A plane wave least squares method for the Maxwell equations in anisotropic media

Abstract

In this paper, we first consider the time-harmonic Maxwell equations with Dirichlet boundary conditions in three-dimensional anisotropic media, where the coefficients of the equations are general symmetric positive definite matrices. By using scaling transformations and coordinate transformations, we build the desired stability estimates between the original electric field and the transformed nonphysical field on the condition number of the anisotropic coefficient matrix. More importantly, we prove that the resulting approximate solutions generated by plane wave least squares (PWLS) methods have the nearly optimal L2 error estimates with respect to the condition number of the coefficient matrix. Finally, numerical results verify the validity of the theoretical results, and the comparisons between the proposed PWLS method and the existing PWDG method are also provided.