报告人:殷 涛（美国加州理工学院）

时  间:2019年3月5日  上午10:30--11:30

地  点:理科楼 LA106

摘  要: In this talk, we discuss the boundary integral equation method for solving elastic scattering by closed-surface、open-arc or locally rough surface. For the open-arc case, our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and Neumann boundary conditions in conjunction with a certain "open-arc elastic Calderón relation" whose validity is demonstrated on the basis of numerical experiments, but whose rigorous mathematical proof is left for future work. For the locally rough surface case, a new windowed Green function method for the numerical integral-equation solutions of the problems is proposed based on the use of smooth windowing functions and free-space Green function. The proposed approach does not require evaluation of expensive Sommerfeld integrals involved in the layer Green function. For all kinds of problems, the integral operators are discretized based on a Chebyshev-based rectangular-polar integral solver that computes the non-adjacent integration via Fejér's fist quadrature rule which enjoys spectral accuracy for smooth integrands and the adjacent integration (involving singular and near-singular kernels) via highly-accurate precomputations of the kernels times Chebyshev polynomials (which are produced by means of a change of variables), together with Chebyshev expansions of the densities. Numerical experiments are presented to demonstrate the accuracy and fast convergence of our methods.

报告人简介:殷涛博士，2011年和2015年分别本科、博士毕业于重庆大学，目前在美国加州理工学院从事博士后研究，主要研究兴趣包括声波、弹性波正反散射问题，流固耦合问题，边界积分方程计算等。

学院联系人:王 坤

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