paper.bib

@article{chipman2024fast,
	title={A Fast Direct Solver for Elliptic PDEs on a Hierarchy of Adaptively Refined Quadtrees},
	author={Chipman, D and Calhoun, D and Burstedde, C},
	journal={arXiv preprint arXiv:2402.14936},
	year={2024},
	doi={10.48550/arXiv.2402.14936}
}

@article{chipman2024parallel,
	author = {Chipman, D and Calhoun, D and Burstedde, C},
	journal = {[Forthcoming]},
	title = {{MPI Implementation of the Quadtree-Adaptive Hierarchical Poincar{\'e}-Steklov Method}},
	year = {2024}
}

@article{gillman2014direct,
    author = {Gillman, A. and Martinsson, P. G.},
    title = {{A Direct Solver with $O(N)$ Complexity for Variable Coefficient Elliptic PDEs Discretized via a High-Order Composite Spectral Collocation Method}},
    journal = {SIAM Journal on Scientific Computing},
    volume = {36},
    number = {4},
    pages = {A2023-A2046},
    year = {2014},
    doi = {10.1137/130918988},
    url = {https://doi.org/10.1137/130918988},
    eprint = {https://doi.org/10.1137/130918988},
}

@book{martinsson2019fast,
	author = {Martinsson, PG},
	publisher = {SIAM},
	title = {{Fast direct solvers for elliptic PDEs}},
	year = {2019},
	doi={10.1137/1.9781611976045}
}

@article{swarztrauber1999fishpack,
	author = {Swarztrauber, P and Sweet, R and Adams, J},
	journal = {UCAR Publication, July},
	title = {FISHPACK: Efficient FORTRAN subprograms for the solution of elliptic partial differential equations},
	year = {1999},
	doi={10.1145/800207.806417}
}

@article{adams2016fishpack90,
	author = {Adams, J C and Swarztrauber, P and Sweet, R},
	journal = {Astrophysics Source Code Library},
	pages = {ascl--1609},
	title = {FISHPACK90: Efficient fortran subprograms for the solution of separable elliptic partial differential equations},
	year = {2016},
	url={https://ui.adsabs.harvard.edu/abs/2016ascl.soft09005A/abstract}
}

@manual{mpi41,
    author = "{Message Passing Interface Forum}",
    title  = "{MPI}: A Message-Passing Interface Standard Version 4.1",
    url    = "https://www.mpi-forum.org/docs/mpi-4.1/mpi41-report.pdf",
    year   = 2023,
    month  = nov
}

@article{burstedde2011p4est,
	author = {Burstedde, C and Wilcox, L and Ghattas, O},
	journal = {SIAM Journal on Scientific Computing},
	number = {3},
	pages = {1103-1133},
	title = {{\texttt{p4est}}: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees},
	volume = {33},
	year = {2011},
	doi={10.1137/100791634}
}

@incollection{paraview,
	author = {Ahrens, J and Geveci, B and Law, C},
	booktitle = {Visualization Handbook},
	publisher = {Elesvier},
	title = {{ParaView}: An End-User Tool for Large Data Visualization},
	year = {2005},
	doi = {10.1016/b978-012387582-2/50038-1}
}

@Misc{            anl2023petsc,
  author        = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed
                  Brown and Peter Brune and Kris Buschelman and Emil~M. Constantinescu and Lisandro
                  Dalcin and Alp Dener and Victor Eijkhout and Jacob Faibussowitsch and William~D.
                  Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet and Dmitry Karpeev
                  and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger and
                  Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell
                  and Todd Munson and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich
                  and Barry~F. Smith and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao
                  Zhang},
  title         = {{PETS}c {W}eb page},
  url           = {https://petsc.org/},
  year          = {2024}
}

@article{martinsson2015hierarchical,
	author = {Martinsson, PG},
	journal = {arXiv preprint arXiv:1506.01308},
	title = {{The hierarchical Poincar{\'e}-Steklov (HPS) solver for elliptic PDEs: A tutorial}},
	year = {2015},
	doi={10.48550/arXiv.1506.01308}
}

@incollection{quarteroni1991theory,
	author = {Quarteroni, A and Valli, A},
	booktitle = {Applied and Industrial Mathematics},
	pages = {179--203},
	publisher = {Springer},
	title = {{Theory and application of Steklov-Poincar{\'e} operators for boundary-value problems}},
	year = {1991},
	doi = {10.1007/978-94-009-1908-2_14}
}

@incollection{HPV:VisIt,
	author = {Hank Childs and Eric Brugger and Brad Whitlock and Jeremy Meredith and Sean Ahern and David Pugmire and Kathleen Biagas and Mark Miller and Cyrus Harrison and Gunther H. Weber and Hari Krishnan and Thomas Fogal and Allen Sanderson and Christoph Garth and E. Wes Bethel and David Camp and Oliver R\"{u}bel and Marc Durant and Jean M. Favre and Paul Navr\'{a}til},
	booktitle = {High Performance Visualization--Enabling Extreme-Scale Scientific Insight},
	month = {October},
	pages = {357-372},
	title = {VisIt: An End-User Tool For Visualizing and Analyzing Very Large Data},
	year = {2012},
	doi={10.1201/b12985-29}
}

@misc{ultraSEM,
	author = {Fortunato, D and Hale, N and Townsend, A},
	title = {ultraSEM: The ultraspherical spectral element method},
	year = {2022},
	publisher = {GitHub},
	journal = {GitHub repository},
	url = {https://github.com/danfortunato/ultraSEM}
}

@misc{HPS_Demos,
	author = {Gillman, A},
	title = {HPS_Demos: A collection of codes applying the HPS method},
	year = {2023},
	publisher = {GitHub},
	journal = {GitHub repository},
	url = {https://github.com/agillman20/HPS_Demos}
}

@misc{Streamer_HPS,
	author = {Semenov, I},
	title = {Streamer_HPS_DGSEM: Implementation of the spectral element method for modelling streamer discharges},
	year = {2023},
	publisher = {GitHub},
	journal = {GitHub repository},
	url = {https://github.com/igsemenov/Streamer_HPS_DGSEM}
}