An effective preconditioner for a PML system for electromagnetic scattering problem

Abstract

In this work we are concerned with an efficient numerical solution of a perfectly matched layer (PML) system for a Maxwell scattering problem. The PML system is discretized by the edge finite element method, resulting in a symmetric but indefinite complex algebraic system. When the real and imaginary parts are considered independently, the complex algebraic system can be further transformed into a real generalized saddle-point system with some special structure. Based on an crucial observation to its Schur complement, we construct a symmetric and positive definite block diagonal preconditioner for the saddle-point system. Numerical experiments are presented to demonstrate the effectiveness and robustness of the new preconditioner.