Adaptive perfectly matched layer method for multiple scattering problems

A uniaxial perfectly matched layer (UPML) method is proposed for solving three-dimensional Helmholtz equation with multiple scatterers. The exterior domain is truncated to enclose each scatterer by a bounded domain individually. Based on reliable a posteriori error estimate, an efficient adaptive finite element algorithm is proposed to solve the multiple scattering problem. The efficiency of the adaptive PML method is demonstrated by extensive numerical experiments.