A Spurious-Free Domain Decomposition Method for 3-D Maxwell’s Eigenvalue Problems

Abstract

A spurious-free domain decomposition method (DDM) based on a nonconforming tetrahedron–hexahedron mesh is proposed to solve 3-D Maxwell’s eigenvalue problems with several boundary conditions. In this DDM, the nonzero spurious modes and zero (dc) spurious modes are eliminated by locally modifying the tetrahedral mesh at the subdomain interface and implementing a tree–cotree technique. This method is a generalization of the Nitsche’s method, in which the mutually conjugate transposed terms present are omitted to reduce the computational costs. Moreover, we derive the constrained equations for the quartic Maxwell’s eigenvalue problem and impose them on Ritz vectors in the Arnoldi algorithm to remove the dc spurious modes. Numerical experiments demonstrate that the DDM is about 2.6 times more efficient than the commercial software COMSOL.