Cited By
View all- Lin LLv JLi S(2024)An adaptive finite element DtN method for the acoustic-elastic interaction problemAdvances in Computational Mathematics10.1007/s10444-024-10160-550:4Online publication date: 8-Jul-2024
An Adaptive Finite Element DtN Method for the Elastic Wave Scattering Problem in Three Dimensions
Authors: 
Gang Bao, Peijun Li, Xiaokai YuanAuthors Info & Claims
Gang Bao, Peijun Li, Xiaokai YuanAuthors Info & ClaimsPages 2900 - 2925
Abstract
Consider the elastic scattering of an incident wave by a rigid obstacle in three dimensions, which is formulated as an exterior problem for the Navier equation. By constructing a Dirichlet-to-Neumann (DtN) operator and introducing a transparent boundary condition, the scattering problem is reduced equivalently to a boundary value problem in a bounded domain. The discrete problem with the truncated DtN operator is solved by using the a posteriori error estimate based adaptive finite element method. The estimate takes account of both the finite element approximation error and the truncation error of the DtN operator, where the latter is shown to converge exponentially with respect to the truncation parameter. Moreover, the generalized Woodbury matrix identity is utilized to solve the resulting linear system efficiently. Numerical experiments are presented to demonstrate the superior performance of the proposed method.
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Published: 01 January 2021
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View all- Lin LLv JLi S(2024)An adaptive finite element DtN method for the acoustic-elastic interaction problemAdvances in Computational Mathematics10.1007/s10444-024-10160-550:4Online publication date: 8-Jul-2024