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Volume 36, Issue 1
A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems

Tao Yin, Andreas Rathsfeld & Liwei Xu

DOI: 10.4208/jcm.1610-m2015-0480

J. Comp. Math., 36 (2018), pp. 47-69.

Published online: 2018-02

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  • Abstract

In this paper, we are concerned with the coupling of finite element methods and boundary integral equation methods solving the classical fluid-solid interaction problem in two dimensions. The original transmission problem is reduced to an equivalent nonlocal boundary value problem via introducing a Dirichlet-to-Neumann mapping by the direct boundary integral equation method. We show the existence and uniqueness of the solution for the corresponding variational equation. Numerical results based on the finite element method coupled with the standard Galerkin boundary element method, the fast multipole method and the Nyström method for approximating the DtN mapping are provided to illustrate the efficiency and accuracy of the numerical schemes.

  • Keywords

Fluid-solid interaction problem, Dirichlet-to-Neumann mapping, Finite element method, Fast multipole method, Nyström method.

  • AMS Subject Headings

65N38, 65N06, 74J05, 76B20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

taoyin_cqu@163.com (Tao Yin)

rathsfeld@wias-berlin.de (Andreas Rathsfeld)

xul@cqu.edu.cn (Liwei Xu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-47, author = {Yin , TaoRathsfeld , Andreas and Xu , Liwei}, title = {A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {1}, pages = {47--69}, abstract = {

In this paper, we are concerned with the coupling of finite element methods and boundary integral equation methods solving the classical fluid-solid interaction problem in two dimensions. The original transmission problem is reduced to an equivalent nonlocal boundary value problem via introducing a Dirichlet-to-Neumann mapping by the direct boundary integral equation method. We show the existence and uniqueness of the solution for the corresponding variational equation. Numerical results based on the finite element method coupled with the standard Galerkin boundary element method, the fast multipole method and the Nyström method for approximating the DtN mapping are provided to illustrate the efficiency and accuracy of the numerical schemes.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1610-m2015-0480}, url = {http://global-sci.org/intro/article_detail/jcm/10582.html} }
TY - JOUR T1 - A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems AU - Yin , Tao AU - Rathsfeld , Andreas AU - Xu , Liwei JO - Journal of Computational Mathematics VL - 1 SP - 47 EP - 69 PY - 2018 DA - 2018/02 SN - 36 DO - http://doi.org/10.4208/jcm.1610-m2015-0480 UR - https://global-sci.org/intro/article_detail/jcm/10582.html KW - Fluid-solid interaction problem, Dirichlet-to-Neumann mapping, Finite element method, Fast multipole method, Nyström method. AB -

In this paper, we are concerned with the coupling of finite element methods and boundary integral equation methods solving the classical fluid-solid interaction problem in two dimensions. The original transmission problem is reduced to an equivalent nonlocal boundary value problem via introducing a Dirichlet-to-Neumann mapping by the direct boundary integral equation method. We show the existence and uniqueness of the solution for the corresponding variational equation. Numerical results based on the finite element method coupled with the standard Galerkin boundary element method, the fast multipole method and the Nyström method for approximating the DtN mapping are provided to illustrate the efficiency and accuracy of the numerical schemes.

Yin , TaoRathsfeld , Andreas and Xu , Liwei. (2018). A BIE-Based DtN-FEM for Fluid-Solid Interaction Problems. Journal of Computational Mathematics. 36 (1). 47-69. doi:10.4208/jcm.1610-m2015-0480
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