Implicit Yee-like scheme on tetrahedral mesh

Abstract

If constitutive laws can be expressed with diagonal matrices in wave propagation problems, Yee-like scheme will be explicit. As finite-element kinds of meshes provide flexibility in modeling complex geometries, they are preferred to regular grids in some cases. However, finding such diagonal matrices for an arbitrary finite-element mesh is not trivial. As a consequence we consider a compromise: find a partially diagonalized matrix to express constitutive laws, and thus, develop an implicit method on tetrahedral mesh.