For scattering problems of time-harmonic waves, the boundary integralequation (BIE) methods are highly competitive, since they are formulated onlower-dimension boundaries or interfaces, and can automatically satisfyoutgoing radiation conditions. For scattering problems in a layered medium,standard BIE methods based on the Green's function of the background mediummust evaluate the expensive Sommefeld integrals. Alternative BIE methods basedon the free-space Green's function give rise to integral equations on unboundedinterfaces which are not easy to truncate, since the wave fields on theseinterfaces decay very slowly. We develop a BIE method based on the perfectlymatched layer (PML) technique. The PMLs are widely used to suppress outgoingwaves in numerical methods that directly discretize the physical space. OurPML-based BIE method uses the Green's function of the PML-transformed freespace to define the boundary integral operators. The method is efficient, sincethe Green's function of the PML-transformed free space is easy to evaluate andthe PMLs are very effective in truncating the unbounded interfaces. Numericalexamples are presented to validate our method and demonstrate its accuracy.
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