題  目：An adaptive finite element DtN method for the transmission problem

内容簡介：In this talk, I will consider the scattering of a time-harmonic acoustic incident wave by a bounded penetrable obstacle, which is immersed in a homogeneous compressible air/fluid. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition is introduced and the model is formulated as a transmission boundary value problem. By a new duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. An adaptive finite element algorithm is proposed for solving the transmission problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are chosen through the finite element discretization error. Numerical experiments are presented to demonstrate 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SIAM J. Numer. Anal.，Math. Comput.，J.Sci. Comput.以及IMA J. 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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