A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems

Yin, Tao; Rathsfeld, Andreas; Xu, Li

doi:10.4208/jcm.1610-m2015-0480

Cited by 9 publications

(3 citation statements)

References 32 publications

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“…One popular method to overcome the difficulty that the acoustic scattered wave propagates in an unbounded domain is known as the Dirichlet-to-Neumann (DtN) method ( [9,28,29]), that is, the original transmission problem is reduced to a boundary value problem by introducing a DtN mapping defined on an artificial boundary enclosing the elastic body inside. Another conventional numerical method is the coupling of the boundary element method (BEM) and the finite element method (FEM) ( [7,8,[10][11][12][13][14]24]).…”

Section: Introductionmentioning

confidence: 99%

Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem

Yin¹,

Hsiao²,

Xu³

2017

SIAM J. Numer. Anal.

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This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect approaches. Existence and uniqueness results for variational solutions of boundary integral equations equations are established. Since in all these boundary variational formulations, the hypersingular boundary integral operator associated with the timeharmonic Navier equation is a dominated integral operator, we also include a new regularization formulation for this hypersingular operator, which allows us to treat the hypersingular kernel by a wealkly singular kernel. Numerical examples are presented to verify and validate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem

Yin¹,

Hsiao²,

Xu³

2017

SIAM J. Numer. Anal.

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“…We consider the scattering of a plane incident wave p inc = e ikx•d with direction d = (1, 0) by a disc-shaped elastic body of radius R 0 (see Figure 2). For the exact solution of this model problem, we refer to [28,39]. In numerical computations, the computational domain Ω and Ω R are discretized by uniform triangle elements and we employ piecewise linear basis functions {ϕ i } i=N1 i=1 and {ψ i } i=N2 i=1 in Ω and Ω R , respectively, to construct the finite element space H h .…”

Section: Numerical Experimentsmentioning

confidence: 99%

Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods

Yin

2021

Numer. Math.

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It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method (FEM), we solve and analyze a two dimensional transmission problem describing elastic waves inside a bounded and closed elastic obstacle and acoustic waves outside it. We are mainly interested in analyzing the DtN boundary condition of the Helmholtz equation in order to establish the well-posedness results of the approximated variational equation, and further derive a priori error estimates involving effects of both the finite element discretization and the DtN boundary condition truncation. Finally, some numerical results are presented to illustrate the accuracy of the numerical scheme.

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“…Some of them provide proper guidance also for time-domain problems. Popular methods include the boundary integral equation (BIE) method, see [33,46] and coupling methods such as the so-called coupled FEM-BEM method, see [47]. An artificial boundary or an absorbing layer ( [43]) can be introduced to reduce the original unbounded problem to a bounded problem which could be solved using field equation solvers such as the finite element method.…”

Section: Introductionmentioning

confidence: 99%

An interior penalty discontinuous Galerkin method for the time-domain acoustic-elastic wave interaction problem

Cheng¹,

Huang²,

Li³

et al. 2019

Preprint

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In this paper, we consider numerical solutions of a time domain acoustic-elastic wave interaction problem which occurs between a bounded penetrable elastic body and a compressible inviscid fluid. It is also called the fluid-solid interaction problem. First, we introduce an artificial boundary to transform the original transmission problem into a problem in a bounded region, and then we employ a symmetric interior penalty discontinuous Galerkin method for the solution of the reduced interaction problem consisting of second-order wave equations. A priori error estimate in the energy norm is presented, and numerical results confirm the accuracy and validity of the proposed method.

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A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems

Cited by 9 publications

References 32 publications

Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem

Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem

Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods

An interior penalty discontinuous Galerkin method for the time-domain acoustic-elastic wave interaction problem

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