报告题目： PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface

报 告 人： 鲁汪涛 研究员

所在单位： 浙江大学

报告时间：2022年06月30日 星期四 下午 14:00-15:00

报告地点：腾讯会议 ID：737-777-758

链接：https://meeting.tencent.com/dm/c17ThJiOvNRg

校内联系人：袁晓凯 yuanxk@jlu.edu.cn

报告摘要： In this talk, we shall study the perfectly-matched-layer (PML) method for wave scattering in a half space of homogeneous medium bounded by a two-dimensional, perfectly conducting, and locally defected periodic surface, and develops a high-accuracy boundary-integral-equation (BIE) solver. Along the vertical direction, we place a PML to truncate the unbounded domain onto a strip and prove that the PML solution converges to the true solution in the physical subregion of the strip with an error bounded by the reciprocal PML thickness. Laterally, we divide the unbounded strip into three regions: a region containing the defect and two semi-waveguide regions, separated by two vertical line segments. In both semi-waveguides, we prove the well-posedness of an associated scattering problem so as to well define a Neumann-to-Dirichlet (NtD) operator on the associated vertical segment. The two NtD operators, serving as exact lateral boundary conditions, reformulate the unbounded strip problem as a boundary value problem over the defected region. It is proved that the PML solution decays exponentially fast along both lateral directions. A high-accuracy PML-based BIE method is developed to solve the boundary value problem on the defected region. Numerical experiments demonstrate that the PML solution converges exponentially fast to the true solution in any compact subdomain of the strip.

报告人简介： 2007年中国科学技术大学学士，2012年中国科学技术大学博士，并于同年获得香港城市大学联合培养博士学位，2017年8月回浙大工作至今。2021年获浙江省自然科学基金杰出青年项目,主持及参与国家自然科学基金多项，在JCP及SIAM期刊SINUM、SISC、SIAP、MMS等发表多篇文章。