost associated with experimental analysis. For the case of LPBF, however, numerical methods are computationally expensive whenever the thermal history of a relatively large part is required. This paper proposes a scan-wise adaptive remeshing framework using tetrahedral elements that can simulate the process efficiently, and better capture complex features than using hexahedral elements. Results from four structures demonstrated the efficiency of the proposed work compared to the layer-wise remeshing and the uniform mesh approach.},
  annotation = {4 citations (Crossref) [2023-03-27]}
}

@article{perroneGeneralFiniteDifference1975,
  title = {A General Finite Difference Method for Arbitrary Meshes},
  author = {Perrone, Nicholas and Kao, Robert},
  year = {1975},
  month = apr,
  journal = {Computers \& Structures},
  volume = {5},
  number = {1},
  pages = {45--57},
  issn = {0045-7949},
  doi = {10.1016/0045-7949(75)90018-8},
  url = {https://www.sciencedirect.com/science/article/pii/0045794975900188},
  urldate = {2024-02-13},
  abstract = {A two-dimensional finite-difference technique for irregular meshes is formulated for derivatives up to the second order. The domain in the vicinity of a given central point is broken into eight 45 degree pie shaped segments and the closest finite-difference point in each segment to the center point is noted. By utilizing Taylor series expansions about a central point with a unique averaging process for the points in the four diagonal segments, good approximations to all derivatives up to the second order and including the mixed derivatives are obtained. For square meshes the general derivative expressions for arbitrary meshes which were determined reduce to the usual finite difference formulae. In one example problem the Poisson equation is solved for an irregular mesh. In a second example for the first time a problem with a geometric nonlinearity, namely large deflection response of a flat membrane, is solved with an irregular mesh. The solutions compare very favorably with results obtained previously. Some discussion is given on possible approaches for determination of finite difference derivatives higher than the second.},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/2KXJMRKY/0045794975900188.html}
}

@inproceedings{petsc-efficient,
  title = {Efficient Management of Parallelism in Object Oriented Numerical Software Libraries},
  booktitle = {Modern Software Tools in Scientific Computing},
  author = {Balay, Satish and Gropp, William D. and McInnes, Lois Curfman and Smith, Barry F.},
  editor = {Arge, E. and Bruaset, A. M. and Langtangen, H. P.},
  year = {1997},
  pages = {163--202},
  publisher = {{Birkh{\"a}user Press}},
  address = {{Basel}}
}

@techreport{petsc-user-ref,
  title = {{{PETSc}}/{{TAO}} Users Manual},
  author = {Balay, Satish and Abhyankar, Shrirang and Adams, Mark F. and Benson, Steven and Brown, Jed and Brune, Peter and Buschelman, Kris and Constantinescu, Emil and Dalcin, Lisandro and Dener, Alp and Eijkhout, Victor and Faibussowitsch, Jacob and Gropp, William D. and Hapla, V'aclav and Isaac, Tobin and Jolivet, Pierre and Karpeev, Dmitry and Kaushik, Dinesh and Knepley, Matthew G. and Kong, Fande and Kruger, Scott and May, Dave A. and McInnes, Lois Curfman and Mills, Richard Tran and Mitchell, Lawrence and Munson, Todd and Roman, Jose E. and Rupp, Karl and Sanan, Patrick and Sarich, Jason and Smith, Barry F. and Zampini, Stefano and Zhang, Hong and Zhang, Hong and Zhang, Junchao},
  year = {2023},
  number = {ANL-21/39 - Revision 3.19},
  institution = {{Argonne National Laboratory}}
}

@article{PilipenkoFleckEmmerich2011,
  title = {On Numerical Aspects of Phase Field Fracture Modelling},
  author = {Pilipenko, D. and Fleck, M. and Emmerich, H.},
  year = {2011},
  month = oct,
  journal = {The European Physical Journal Plus},
  volume = {126},
  number = {10},
  pages = {100},
  issn = {2190-5444},
  doi = {10.1140/epjp/i2011-11100-3},
  url = {https://doi.org/10.1140/epjp/i2011-11100-3},
  urldate = {2023-09-25},
  abstract = {Recently, a continuum model for crack propagation in brittle visco-elastic materials has been presented (M. Fleck et al., Phys. Rev. E 83, 046213 (2011)), in which fracture is described as an elastically induced nonequilibrium interfacial pattern formation process. The underlying mesoscopic description of a propagating crack results in a complicated moving boundary problem, that allows the self-consistent determination of the crack velocity as well as the entire time-dependent crack surface. Here we focus on the numerical aspects tied to the approximative solution of the arising moving boundary problem and discuss several strategies to develop efficient numerical schemes applying to it: i) a finite difference scheme, ii) a scheme based on the finite element method and iii) a scheme based on the multipole expansion method. The pros and cons of each method are elucidated in detail. Further, we present a comprehensive view on how the different approaches can be employed to validate each other in comparative studies, which is then illustrated for the example of crack propagation under mode I loading.},
  langid = {english},
  keywords = {Break Phase,Crack Shape,Crack Velocity,Move Boundary Problem,Numerical Aspect},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/B3SALJYV/Pilipenko et al. - 2011 - On numerical aspects of phase field fracture model.pdf}
}

@book{pinchoverIntroductionPartialDifferential2005,
  title = {An {{Introduction}} to {{Partial Differential Equations}}},
  author = {Pinchover, Yehuda and Rubinstein, Jacob},
  year = {2005},
  month = may,
  publisher = {{Cambridge University Press}},
  abstract = {A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students and extended solution sets are available to lecturers from solutions@cambridge.org.},
  googlebooks = {CnvDS9twvUMC},
  isbn = {978-0-521-84886-2},
  langid = {english},
  keywords = {Mathematics / Differential Equations / General,Mathematics / General},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/X4ZZZCCN/Pinchover und Rubinstein - 2005 - An Introduction to Partial Differential Equations.pdf}
}

@misc{proellHighlyEfficientComputational2023,
  title = {A Highly Efficient Computational Framework for Fast Scan-Resolved Simulations of Metal Additive Manufacturing Processes on the Scale of Real Parts},
  author = {Proell, Sebastian D. and Munch, Peter and Wall, Wolfgang A. and Meier, Christoph},
  year = {2023},
  month = feb,
  number = {arXiv:2302.05164},
  eprint = {2302.05164},
  primaryclass = {cs},
  publisher = {{arXiv}},
  url = {http://arxiv.org/abs/2302.05164},
  urldate = {2023-02-16},
  abstract = {This article presents a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion additive manufacturing processes. In contrast to many existing approaches to part-scale simulations, this work simulates resolved scan tracks. A growing, adaptively refined mesh accurately captures the fine laser beam movement. However, the fine spatial resolution required for resolved scan tracks in combination with the high scan velocities mandates the use of comparatively small time steps. Explicit time integration schemes are well-suited for this setting, while unconditionally stable implicit time integration schemes are well-suited for the interlayer cool down phase. These two schemes are implemented in an efficient fast operator evaluation framework which provides significant performance gains and optimization opportunities. The capabilities of the novel framework are demonstrated through examples on the centimeter scale and a scan-resolved simulation of the NIST AM Benchmark cantilever specimen.},
  archiveprefix = {arxiv},
  langid = {english},
  keywords = {Computer Science - Computational Engineering Finance and Science},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/Y2NKAHQW/Proell et al. - 2023 - A highly efficient computational framework for fas.pdf}
}

@article{PTSCOTCH,
  title = {{{PT-SCOTCH}}: A Tool for Efficient Parallel Graph Ordering},
  author = {Chevalier, C. and Pellegrini, F.},
  year = {2008},
  journal = {Parallel Computing},
  volume = {34},
  number = {6},
  pages = {318--331},
  doi = {10.1016/j.parco.2007.12.001}
}

@article{rackauckas2019confederated,
  title = {Confederated Modular Differential Equation {{APIs}} for Accelerated Algorithm Development and Benchmarking},
  author = {Rackauckas, Christopher and Nie, Qing},
  year = {2019},
  journal = {Advances in Engineering Software},
  volume = {132},
  pages = {1--6},
  publisher = {{Elsevier}}
}

@article{rackauckasDifferentialequationsJlPerformant2017,
  title = {Differentialequations.Jl{\textendash}a Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia},
  author = {Rackauckas, Christopher and Nie, Qing},
  year = {2017},
  journal = {Journal of Open Research Software},
  volume = {5},
  number = {1},
  publisher = {{Ubiquity Press}}
}

@article{Rathgeber2016,
  title = {Firedrake: Automating the Finite Element Method by Composing Abstractions},
  author = {Rathgeber, Florian and Ham, David A. and Mitchell, Lawrence and Lange, Michael and Luporini, Fabio and McRae, Andrew T. T. and Bercea, Gheorghe-Teodor and Markall, Graham R. and Kelly, Paul H. J.},
  year = {2016},
  journal = {ACM Trans. Math. Softw.},
  volume = {43},
  number = {3},
  eprint = {1501.01809},
  pages = {24:1--24:27},
  issn = {0098-3500},
  doi = {10.1145/2998441},
  url = {http://arxiv.org/abs/1501.01809},
  archiveprefix = {arxiv}
}

@article{reedTriangularMeshMethods1973,
  title = {Triangular Mesh Methods for the Neutron Transport Equation},
  author = {Reed, W H and Hill, T R},
  year = {1973},
  month = oct,
  address = {{United States}},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/IIPC99AL/Reed und Hill - 1973 - Triangular mesh methods for the neutron transport .pdf}
}

@inproceedings{scroggsDefElementEncyclopediaFinite2023,
  title = {{{DefElement}}: An Encyclopedia of Finite Element Definitions},
  booktitle = {{{FEniCS}} 2023},
  author = {Scroggs, Matthew W.},
  year = {2023},
  address = {{Cagliari, Italy}},
  doi = {10.6084/m9.figshare.23294939.v1}
}

@inproceedings{shademanEvaluationOpenFOAMAcademic2013,
  title = {Evaluation of {{OpenFOAM}} in {{Academic Research}} and {{Industrial Applications}}},
  booktitle = {21st {{Conference}} of the {{CFD Society}} of {{Canada}}},
  author = {Shademan, M and Barron, R M and Balachandar, R},
  year = {2013},
  address = {{Canada}},
  abstract = {The capability of the open source software OpenFOAM is analyzed for both academic and industrial applications. Two test cases are formulated, heat and fluid flow in an automotive water jacket and flow over a flat plate in proximity to the ground. Due to difficulties associated with conducting experiments in engines, the results obtained from OpenFOAM are compared with those from a commercial CFD code (ANSYS Fluent). Based on the simulations performed, it is shown that OpenFOAM is capable of handling the complicated geometries which are common in industry. A number of limitations exist for commercial CFD software in academic research. This includes generation of a realistic inflow for LES, which has been resolved in the current study by using the OpenFOAM software. Based on the analyses performed, there is clear evidence to support the use of OpenFOAM for both academic research and industrial applications.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/CVX7956R/Shademan et al. - Evaluation of OpenFOAM in Academic Research and In.pdf}
}

@article{shuHighorderFiniteDifference2003,
  title = {High-Order {{Finite Difference}} and {{Finite Volume WENO Schemes}} and {{Discontinuous Galerkin Methods}} for {{CFD}}},
  author = {Shu, Chi-Wang},
  year = {2003},
  month = mar,
  journal = {International Journal of Computational Fluid Dynamics},
  volume = {17},
  number = {2},
  pages = {107--118},
  publisher = {{Taylor \& Francis}},
  issn = {1061-8562},
  doi = {10.1080/1061856031000104851},
  url = {https://doi.org/10.1080/1061856031000104851},
  urldate = {2023-06-30},
  abstract = {In recent years, high order numerical methods have been widely used in computational fluid dynamics (CFD), to effectively resolve complex flow features using meshes which are reasonable for today's computers. In this paper, we review and compare three types of high order methods being used in CFD, namely the weighted essentially non-oscillatory (WENO) finite difference methods, the WENO finite volume methods, and the discontinuous Galerkin (DG) finite element methods. We summarize the main features of these methods, from a practical user's point of view, indicate their applicability and relative strength, and show a few selected numerical examples to demonstrate their performance on illustrative model CFD problems.},
  keywords = {Computational Fluid Dynamics,Discontinuous Galerkin,Finite Difference Method,Finite Volume Method,Weighted Essentially Non-oscillatory},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/B6V33MAP/Shu - 2003 - High-order Finite Difference and Finite Volume WEN.pdf}
}

@article{solinArbitrarylevelHangingNodes2008,
  title = {Arbitrary-Level Hanging Nodes and Automatic Adaptivity in the Hp-{{FEM}}},
  author = {{\v S}ol{\'i}n, Pavel and {\v C}erven{\'y}, Jakub and Dole{\v z}el, Ivo},
  year = {2008},
  month = feb,
  journal = {Mathematics and Computers in Simulation},
  volume = {77},
  number = {1},
  pages = {117--132},
  issn = {0378-4754},
  doi = {10.1016/j.matcom.2007.02.011},
  url = {https://www.sciencedirect.com/science/article/pii/S0378475407001504},
  urldate = {2023-07-10},
  abstract = {In this paper we present a new automatic adaptivity algorithm for the hp-FEM which is based on arbitrary-level hanging nodes and local element projections. The method is very simple to implement compared to other existing hp-adaptive strategies, while its performance is comparable or superior. This is demonstrated on several numerical examples which include the L-shape domain problem, a problem with internal layer, and the Girkmann problem of linear elasticity. With appropriate simplifications, the proposed technique can be applied to standard lower-order and spectral finite element methods.},
  langid = {english},
  keywords = {-FEM,35B50,65N60,Automatic -adaptivity,Constrained approximation,Hanging nodes}
}

@inproceedings{sonntagShockCapturingDiscontinuous2014,
  title = {Shock {{Capturing}} for {{Discontinuous Galerkin Methods}} Using {{Finite Volume Subcells}}},
  booktitle = {Finite {{Volumes}} for {{Complex Applications VII-Elliptic}}, {{Parabolic}} and {{Hyperbolic Problems}}},
  author = {Sonntag, Matthias and Munz, Claus-Dieter},
  editor = {Fuhrmann, J{\"u}rgen and Ohlberger, Mario and Rohde, Christian},
  year = {2014},
  series = {Springer {{Proceedings}} in {{Mathematics}} \& {{Statistics}}},
  pages = {945--953},
  publisher = {{Springer International Publishing}},
  address = {{Cham}},
  doi = {10.1007/978-3-319-05591-6_96},
  abstract = {We present a shock capturing procedure for high order discontinuous Galerkin methods, by which shock regions are refined and treated by the finite volume techniques. Hence, our approach combines the good properties of the discontinuous Galerkin method in smooth parts of the flow with the perfect properties of a total variation diminishing finite volume method for resolving shocks without spurious oscillations. Due to the subcell approach the interior resolution on the discontinuous Galerkin grid cell is preserved and the number of degrees of freedom remains the same. In this paper we focus on an implementation of this coupled method and show our first results.},
  isbn = {978-3-319-05591-6},
  langid = {english},
  keywords = {Discontinuous Galerkin,Finite volume subcells,Shock capturing},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/6ZXB6EK7/Sonntag und Munz - 2014 - Shock Capturing for Discontinuous Galerkin Methods.pdf}
}

@article{sukumarVoronoiCellFinite2003,
  title = {Voronoi Cell Finite Difference Method for the Diffusion Operator on Arbitrary Unstructured Grids},
  author = {Sukumar, N.},
  year = {2003},
  journal = {International Journal for Numerical Methods in Engineering},
  volume = {57},
  number = {1},
  pages = {1--34},
  issn = {1097-0207},
  doi = {10.1002/nme.664},
  url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.664},
  urldate = {2023-03-01},
  abstract = {Voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framework for the solution of partial differential equations. In this paper, we focus on the Laplace interpolant with a two-fold objective: first, to unify the previous developments related to the Laplace interpolant and to indicate its ties to some well-known numerical methods; and secondly to propose a Voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids. A conservation law in integral form is discretized on Voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids. The proposed scheme can also be viewed as a point collocation technique. A detailed study on consistency is conducted, and the satisfaction of the discrete maximum principle (stability) is established. Owing to symmetry of the Laplace weight, a symmetric positive-definite stiffness matrix is realized which permits the use of efficient linear solvers. On a regular (rectangular or hexagonal) grid, the difference scheme reduces to the classical finite difference method. Numerical examples for the Poisson equation with Dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme. Copyright {\copyright} 2003 John Wiley \& Sons, Ltd.},
  langid = {english},
  keywords = {finite difference,finite volume,irregular grids,natural neighbour,Poisson equation,Sibson and Laplace interpolants},
  annotation = {56 citations (Crossref) [2023-03-27]}
}

@article{thomeeFiniteDifferenceFinite1984,
  title = {The Finite Difference versus the Finite Element Method for the Solution of Boundary Value Problems},
  author = {Thom{\'e}e, Vidar},
  year = {1984},
  month = apr,
  journal = {Bulletin of the Australian Mathematical Society},
  volume = {29},
  number = {2},
  pages = {267--288},
  issn = {0004-9727, 1755-1633},
  doi = {10.1017/S000497270002150X},
  url = {https://www.cambridge.org/core/product/identifier/S000497270002150X/type/journal_article},
  urldate = {2022-09-30},
  abstract = {In this lecture we describe, discuss and compare the two classes of methods most commonly used for the numerical solution of boundary value problems for partial differential equations, namely, the finite difference method and the finite element method. For both of these methods an extensive development of mathematical error analysis has taken place but individual numerical analysts often express strong prejudices in favor of one of them. Our purpose is to try to convey our conviction that this attitude is both historically unjustified and inhibiting, and that familiarity with both methods provides a wider range of techniques for constructing and analyzing discretization schemes.},
  langid = {english},
  annotation = {0 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/TBCWCI7B/Thomée - 1984 - The finite difference versus the finite element me.pdf}
}

@article{visbalUseHigherOrderFiniteDifference2002,
  title = {On the {{Use}} of {{Higher-Order Finite-Difference Schemes}} on {{Curvilinear}} and {{Deforming Meshes}}},
  author = {Visbal, Miguel R and Gaitonde, Datta V},
  year = {2002},
  month = sep,
  journal = {Journal of Computational Physics},
  volume = {181},
  number = {1},
  pages = {155--185},
  issn = {0021-9991},
  doi = {10.1006/jcph.2002.7117},
  url = {https://www.sciencedirect.com/science/article/pii/S0021999102971172},
  urldate = {2023-07-06},
  abstract = {This study enables the use of very high-order finite-difference schemes for the solution of conservation laws on stretched, curvilinear, and deforming meshes. To illustrate these procedures, we focus on up to 6th-order Pade-type spatial discretizations coupled with up to 10th-order low-pass filters. These are combined with explicit and implicit time integration methods to examine wave propagation and wall-bounded flows described by the Navier{\textendash}Stokes equations. It is shown that without the incorporation of the filter, application of the high-order compact scheme to nonsmooth meshes results in spurious oscillations which inhibit their applicability. Inclusion of the discriminating low-pass high-order filter restores the advantages of high-order approach even in the presence of large grid discontinuities. When three-dimensional curvilinear meshes are employed, the use of standard metric evaluation procedures significantly degrades accuracy since freestream preservation is violated. To overcome this problem, a simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes. For dynamically deforming grids, an effective numerical treatment is described to evaluate expressions containing the time-varying transformation metrics. With these techniques, metric cancellation is guaranteed regardless of the manner in which grid speeds are defined. The efficacy of the new procedures is demonstrated by solving several model problems as well as by application to flow past a rapidly pitching airfoil and past a flexible panel.},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/DTKXI4XJ/S0021999102971172.html}
}

@inproceedings{wangAUGEMAutomaticallyGenerate2013,
  title = {{{AUGEM}}: Automatically Generate High Performance Dense Linear Algebra Kernels on X86 {{CPUs}}},
  shorttitle = {{{AUGEM}}},
  booktitle = {Proceedings of the {{International Conference}} on {{High Performance Computing}}, {{Networking}}, {{Storage}} and {{Analysis}}},
  author = {Wang, Qian and Zhang, Xianyi and Zhang, Yunquan and Yi, Qing},
  year = {2013},
  month = nov,
  pages = {1--12},
  publisher = {{ACM}},
  address = {{Denver Colorado}},
  doi = {10.1145/2503210.2503219},
  url = {https://dl.acm.org/doi/10.1145/2503210.2503219},
  urldate = {2023-06-30},
  abstract = {Basic Liner algebra subprograms (BLAS) is a fundamental library in scientific computing. In this paper, we present a template-based optimization framework, AUGEM, which can automatically generate fully optimized assembly code for several dense linear algebra (DLA) kernels, such as GEMM, GEMV, AXPY and DOT, on varying multi-core CPUs without requiring any manual interference from developers. In particular, based on domain-specific knowledge about algorithms of the DLA kernels, we use a collection of parameterized code templates to formulate a number of commonly occurring instruction sequences within the optimized low-level C code of these DLA kernels. Then, our framework uses a specialized low-level C optimizer to identify instruction sequences that match the pre-defined code templates and thereby translates them into extremely efficient SSE/AVX instructions. The DLA kernels generated by our templatebased approach surpass the implementations of Intel MKL and AMD ACML BLAS libraries, on both Intel Sandy Bridge and AMD Piledriver processors.},
  isbn = {978-1-4503-2378-9},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/2SBFRRRF/Wang et al. - 2013 - AUGEM automatically generate high performance den.pdf}
}

@article{wangHighorderCFDMethods2013,
  title = {High-Order {{CFD}} Methods: Current Status and Perspective: {{HIGH-ORDER CFD METHODS}}},
  shorttitle = {High-Order {{CFD}} Methods},
  author = {Wang, Z.J. and Fidkowski, Krzysztof and Abgrall, R{\'e}mi and Bassi, Francesco and Caraeni, Doru and Cary, Andrew and Deconinck, Herman and Hartmann, Ralf and Hillewaert, Koen and Huynh, H.T. and Kroll, Norbert and May, Georg and Persson, Per-Olof and {van Leer}, Bram and Visbal, Miguel},
  year = {2013},
  month = jul,
  journal = {International Journal for Numerical Methods in Fluids},
  volume = {72},
  number = {8},
  pages = {811--845},
  issn = {02712091},
  doi = {10.1002/fld.3767},
  url = {https://onlinelibrary.wiley.com/doi/10.1002/fld.3767},
  urldate = {2022-02-21},
  abstract = {After several years of planning, the 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7{\textendash}8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astronautics, the Air Force Office of Scientific Research, and the German Aerospace Center provided much needed support, financial and moral. Over 70 participants from all over the world across the research spectrum of academia, government labs, and private industry attended the workshop. Many exciting results were presented. In this review article, the main motivation and major findings from the workshop are described. Pacing items requiring further effort are presented. Copyright {\copyright} 2013 John Wiley \& Sons, Ltd.},
  langid = {english},
  annotation = {611 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/J97INCFA/Wang et al. - 2013 - High-order CFD methods current status and perspec.pdf}
}

@article{warburtonDiscontinuousGalerkinMethod1999,
  title = {A {{Discontinuous Galerkin Method}} for the {{Viscous MHD Equations}}},
  author = {Warburton, T.C and Karniadakis, G.E},
  year = {1999},
  month = jul,
  journal = {Journal of Computational Physics},
  volume = {152},
  number = {2},
  pages = {608--641},
  issn = {00219991},
  doi = {10.1006/jcph.1999.6248},
  url = {https://linkinghub.elsevier.com/retrieve/pii/S0021999199962484},
  urldate = {2023-06-29},
  langid = {english},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/V6XNMIHM/Warburton und Karniadakis - 1999 - A Discontinuous Galerkin Method for the Viscous MH.pdf}
}

@inproceedings{xianyiModeldriven,
  title = {Model-Driven {{Level}} 3 {{BLAS Performance Optimization}} on {{Loongson 3A Processor}}},
  booktitle = {2012 {{IEEE}} 18th {{International Conference}} on {{Parallel}} and {{Distributed Systems}}},
  author = {Xianyi, Zhang and Qian, Wang and Yunquan, Zhang},
  year = {2012},
  month = dec,
  pages = {684--691},
  issn = {1521-9097},
  doi = {10.1109/ICPADS.2012.97},
  abstract = {Every mainstream processor vendor provides an optimized BLAS implementation for its CPU, as BLAS is a fundamental math library in scientific computing. The Loongson 3A CPU is a general-purpose 64-bit MIPS64 quad-core processor, developed by the Institute of Computing Technology, Chinese Academy of Sciences. To date, there has not been a sufficiently optimized BLAS on the Loongson 3A CPU. The purpose of this research is to optimize level 3 BLAS performance on the Loongson 3A CPU. We analyzed the Loongson 3A architecture and built a performance model to highlight the key point, L1 data cache misses, which is different from level 3 BLAS optimization on the mainstream x86 CPU. Therefore, we employed a variety of methods to avoid L1 cache misses in single thread optimization, including cache and register blocking, the Loongson 3A 128-bit memory accessing extension instructions, software prefetching, and single precision floating-point SIMD instructions. Furthermore, we improved parallel performance by reducing bank conflicts among multiple threads in the shared L2 cache. We created an open source BLAS project, OpenBLAS, to demonstrate the performance improvement on the Loongson 3A quad-core processor.},
  keywords = {BLAS,Kernel,Loongson 3A,MIPS64,Multi-core,Optimization,Pipelines,Prefetching,Registers},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/3ARWP7PT/Xianyi et al. - 2012 - Model-driven Level 3 BLAS Performance Optimization.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/JDN9AFQK/stamp.html}
}

@article{yakovlevCGHDGComparative2016,
  title = {To {{CG}} or to {{HDG}}: {{A Comparative Study}} in {{3D}}},
  shorttitle = {To {{CG}} or to {{HDG}}},
  author = {Yakovlev, Sergey and Moxey, David and Kirby, Robert M. and Sherwin, Spencer J.},
  year = {2016},
  month = apr,
  journal = {Journal of Scientific Computing},
  volume = {67},
  number = {1},
  pages = {192--220},
  issn = {1573-7691},
  doi = {10.1007/s10915-015-0076-6},
  url = {https://doi.org/10.1007/s10915-015-0076-6},
  urldate = {2023-03-30},
  abstract = {Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as static condensation, available within CG framework made it challenging for DG methods to be competitive until recently. However, with the introduction of a static-condensation-amenable DG method{\textemdash}the hybridizable discontinuous Galerkin (HDG) method{\textemdash}it has become possible to perform a realistic comparison of CG and HDG methods when applied to elliptic problems. In this work, we extend upon an earlier 2D comparative study, providing numerical results and discussion of the CG and HDG method performance in three dimensions. The comparison categories covered include steady-state elliptic and time-dependent parabolic problems, various element types and serial and parallel performance. The postprocessing technique, which allows for superconvergence in the HDG case, is also discussed. Depending on the direct linear system solver used and the type of the problem (steady-state vs. time-dependent) in question the HDG method either outperforms or demonstrates a comparable performance when compared with the CG method. The HDG method however falls behind performance-wise when the iterative solver is used, which indicates the need for an effective preconditioning strategy for the method.},
  langid = {english},
  keywords = {Discontinuous Galerkin method,High-order finite elements,Hybridization,Parallel computing,Postprocessing,Spectral/hp elements,Superconvergence},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/CZN4TPPG/Yakovlev et al. - 2016 - To CG or to HDG A Comparative Study in 3D.pdf}
}

@article{yangOptimallyEfficientTechnique2017,
  title = {An Optimally Efficient Technique for the Solution of Systems of Nonlinear Parabolic Partial Differential Equations},
  author = {Yang, F. W. and Goodyer, C. E. and Hubbard, M. E. and Jimack, P. K.},
  year = {2017},
  month = jan,
  journal = {Advances in Engineering Software},
  series = {Special {{Issue}}{\textbackslash}: {{Civil-Comp}}{\textbackslash}: {{Parallel}}, {{Distributed}} and {{Cloud Computing}}},
  volume = {103},
  pages = {65--84},
  issn = {0965-9978},
  doi = {10.1016/j.advengsoft.2016.06.003},
  url = {https://www.sciencedirect.com/science/article/pii/S0965997816301259},
  urldate = {2023-07-06},
  abstract = {This paper describes a new software tool that has been developed for the efficient solution of systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Specifically, the software is designed to provide optimal computational performance for multiscale problems, which require highly stable, implicit, time-stepping schemes combined with a parallel implementation of adaptivity in both space and time. By combining these implicit, adaptive discretizations with an optimally efficient nonlinear multigrid solver it is possible to obtain computational solutions to a very high resolution with relatively modest computational resources. The first half of the paper describes the numerical methods that lie behind the software, along with details of their implementation, whilst the second half of the paper illustrates the flexibility and robustness of the tool by applying it to two very different example problems. These represent models of a thin film flow of a spreading viscous droplet and a multi-phase-field model of tumour growth. We conclude with a discussion of the challenges of obtaining highly scalable parallel performance for a software tool that combines both local mesh adaptivity, requiring efficient dynamic load-balancing, and a multigrid solver, requiring careful implementation of coarse grid operations and inter-grid transfer operations in parallel.},
  langid = {english},
  keywords = {Adaptive mesh refinement,Finite difference,Implicit,Multigrid,Parallel,Thin film flow,Tumour growth},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/4F679J3Q/Yang et al. - 2017 - An optimally efficient technique for the solution .pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/NEAES3RX/S0965997816301259.html}
}

@article{yanLocalDiscontinuousGalerkin2002,
  title = {Local {{Discontinuous Galerkin Methods}} for {{Partial Differential Equations}} with {{Higher Order Derivatives}}},
  author = {Yan, Jue and Shu, Chi-Wang},
  year = {2002},
  month = dec,
  journal = {Journal of Scientific Computing},
  volume = {17},
  number = {1},
  pages = {27--47},
  issn = {1573-7691},
  doi = {10.1023/A:1015132126817},
  url = {https://doi.org/10.1023/A:1015132126817},
  urldate = {2022-04-13},
  abstract = {In this paper we review the existing and develop new local discontinuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L2 stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.},
  langid = {english},
  keywords = {discontinuous Galerkin method,error estimate,partial differential equations with higher derivatives,post-processing,stability},
  annotation = {124 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/23TK66Y6/Yan und Shu - 2002 - Local Discontinuous Galerkin Methods for Partial D.pdf}
}

@article{yeRelationshipFiniteVolume2001,
  title = {On the Relationship between Finite Volume and Finite Element Methods Applied to the {{Stokes}} Equations},
  author = {Ye, Xiu},
  year = {2001},
  journal = {Numerical Methods for Partial Differential Equations},
  volume = {17},
  number = {5},
  pages = {440--453},
  issn = {1098-2426},
  doi = {10.1002/num.1021},
  url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.1021},
  urldate = {2022-10-21},
  abstract = {We investigate the relationship between finite volume and finite element approximations for the lower-order elements, both conforming and nonconforming for the Stokes equations. These elements include conforming, linear velocity-constant pressure on triangles, conforming bilinear velocity-constant pressure on rectangles and their macro-element versions, and nonconforming linear velocity-constant pressure on triangles and nonconforming rotated bilinear velocity-constant pressure on rectangles. By applying the relationship between the two methods, we obtain the convergence finite volume solutions for the Stokes equations. {\copyright} 2001 John Wiley \& Sons, Inc. Numer Methods Partial Differential Eq 17: 440{\textendash}453, 2001.},
  langid = {english},
  keywords = {finite element methods,finite volume methods,Stokes problems},
  annotation = {69 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/ZKPQCA2K/Ye - 2001 - On the relationship between finite volume and fini.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/U8AILGNA/num.html}
}

@article{yurunComparativeStudyDiscontinuous1997,
  title = {A Comparative Study of the Discontinuous {{Galerkin}} and Continuous {{SUPG}} Finite Element Methods for Computation of Viscoelastic Flows},
  author = {Yurun, Fan},
  year = {1997},
  month = feb,
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {141},
  number = {1},
  pages = {47--65},
  issn = {0045-7825},
  doi = {10.1016/S0045-7825(96)01102-4},
  url = {https://www.sciencedirect.com/science/article/pii/S0045782596011024},
  urldate = {2024-02-13},
  abstract = {The performance of the discontinuous Galerkin (DG) method and the continuous streamline upwind Petrov-Galerkin (SUPG) method in the computation of steady viscoelastic flows have been compared in this paper. For the continuous SUPG method it is necessary to include the elastic-viscous-split-stress (EVSS) formulation to satisfy the compatibility requirement on the velocity-stress interpolation (SUPG/ EVSS), while for the discontinuous Galerkin method both the pure mixed formulation (DG/MIX) and the EVSS formulation (DG/EVSS) have been tested. We first examine a benchmark smooth problem, i.e. the steady flow of an upper convected Maxwell (UCM) fluid around a sphere falling along the axis of a cylindrical tube, by using high-order finite element approximation. DG/MIX is found not to be a stable discretization in this problem, its limiting Weissenberg number decreases with increasing the interpolation order; on the other hand, DG/EVSS is an accurate and stable algorithm, its solution converges as the approximation order increases (the so-called p-convergence) and it produces almost identical stress boundary layers to that of the SUPG/EVSS algorithm at a Weissenberg number as high as 2.0. To explore benefits of the discontinuous interpolation for the stress in the DG method, we further examine two benchmark problems with stress singularities by using low-order interpolations on sufficiently fine meshes; they are the axisymmetric steady flows of the modified Chilcott and Rallison (MCR) fluid through a four-to-one abrupt contraction and in a tube with the stick-to-slip transition in the wall velocity boundary condition. In the contraction problem the DG/EVSS method is found to be a significant improvement over the SUPG/EVSS method, quality of the solutions is better for DG/EVSS and a much higher Weissenberg number limit is observed. In the stick-slip problem both DG/EVSS and SUPG/EVSS are very robust, they confront no limit of the Weissenberg number and predict asymptotic stress profiles as the number becomes sufficiently large. In both problems the pure mixed method DG/MIX produces severe stress oscillations near the singularities and fails to converge at medium Weissenberg numbers.},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/3AUA559U/S0045782596011024.html}
}

@article{zhangThreedimensionalElasticWave2012,
  title = {Three-Dimensional Elastic Wave Numerical Modelling in the Presence of Surface Topography by a Collocated-Grid Finite-Difference Method on Curvilinear Grids},
  author = {Zhang, Wei and Zhang, Zhenguo and Chen, Xiaofei},
  year = {2012},
  month = aug,
  journal = {Geophysical Journal International},
  volume = {190},
  number = {1},
  pages = {358--378},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2012.05472.x},
  url = {https://doi.org/10.1111/j.1365-246X.2012.05472.x},
  urldate = {2023-07-06},
  abstract = {Surface topography has been considered a difficult task for seismic wave numerical modelling by the finite-difference method (FDM) because the most popular staggered finite-difference scheme requires a rectilinear grid. Even though there are numerous collocated grid schemes in other computational fields that could be used to solve the first-order hyperbolic equations, the lack of a stable free-surface boundary condition implementation for curvilinear grids also obstructs the adoption of curvilinear grids in seismic wave FDM modelling. In this study, we use generalized curvilinear grids that can fit the surface topography to discretize the computational domain and describe the implementation of a collocated grid finite-difference scheme, a higher order MacCormack scheme, to solve the first-order hyperbolic velocity-stress equations on the curvilinear grid. To achieve a sufficiently accurate and stable free-surface boundary condition implementation on the curvilinear grids, we propose the traction image method that antisymmetrically images the traction components instead of the stress components to the ghost points above the free surface. Since the velocity derivatives at the free surface are provided by the free-surface condition, we use a compact scheme to compute the velocity derivatives near the free surface and avoid the use of velocity values on the ghost points. Numerical tests verify that using the curvilinear grid, the collocated finite-difference scheme and the traction image technique can simulate seismic wave propagation in the presence of surface topography with sufficient accuracy.},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/Q47N6JTK/Zhang et al. - 2012 - Three-dimensional elastic wave numerical modelling.pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/VGK4UCNY/598545.html}
}

@article{zhouNumericalComparisonWENO2001,
  title = {Numerical {{Comparison}} of {{WENO Finite Volume}} and {{Runge}}{\textendash}{{Kutta Discontinuous Galerkin Methods}}},
  author = {Zhou, Tie and Li, Yinfan and Shu, Chi-Wang},
  year = {2001},
  month = jun,
  journal = {Journal of Scientific Computing},
  volume = {16},
  number = {2},
  pages = {145--171},
  issn = {1573-7691},
  doi = {10.1023/A:1012282706985},
  url = {https://doi.org/10.1023/A:1012282706985},
  urldate = {2023-06-30},
  abstract = {High order WENO (weighted essentially non-oscillatory) schemes and discontinuous Galerkin methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In this paper we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing.},
  langid = {english},
  keywords = {comparison,discontinuous Galerkin,finite volume,WENO},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/SP2NVCKY/Zhou et al. - 2001 - Numerical Comparison of WENO Finite Volume and Run.pdf}
}

@inproceedings{zimbrodEfficientSimulationComplex2022,
  title = {Efficient {{Simulation}} of {{Complex Capillary Effects}} in {{Advanced Manufacturing Processes}} Using the {{Finite Volume Method}}},
  booktitle = {2022 {{International Conference}} on {{Electrical}}, {{Computer}}, {{Communications}} and {{Mechatronics Engineering}} ({{ICECCME}})},
  author = {Zimbrod, Patrick and Schreter, Magdalena and Schilp, Johannes},
  year = {2022},
  month = nov,
  pages = {1--6},
  doi = {10.1109/ICECCME55909.2022.9988504},
  abstract = {The accurate representation of surface tension driven flows in multi phase systems is considered a challenging problem to resolve numerically. Although there have been extensive works in the past that have presented approaches to resolve these so called Marangoni flows at the phase boundaries, the question of how to efficiently resolve the interface in a universal and conservative manner remains largely open in comparison. Such problems are of high practical relevance in many manufacturing processes, especially in the microfluidic regime where capillary effects dominate the local force equilibria. In this work, we present a freely available numerical solver based on the Finite Volume Method that is able to resolve arbitrarily complex, incompressible multi phase systems with the mentioned physics at phase boundaries. An efficient solution with respect to the number of degrees of freedom can be obtained by either using high order WENO stencils or by employing adaptive cell refinement. We demonstrate the capabilities of the solver by investigating a model benchmark case as well as a single track laser melting process that is highly relevant within laser additive manufacturing.},
  keywords = {Adaptation models,adaptive refinement,Computational modeling,finite volume method,Laser modes,Manufacturing processes,marangoni flow,open source software,Solid modeling,Surface tension,Three-dimensional printing},
  annotation = {0 citations (Crossref) [2023-03-27]},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/3R8TJJAT/Zimbrod et al. - 2022 - Efficient Simulation of Complex Capillary Effects .pdf;/Users/zimbropa/Documents/Literaturverwaltung/storage/GT3YQBPW/9988504.html}
}

@article{zimbrodModellingMicrostructuresInsitu2021,
  title = {Modelling of Microstructures during In-Situ Alloying in Additive Manufacturing for Efficient Material Qualification Processes},
  author = {Zimbrod, Patrick and Schilp, Johannes},
  editor = {Franke, J{\"o}rg and Schuderer, Peter},
  year = {2021},
  journal = {Simulation in Produktion und Logistik 2021: 19. ASIM-Fachtagung Simulation in Produktion und Logistik, Erlangen, 15. {\textendash} 17. September 2021},
  pages = {177--188},
  url = {https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/87973},
  file = {/Users/zimbropa/Documents/Literaturverwaltung/storage/Z8GD2UQ2/Zimbrod und Schilp - Modelling of microstructures during in-situ alloyi.pdf}
}