An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures
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Published:2021-11
Issue:6
Volume:55
Page:2921-2947
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ISSN:0764-583X
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Container-title:ESAIM: Mathematical Modelling and Numerical Analysis
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language:
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Short-container-title:ESAIM: M2AN
Author:
Bao Gang,Jiang Xue,Li Peijun,Yuan Xiaokai
Abstract
Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an unbounded domain above the surface. Based on the Dirichlet-to-Neumann (DtN) operator, which is given as an infinite series, an exact transparent boundary condition is introduced and the scattering problem is formulated equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed to solve the discrete variational problem where the DtN operator is truncated into a finite number of terms. The a posteriori error estimate takes account of the finite element approximation error and the truncation error of the DtN operator which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to illustrate the effectiveness of the proposed method.
Funder
Innovative Research Group Project of the National Natural Science Foundation of China
National Natural Science Foundation of China
Division of Mathematical Sciences
Subject
Applied Mathematics,Modelling and Simulation,Numerical Analysis,Analysis,Computational Mathematics
Cited by
1 articles.
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