Perfectly-matched-layer boundary integral equation method for wave scattering in a layered medium


报告人:鲁汪涛 研究员 浙江大学
时间:2019年126日(周五) 15:00-16:00
摘要:For scattering problems of time-harmonic waves, the boundary integral  equation (BIE) methods are highly competitive, since they are formulated  on lower-dimension boundaries or interfaces and can automatically satisfy outgoing radiation conditions. For scattering problems in a layered medium, standard BIE methods based on the Green's function of the background medium need to evaluate the expensive Sommerfeld  integrals. Alternative BIE methods based on the free-space Green's  function give rise to integral equations on unbounded interfaces which  are not easy to truncate, since the wave fields on these interfaces  decay very slowly. We develop a BIE method based on the perfectly  matched layer (PML) technique. The PMLs are widely used to suppress outgoing waves in numerical methods that directly discretize the  physical space. Our PML-based BIE method uses the PML-transformed  free-space Green's function to define the boundary integral operators.  The method is efficient, since the PML-transformed free-space Green's function is easy to evaluate and the PMLs are very effective in truncating the unbounded interfaces. Numerical examples are presented to validate our method and demonstrate its accuracy.