Motivation

Many physical systems manifest as eigenvalue problems. For such classes of problems, there exist Hypre-based MFEM solvers which can obtain the lowest n eigenvalues and eigenvectors. These solvers have not yet been implemented on MOOSE, but they would be useful for many problems, for instance EM modes within waveguides.

Design

Eigensolvers require special treatment when building the stiffness matrix and they assume the existence of a mass matrix on the RHS of the problem. As such, one possible design would be to create a class MFEMEigensolverBase which inherits from MFEMSolverBase and overrides some of its methods. Then, we can have specific eigensolvers like MFEMHypreLOBPCG inherit from MFEMEigensolverBase. It is also necessary to further split up the EquationSystem::FormLinearSystem method so as to accommodate eigenvalue problems.

Impact

MFEM-MOOSE would be able to solve eigenvalue problems for any number of selected eigenvalues.