Add MFEM-native mesh generator infrastructure

Introduces MFEMMeshGenerator (abstract base + carrier pipeline), MFEMGeneratedMeshGenerator
(structured Cartesian meshes in 1D/2D/3D with named boundary sets), and refactors the existing
MFEM mesh hierarchy so MFEMMesh is the abstract base and MFEMFileMesh is the concrete
file-reading subclass. Updates MFEMProblem::mesh() to accept any MFEMMesh subclass,
bulk-renames test input files from MFEMMesh to MFEMFileMesh, and adds doc pages for
MFEMGeneratedMeshGenerator, MFEMFileMesh, and MFEMElementAverageValue.

Closes #32827

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: lindsayad

framework/doc/content/source/mfem/mesh/MFEMFileMesh.md

@@ -0,0 +1,28 @@
+# MFEMFileMesh
+
+!if! function=hasCapability('mfem')
+
+## Overview
+
+`MFEMFileMesh` reads an `mfem::ParMesh` from file for use in an `MFEMProblem`. Exodus files are
+supported, along with other mesh formats listed [here](https://mfem.org/mesh-formats/).
+
+As MOOSE checks for the existence of a `libMesh` MOOSE mesh at various points during setup,
+`MFEMFileMesh` builds a dummy MOOSE mesh of a single point alongside the MFEM mesh. This dummy
+mesh should not be used in an `MFEMProblem`; all MFEM objects should access the `mfem::ParMesh` via
+the `getMFEMParMesh()` accessor as needed.
+
+## Example Input File Syntax
+
+!listing test/tests/mfem/kernels/diffusion.i block=Problem Mesh
+
+!syntax parameters /Mesh/MFEMFileMesh
+
+!syntax inputs /Mesh/MFEMFileMesh
+
+!syntax children /Mesh/MFEMFileMesh
+
+!if-end!
+
+!else
+!include mfem/mfem_warning.md

framework/doc/content/source/mfem/mesh/MFEMMesh.md

@@ -0,0 +1,37 @@
+# MFEMGeneratedMeshGenerator
+
+!if! function=hasCapability('mfem')
+
+## Overview
+
+`MFEMGeneratedMeshGenerator` generates a structured Cartesian MFEM mesh for use in an
+`MFEMProblem`. It produces a line (1D), rectangle (2D), or box (3D) with uniformly spaced
+elements, and is the MFEM analog of [GeneratedMeshGenerator.md].
+
+The [!param](/Mesh/MFEMGeneratedMeshGenerator/dim) parameter is required and selects the spatial
+dimension. Element type defaults to `QUAD` for 2D and `HEX` for 3D; `TRI` and `TET` are also
+supported via [!param](/Mesh/MFEMGeneratedMeshGenerator/elem_type).
+
+Named boundary sets are assigned automatically so boundaries can be referenced by name in
+`[BCs]` blocks:
+
+| Dimension | Boundary names |
+|-----------|----------------|
+| 1D | `left`, `right` |
+| 2D | `bottom`, `right`, `top`, `left` |
+| 3D | `bottom`, `front`, `right`, `back`, `left`, `top` |
+
+## Example Input File Syntax
+
+!listing test/tests/mfem/meshgenerators/generated/test.i block=Mesh BCs
+
+!syntax parameters /Mesh/MFEMGeneratedMeshGenerator
+
+!syntax inputs /Mesh/MFEMGeneratedMeshGenerator
+
+!syntax children /Mesh/MFEMGeneratedMeshGenerator
+
+!if-end!
+
+!else
+!include mfem/mfem_warning.md

framework/doc/content/source/mfem/meshgenerators/MFEMGeneratedMeshGenerator.md

@@ -0,0 +1,29 @@
+# MFEMElementAverageValue
+
+!if! function=hasCapability('mfem')
+
+## Overview
+
+Computes the volumetric average of a scalar MFEM variable over the mesh or a block-restricted
+subset of subdomains:
+
+!equation
+\bar{u} = \frac{\int_\Omega u \, \mathrm{d}V}{\int_\Omega \mathrm{d}V}
+
+where $\Omega$ is the full mesh domain, or the union of subdomains specified by
+[!param](/Postprocessors/MFEMElementAverageValue/block).
+
+## Example Input File Syntax
+
+!listing test/tests/mfem/meshgenerators/generated/test.i block=Postprocessors
+
+!syntax parameters /Postprocessors/MFEMElementAverageValue
+
+!syntax inputs /Postprocessors/MFEMElementAverageValue
+
+!syntax children /Postprocessors/MFEMElementAverageValue
+
+!if-end!
+
+!else
+!include mfem/mfem_warning.md

framework/doc/content/source/mfem/postprocessors/MFEMElementAverageValue.md

@@ -0,0 +1,35 @@
+//* This file is part of the MOOSE framework
+//* https://mooseframework.inl.gov
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#ifdef MOOSE_MFEM_ENABLED
+
+#pragma once
+
+#include "MFEMMesh.h"
+
+/**
+ * Reads an mfem::ParMesh from a file. All shared MFEM mesh plumbing lives in
+ * MFEMMesh; this class only adds the file parameter and implements
+ * buildSerialMFEMMesh() to load the mesh from disk.
+ */
+class MFEMFileMesh : public MFEMMesh
+{
+public:
+  static InputParameters validParams();
+
+  MFEMFileMesh(const InputParameters & parameters);
+  virtual ~MFEMFileMesh();
+
+  std::unique_ptr<MooseMesh> safeClone() const override;
+
+protected:
+  mfem::Mesh buildSerialMFEMMesh() override;
+};
+
+#endif

framework/include/mfem/mesh/MFEMFileMesh.h

@@ -11,61 +11,34 @@
 
 #pragma once
 
-#include "FileMesh.h"
+#include "MooseMesh.h"
 
 /**
- * MFEMMesh inherits a MOOSE mesh class which allows us to work with
- * other MOOSE objects. It contains a pointer to the parallel MFEM mesh.
+ * Abstract MooseMesh base for all MFEM-backed mesh types (MFEMFileMesh,
+ * MFEMMeshGeneratorMesh). Holds the mfem::ParMesh and owns the shared
+ * MFEM mesh interface. Subclasses implement buildSerialMFEMMesh() to
+ * supply the serial mesh; buildMesh() handles the common post-processing
+ * (refinement, reordering, partitioning) using the template-method pattern.
  */
-class MFEMMesh : public FileMesh
+class MFEMMesh : public MooseMesh
 {
 public:
   static InputParameters validParams();
 
   MFEMMesh(const InputParameters & parameters);
 
-  virtual ~MFEMMesh();
-
-  /**
-   * Accessors for the _mfem_par_mesh object. If the mesh has
-   * not been build, the methods will call the appropriate protected methods to
-   * build them.
-   */
   mfem::ParMesh & getMFEMParMesh() { return *_mfem_par_mesh; }
   const mfem::ParMesh & getMFEMParMesh() const;
 
-  /**
-   * Copy a shared_ptr to the mfem::ParMesh object.
-   */
   std::shared_ptr<mfem::ParMesh> getMFEMParMeshPtr() { return _mfem_par_mesh; }
 
-  /**
-   * Build MFEM ParMesh and a placeholder MOOSE mesh.
-   */
-  void buildMesh() override;
-
-  /**
-   * Clones the mesh.
-   */
-  std::unique_ptr<MooseMesh> safeClone() const override;
-
-  /**
-   * Returns true if mesh displacement is required.
-   */
   bool shouldDisplace() const { return _mesh_displacement_variable.has_value(); }
 
-  /**
-   * Returns an optional reference to displacement variable name.
-   */
   std::optional<std::reference_wrapper<std::string const>> getMeshDisplacementVariable() const
   {
     return _mesh_displacement_variable;
   }
 
-  /**
-   * Displace the nodes of the mesh by the given displacement.
-   * Does not update FE spaces for variables.
-   */
   void displace(mfem::GridFunction const & displacement);
 
   bool isDistributedMesh() const override { return true; }
@@ -75,26 +48,22 @@ class MFEMMesh : public FileMesh
   dof_id_type nActiveElem() const override { return _mfem_par_mesh->GetGlobalNE(); }
   dof_id_type nActiveLocalElem() const override { return _mfem_par_mesh->GetNE(); }
 
-private:
+  void buildMesh() override;
+
+protected:
   /**
-   * Builds a placeholder mesh when no MOOSE mesh is required.
+   * Build and return the serial mfem::Mesh for this object. Also responsible
+   * for setting up the libMesh dummy placeholder (via buildDummyMooseMesh()).
    */
+  virtual mfem::Mesh buildSerialMFEMMesh() = 0;
+
+  /// Replaces the underlying libMesh mesh with a single-point placeholder.
   void buildDummyMooseMesh();
 
-  /**
-   * Performs a uniform refinement on the chosen mesh nref times.
-   */
-  void uniformRefinement(mfem::Mesh & mesh, const unsigned int nref) const;
+  /// Applies uniform refinement to mesh nref times.
+  void uniformRefinement(mfem::Mesh & mesh, unsigned int nref) const;
 
-  /**
-   * Holds name of variable used for mesh displacement, if set.
-   */
   std::optional<std::string> _mesh_displacement_variable;
-
-  /**
-   * Smart pointers to mfem::ParMesh object. Do not access directly.
-   * Use the accessors instead.
-   */
   std::shared_ptr<mfem::ParMesh> _mfem_par_mesh{nullptr};
 };
 

framework/include/mfem/mesh/MFEMMesh.h

@@ -0,0 +1,39 @@
+//* This file is part of the MOOSE framework
+//* https://mooseframework.inl.gov
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#ifdef MOOSE_MFEM_ENABLED
+
+#pragma once
+
+#include "libmesh/replicated_mesh.h"
+
+/**
+ * A thin libMesh::ReplicatedMesh subclass that carries an mfem::Mesh through the
+ * MeshGenerator pipeline. The libMesh side is always empty; it exists only to satisfy
+ * the std::unique_ptr<MeshBase> return type of MeshGenerator::generate(). MFEM mesh
+ * generators wrap their output in this carrier and unwrap their inputs from it.
+ */
+class MFEMMeshCarrier : public libMesh::ReplicatedMesh
+{
+public:
+  explicit MFEMMeshCarrier(const Parallel::Communicator & comm);
+
+  void setMFEMMesh(mfem::Mesh mesh) { _mfem_mesh = std::move(mesh); }
+
+  mfem::Mesh & getMFEMMesh() { return _mfem_mesh; }
+  const mfem::Mesh & getMFEMMesh() const { return _mfem_mesh; }
+
+  /// Move the held mfem::Mesh out; leaves the carrier with a default-constructed (empty) mesh.
+  mfem::Mesh releaseMFEMMesh() { return std::move(_mfem_mesh); }
+
+private:
+  mfem::Mesh _mfem_mesh;
+};
+
+#endif

framework/include/mfem/mesh/MFEMMeshCarrier.h

@@ -0,0 +1,39 @@
+//* This file is part of the MOOSE framework
+//* https://mooseframework.inl.gov
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#ifdef MOOSE_MFEM_ENABLED
+
+#pragma once
+
+#include "MFEMMesh.h"
+
+/**
+ * MooseMesh subclass that consumes the MeshGenerator pipeline to build an
+ * mfem::ParMesh. It is the MFEM analog of MeshGeneratorMesh: use it as the
+ * [Mesh] type (or let SetupMeshAction auto-select it) whenever one or more
+ * MFEMMeshGenerator objects are present.
+ *
+ * All shared MFEM mesh plumbing lives in MFEMMesh; this class implements
+ * buildSerialMFEMMesh() to extract the mfem::Mesh from the MFEMMeshCarrier
+ * produced by the generator pipeline.
+ */
+class MFEMMeshGeneratorMesh : public MFEMMesh
+{
+public:
+  static InputParameters validParams();
+
+  MFEMMeshGeneratorMesh(const InputParameters & parameters);
+
+  std::unique_ptr<MooseMesh> safeClone() const override;
+
+protected:
+  mfem::Mesh buildSerialMFEMMesh() override;
+};
+
+#endif

framework/include/mfem/mesh/MFEMMeshGeneratorMesh.h

@@ -0,0 +1,41 @@
+//* This file is part of the MOOSE framework
+//* https://mooseframework.inl.gov
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#ifdef MOOSE_MFEM_ENABLED
+
+#pragma once
+
+#include "MFEMMeshGenerator.h"
+
+/**
+ * Generates a structured Cartesian MFEM mesh: a line (1D), rectangle (2D), or
+ * box (3D) with uniformly spaced elements. Analogous to GeneratedMeshGenerator
+ * for the MFEM mesh pipeline.
+ */
+class MFEMGeneratedMeshGenerator : public MFEMMeshGenerator
+{
+public:
+  static InputParameters validParams();
+
+  MFEMGeneratedMeshGenerator(const InputParameters & parameters);
+
+protected:
+  mfem::Mesh generateMFEMMesh() override;
+
+private:
+  const unsigned int _dim;
+  const unsigned int _nx;
+  const unsigned int _ny;
+  const unsigned int _nz;
+  const Real _xmax;
+  const Real _ymax;
+  const Real _zmax;
+};
+
+#endif