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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)
Wednesday, June 24th, 2020, 3:00 PM  
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.
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