6月24日 郑伟英:A CIP-FEM for high-frequency scattering problem with the truncated DtN boundary condition

来源:pt真人平台 时间:2020-06-16浏览:29设置


讲座题目:A CIP-FEM  for high-frequency scattering problem with the truncated DtN boundary  condition

主讲人:郑伟英  研究员

主持人:郑海标  副教授

开始来源:pt真人平台 时间:2020-06-24   15:00:00

讲座地址:腾讯会议   房间号:300 829 284

主办单位:数学科学学院

 

报告人简介:

        郑伟英,中科院数学与系统科学研究院研究员,“科学与工程计算”国家重点实验室副主任。1996年于郑州大学获学士学位,2002年于北京大学获博士学位,2006-2007年为德国慕尼黑科技大学洪堡基金访问学者,2017年获杰出青年科学基金资助,2019年被聘为中科院数学与系统科学研究院“冯康首席研究员”。主要研究方向为电磁场、磁流体计算,在大型变压器的可计算建模、分层介质电磁散射的PML方法和三维磁流体力学的守恒型有限元方法等方面取得了一系列有重要意义的创新成果,对相关问题的研究产生了重要影响。


报告内容:

A continuous interior-penalty finite element   method (CIP-FEM) is proposed to solve high-frequency Helmholtz scattering   problem by an impenetrable obstacle in two dimensions. To formulate the   problem on a bounded domain, a Dirichlet-to-Neumann (DtN) boundary condition   is proposed on the outer boundary by truncating the Fourier series of the   original DtN mapping into finite terms. Assuming the truncation order N   >kR, the H^j-stabilities, j=0,1,2, are established for both forward and   dual problems, with explicit and sharp estimates of the upper bounds with   respect to the wave number k. Moreover, we prove that, when N>kR, the   solution to the DtN-truncation problem converges exponentially to the   original scattering problem as N increases. Under the condition that k^3h^2 is   sufficiently small, we prove that the preasymptotic error estimates for the   linear CIP-FEM as well as the linear continuous FEM are C(kh+k^3h^2).   Numerical experiments are presented to validate the theoretical results.

 


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