An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems (Communications in Computational Physics, 2018)
A uniaxial perfectly matched layer (PML) method is proposed for solvingthe scattering problem with multiple cavities. By virtue of the integral representationof the scattering field, we decompose the problem into a system of single-cavityscattering problems which are coupled with Dirichlet-to-Neumann maps. A PML isintroduced to truncate the exterior domain of each cavity such that the computationaldomain does not intersect those for other cavities. Based on a posteriori error estimates,an adaptive finite element algorithm is proposed to solve the coupled system.The novelty of the proposed method is that its computational complexity is comparableto that for solving uncoupled single-cavity problems. Numerical experiments arepresented to demonstrate the efficiency of the adaptive PML method.