Merge branch 'aurora-multiphysics:main' into sr_kc/non-linear-diffusion

.github/workflows/lint.yml

@@ -34,9 +34,9 @@ jobs:
         uses: super-linter/super-linter/[email protected]
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-          # External doxygen style files and MOOSE Doxygen header do not meet Platypus
-          # linting requirements; exclude them from lint checks:
-          FILTER_REGEX_EXCLUDE: ((^|/)doxygen-awesome|moose_doxy_header.html|doxygen.css|tabs.css)
+          # External doxygen style files, the MOOSE Doxygen header, and the CodeCov upload script 
+          # do not meet Platypus linting requirements; exclude them from lint checks:
+          FILTER_REGEX_EXCLUDE: ((^|/)doxygen-awesome|moose_doxy_header.html|doxygen.css|tabs.css|codecov.sh)
           VALIDATE_ANSIBLE: false
           VALIDATE_CHECKOV: false
           VALIDATE_CPP: false

doc/content/examples/GradDiv.md

@@ -0,0 +1,50 @@
+# Grad-div Problem
+
+## Summary
+
+Solves a diffusion problem for a vector field on a cuboid domain, discretized
+using $H(\mathrm{div})$ conforming Raviart-Thomas elements. This example is
+based on [MFEM Example 4](https://mfem.org/examples/) and is relevant for
+solving Maxwell's equations using potentials without the Coulomb gauge.
+
+
+## Description
+
+This problem solves a grad-div equation with strong form:
+
+\begin{equation}
+\begin{split}
+\vec\nabla \left( \alpha \vec\nabla \cdot \vec F \right) + \beta \vec F = \vec f \,\,\,&\mathrm{on}\,\, \Omega \\
+\vec F \cdot \hat n= \vec g \,\,\, &\mathrm{on}\,\, \partial\Omega
+\end{split}
+\end{equation}
+
+where
+
+\begin{equation}
+\vec g = \begin{pmatrix}
+    \cos(k x)\sin(k y)\\
+    \cos(k y)\sin(k x)\\
+    0
+\end{pmatrix},\,\,\,
+\vec f = \left( \beta + 2 \alpha k^2 \right) \vec g
+\end{equation}
+
+In this example, we solve this using the weak form
+
+!equation
+(\alpha \vec\nabla \cdot \vec F , \vec\nabla \cdot \vec v)_\Omega + (\beta \vec F, \vec F)_\Omega
+= (\vec f, \vec v)_\Omega \,\,\, \forall \vec v \in V
+
+where
+
+\begin{equation}
+\begin{split}
+\vec F \in H(\mathrm{div})(\Omega) &: \vec F \cdot \hat n= \vec g \,\,\, \mathrm{on}\,\, \partial\Omega \\
+\vec v \in H(\mathrm{div})(\Omega) &: \vec v \cdot \hat n= \vec 0 \,\,\, \mathrm{on}\,\, \partial\Omega
+\end{split}
+\end{equation}
+
+## Example File
+
+!listing kernels/graddiv.i

doc/content/examples/LinearElasticity.md

@@ -0,0 +1,75 @@
+# Linear Elasticity Problem
+
+## Summary
+
+Solves a 3D linear elasticity problem for
+the deformation of a mult-material cantiliver beam. This example
+is based on [MFEM Example 2](https://mfem.org/examples/).
+
+
+## Description
+
+This problem solves a linear elasticity problem for small deformations with strong form:
+
+\begin{equation}
+\begin{split}
+-\partial_j \sigma_{ij} =0
+\,\,\,&\mathrm{on}\,\, \Omega \\
+u_i = 0 \,\,\, &\mathrm{on}\,\, \Gamma_1 \\
+\sigma_{ij} \hat n_j= f_i \,\,\, &\mathrm{on}\,\, \Gamma_2
+\end{split}
+\end{equation}
+
+where Einstein notation for summation over repeated indices has been used, and the pull-down force
+$\vec f = f_i \hat e_i$ is given by
+
+\begin{equation}
+\vec f = \begin{pmatrix}
+    0.0\\
+    0.0\\
+    -0.01
+\end{pmatrix}
+\end{equation}
+
+In this example,
+the stress/strain relation is taken to be isotropic, such that
+
+\begin{equation}
+\begin{split}
+\sigma_{ij} \equiv C_{ijkl} \varepsilon_{kl} = \lambda \delta_{ij} \varepsilon_{kk} + 2 \mu \varepsilon_{ij} \\
+\varepsilon_{ij} = \frac{1}{2} \left(\partial_i u_j + \partial_j u_i\right)
+\end{split}
+\end{equation}
+
+In this example, we solve this using the weak form
+
+\begin{equation}
+(\sigma_{ij}, \partial_j v_i)_\Omega - (\sigma_{ij} \hat n_j, v_i)_{\partial \Omega}
+= 0 \,\,\,\, \forall v_i \in V
+\end{equation}
+
+where
+
+\begin{equation}
+v_i \in H^1(\Omega) : v_i = 0 \,\,\, \mathrm{on} \,\, \Gamma_1
+\end{equation}
+
+## Material Parameters
+
+In this example, the cantilever beam is comprised of two materials; a stiffer material on the block
+with domain attribute 1, and a more flexible material defined on the block with domain attribute 2.
+These materials are parametrised with different  values for the Lamé parameters, $\lambda$ and
+$\mu$, on the two domains.
+
+The two Lamé parameters can be expressed in terms of the Young's modulus $E$ and the Poisson ratio $\nu$ in each material, using
+
+\begin{equation}
+\begin{split}
+\lambda &= \frac{E\nu}{(1-2\nu)(1+\nu)} \\
+\mu &= \frac{E}{2(1+\nu)}
+\end{split}
+\end{equation}
+
+## Example File
+
+!listing kernels/linearelasticity.i

doc/content/examples/index.md

@@ -14,8 +14,19 @@ starting point for users to adapt:
   boundary parameterized by a heat transfer coefficient that exchanges heat with a thermal
   reservoir.
 
+## Mechanical Problems
+
+- [Linear Elasticity](examples/LinearElasticity.md): Solves a 3D linear elasticity problem for
+  the deformation of a multi-material cantiliver beam. This example
+  is based on [MFEM Example 2](https://mfem.org/examples/).
+
 ## Electromagnetic Problems
 
-- [DefiniteMaxwell](examples/DefiniteMaxwell.md): Solves a 3D electromagnetic diffusion problem for
+- [Definite Maxwell](examples/DefiniteMaxwell.md): Solves a 3D electromagnetic diffusion problem for
   the electric field on a cube missing an octant, discretized using $H(\mathrm{curl})$ conforming
   Nédélec elements. This example is based on [MFEM Example 3](https://mfem.org/examples/).
+
+- [GradDiv](examples/GradDiv.md): Solves a diffusion problem for a vector field
+  on a cuboid domain, discretized using $H(\mathrm{div})$ conforming
+  Raviart-Thomas elements. This example is based on [MFEM Example 4](https://mfem.org/examples/)
+  and is relevant for solving Maxwell's equations using potentials without the Coulomb gauge.

doc/content/source/actions/SetMeshFESpaceAction.md

@@ -0,0 +1,18 @@
+# SetMeshFESpaceAction
+
+## Summary
+
+Sets the nodal mesh FESpace to use the same FESpace as the
+[`MFEMVariable`](source/variables/MFEMVariable.md) used to describe node displacements.
+
+## Overview
+
+Action called to set the nodal mesh FESpace to use the same FESpace as the variable used to describe
+node displacements in problems involving deformed meshes, parsing content inside the `Mesh` block in
+the user input. Only has an effect if the `Problem` type is set to
+[`MFEMProblem`](source/problem/MFEMProblem.md), the `Mesh` type is set to [`MFEMMesh`](source/mesh/MFEMMesh.md)
+and the `displacement` field is set.
+
+## Example Input File Syntax
+
+!listing test/tests/kernels/linearelasticity.i block=Mesh

doc/content/source/bcs/MFEMScalarBoundaryIntegratedBC.md

@@ -0,0 +1,21 @@
+# MFEMScalarBoundaryIntegratedBC
+
+## Summary
+
+!syntax description /BCs/MFEMScalarBoundaryIntegratedBC
+
+## Overview
+
+Adds the boundary integrator for integrating the linear form
+
+!equation
+(f, v)_{\partial\Omega} \,\,\, \forall v \in V
+
+where the test variable $v \in H^1$ and $f$ is a scalar coefficient. Often used for representing
+Neumann-type boundary conditions.
+
+!syntax parameters /BCs/MFEMScalarBoundaryIntegratedBC
+
+!syntax inputs /BCs/MFEMScalarBoundaryIntegratedBC
+
+!syntax children /BCs/MFEMScalarBoundaryIntegratedBC

doc/content/source/bcs/MFEMScalarDirichletBC.md

@@ -7,7 +7,7 @@
 ## Overview
 
 Boundary condition for enforcing an essential (Dirichlet) condition on a scalar variable on the
-boundary, fixing its values to the input scalar coefficient on the boundary.
+boundary, fixing its values to the input on the boundary.
 
 ## Example Input File Syntax
 

doc/content/source/bcs/MFEMScalarFunctionDirichletBC.md

@@ -0,0 +1,19 @@
+# MFEMScalarFunctionDirichletBC
+
+## Summary
+
+!syntax description /BCs/MFEMScalarFunctionDirichletBC
+
+## Overview
+
+Boundary condition for enforcing an essential (Dirichlet) condition on
+a scalar variable on the boundary, fixing its values to the input
+scalar function on the boundary.
+
+## Example Input File Syntax
+
+!syntax parameters /BCs/MFEMScalarFunctionDirichletBC
+
+!syntax inputs /BCs/MFEMScalarFunctionDirichletBC
+
+!syntax children /BCs/MFEMScalarFunctionDirichletBC

doc/content/source/bcs/MFEMVectorBoundaryIntegratedBC.md

@@ -0,0 +1,24 @@
+# MFEMVectorBoundaryIntegratedBC
+
+## Summary
+
+!syntax description /BCs/MFEMVectorBoundaryIntegratedBC
+
+## Overview
+
+Adds the boundary integrator for integrating the linear form
+
+!equation
+(\vec f, \vec v)_{\partial\Omega} \,\,\, \forall \vec v \in V
+
+where $\vec v \in \vec H^1$ and $\vec f$ is a constant vector of the same dimension.
+
+## Example Input File Syntax
+
+!listing test/tests/kernels/linearelasticity.i block=BCs
+
+!syntax parameters /BCs/MFEMVectorBoundaryIntegratedBC
+
+!syntax inputs /BCs/MFEMVectorBoundaryIntegratedBC
+
+!syntax children /BCs/MFEMVectorBoundaryIntegratedBC

doc/content/source/bcs/MFEMVectorDirichletBC.md

@@ -6,12 +6,12 @@
 
 ## Overview
 
-Boundary condition for enforcing an essential (Dirichlet) boundary condition on a vector variable on the
-boundary.
+Boundary condition for enforcing an essential (Dirichlet) boundary condition on all components of a
+vector $H^1$ conforming variable on the boundary. The boundary value is constant in space and time.
 
 ## Example Input File Syntax
 
-!listing test/tests/kernels/curlcurl.i block=BCs
+!listing test/tests/kernels/linearelasticity.i block=BCs
 
 !syntax parameters /BCs/MFEMVectorDirichletBC
 

doc/content/source/bcs/MFEMVectorDirichletBCBase.md

@@ -0,0 +1,12 @@
+# MFEMVectorDirichletBCBase
+
+## Summary
+
+Base class for objects applying essential boundary conditions on vector variables in an MFEM FE problem.
+
+## Overview
+
+Classes deriving from `MFEMVectorDirichletBCBase` are used for the application of Dirichlet-like BCs that
+remove degrees of freedom from vector variables in the problem on the specified boundary. These are commonly used when
+strongly constraining the values a solution may take on boundaries. The imposed values are uniform in space and constant
+in time.

doc/content/source/bcs/MFEMVectorFunctionBoundaryIntegratedBC.md

@@ -0,0 +1,22 @@
+# MFEMVectorFunctionBoundaryIntegratedBC
+
+## Summary
+
+!syntax description /BCs/MFEMVectorFunctionBoundaryIntegratedBC
+
+## Overview
+
+Adds the boundary integrator for integrating the linear form
+
+!equation
+(\vec f, \vec v)_{\partial\Omega} \,\,\, \forall \vec v \in V
+
+where $v \in \vec H^1$ and $\vec f$ is a vector function of the same dimension.
+
+## Example Input File Syntax
+
+!syntax parameters /BCs/MFEMVectorFunctionBoundaryIntegratedBC
+
+!syntax inputs /BCs/MFEMVectorFunctionBoundaryIntegratedBC
+
+!syntax children /BCs/MFEMVectorFunctionBoundaryIntegratedBC

doc/content/source/bcs/MFEMVectorFunctionDirichletBC.md

@@ -0,0 +1,20 @@
+# MFEMVectorFunctionDirichletBC
+
+## Summary
+
+!syntax description /BCs/MFEMVectorFunctionDirichletBC
+
+## Overview
+
+Boundary condition for enforcing an essential (Dirichlet) boundary condition on all components of a
+vector $H^1$ conforming variable on the boundary. The boundary value is a function of space and/or time.
+
+## Example Input File Syntax
+
+!listing test/tests/kernels/linearelasticity.i block=BCs
+
+!syntax parameters /BCs/MFEMVectorFunctionDirichletBC
+
+!syntax inputs /BCs/MFEMVectorFunctionDirichletBC
+
+!syntax children /BCs/MFEMVectorFunctionDirichletBC

doc/content/source/bcs/MFEMVectorFunctionDirichletBCBase.md

@@ -0,0 +1,11 @@
+# MFEMVectorFunctionDirichletBCBase
+
+## Summary
+
+Base class for objects applying essential boundary conditions on vector variables in an MFEM FE problem.
+
+## Overview
+
+Classes deriving from `MFEMVectorFunctionDirichletBCBase` are used for the application of Dirichlet-like BCs that
+remove degrees of freedom from vector variables in the problem on the specified boundary. These are commonly used when
+strongly constraining the values a solution may take on boundaries. The imposed values may vary in space and/or time.

doc/content/source/bcs/MFEMVectorFunctionNormalDirichletBC.md

@@ -0,0 +1,21 @@
+# MFEMVectorFunctionNormalDirichletBC
+
+## Summary
+
+!syntax description /BCs/MFEMVectorFunctionNormalDirichletBC
+
+## Overview
+
+Boundary condition for enforcing an essential (Dirichlet) boundary condition on the normal
+components of a $H(\mathrm{div})$ conforming vector FE at a boundary. The imposed value is
+a function of space and/or time.
+
+## Example Input File Syntax
+
+!listing test/tests/kernels/graddiv.i block=BCs
+
+!syntax parameters /BCs/MFEMVectorFunctionNormalDirichletBC
+
+!syntax inputs /BCs/MFEMVectorFunctionNormalDirichletBC
+
+!syntax children /BCs/MFEMVectorFunctionNormalDirichletBC