A NEW PERFECTLY MATCHED LAYER METHOD FOR THE HELMHOLTZ EQUATION IN NONCONVEX DOMAINS

A new coupled perfectly matched layer (PML) method is proposed for the Helmholtz equation in the whole space with inhomogeneity concentrated on a nonconvex domain. Rigorous analysis is presented for the stability and convergence of the proposed coupled PML method, which shows that the PML solution converges to the solution of the original Helmholtz problem exponen-tially with respect to the product of the wave number and the width of the layer. An iterative algorithm and a continuous interior penalty finite element method (CIP-FEM) are also proposed for solving the system of equations associated to the coupled PML. Numerical experiments are presented to illustrate the convergence and performance of the proposed coupled PML method, as well as the iterative algorithm and the CIP-FEM.