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A CIP-FEM for high-frequency scattering problem with the truncated DtN boundary condition
郑伟英 研究员(中科院数学与系统科学研究院)
2020年6月24日15:00  

主持人:郑海标 副教授
报告平台:腾讯会议 房间号:300 829 284
报告时间:2020年6月24日15:00

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。

报告内容简介: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.