Convergence analysis of the perfectly matched layer problems for time-harmonic Maxwell's equations

This paper is concerned with convergence analysis of the perfectly matched layer (PML) problem in spherical coordinates for the three-dimensional electromagnetic scattering. Under some simple assumptions on the PML medium parameter, it is shown that the truncated PML problem attains a unique solution. The main result of the paper is to establish an explicit error estimate between the solution of the scattering problem and that of the truncated PML problem. The error estimate implies, in particular, that the PML solution converges exponentially to the scattering solution by increasing either the PML medium parameter or the PML layer thickness. The convergence result is expected to be useful for determining the PML medium parameter in the computational electromagnetic scattering problems.