摘要：This talk will present our recent works on the fast and highly accurate boundary integral equation (BIE) methods, including the windowed Green function (WGF) method and perfectly-matched-layer (PML) BIE method, for solving the acoustic and elastic wave scattering problems in both two- and three-dimensional layered-medium. 1) The WGF method utilize the free-space fundamental solution to derive the BIEs on the whole unbounded surface which requires to be truncated in practical computing. Based on the solutions due to the scattering by flat surface, a correction strategy is introduced to ensure uniform accuracy for all incident angles. 2) For the half-space and two layered-medium case, the original scattering problem can be truncated onto a bounded domain by the PML. Assuming the vanishing of the scattered field on the PML boundary, BIEs on local defects are derived only in terms of using the PML-transformed free-space Green's function. For the considered two methods, a high-order Chebyshev-based rectangular-polar singular-integration solver is used in numerical implementation. Numerical experiments for both two- and three-dimensional problems are carried out to demonstrate the accuracy and efficiency of the proposed solvers.
简介：殷涛，中国科学院数学与系统科学研究院副研究员，2015年博士毕业于重庆大学，期间在德国柏林工业大学联合培养，先后在浙江大学、法国格勒诺布尔大学、美国加州理工学院从事博士后研究工作，入选国家海外高层次人才青年项目和中科院引才计划，主持国家自然科学基金面上项目。主要研究兴趣在边界积分方程、波散射正反问题的理论和数值方法，已在SIAM 系列期刊，Numer. Math.，J. Comput. Phys.，J. Math. Pures Appl.，Inverse Problems等应用和计算数学期刊上发表论文20余篇。