題 目：Anadaptive finite element DtN method for the transmission problem
内容簡介：Inthis talk, I will consider the scattering of a time-harmonic acousticincident wave by a bounded penetrable obstacle, which is immersed ina homogeneous compressible air/fluid. Based on a Dirichlet-to-Neumann(DtN) operator, an exact transparent boundary condition is introducedand the model is formulated as a transmission boundary value problem.By a new duality argument technique, an a posteriori error estimateis derived for the finite element method with the truncated DtNboundary operator. The a posteriori error estimate consists of thefinite element approximation error and the truncation error of theDtN boundary operator, where the latter decays exponentially withrespect to the truncation parameter. An adaptive finite elementalgorithm is proposed for solving the transmission problem, where thetruncation parameter is determined through the truncation error andthe mesh elements for local refinements are chosen through the finiteelement discretization error. Numerical experiments are presented todemonstrate the effectiveness of the proposed method.
報告人：呂俊良
報告人簡介：吉林大學數學學院，教授，博導。研究興趣包括無界域散射問題的數值方法，反散射問題的數值算法與理論，偏微分方程有限體積元法等。研究成果發表在SIAMJ. Numer. Anal.，Math.Comput.，J.Sci.Comput.以及IMAJ. Numer. Anal.等雜志上。承擔國家自然科學基金項目、國防項目、吉林省自然科學基金等。
現任中國數學會計算數學分會理事、中國仿真學會仿真算法專委會委員、吉林省數學會理事、美國數學會數學評論員。
時 間：2023年11月15日（周三）下午15：00開始
地 點：騰訊會議：194-276-676
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