Isogeometric Analysis of the Dual Boundary Element Method for the Laplace Problem With a Degenerate Boundary

In this paper, we develop the isogeometric analysis of the dual boundary element method (IGA-DBEM) to solve the potential problem with a degenerate boundary. The non-uniform rational B-Spline (NURBS) based functions are employed to interpolate the geometry and physical function. To deal with the ran...

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Bibliographic Details
Published in:Journal of mechanics 2020-02, Vol.36 (1), p.35-46
Main Authors: Kao, J. H., Chen, K. H., Chen, J. T., Kuo, S. R.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary element method
Dirichlet problem
Exact solutions
Integral equations
Mathematical analysis
Nonlinear programming
Seepage
Sheet piles
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Summary:In this paper, we develop the isogeometric analysis of the dual boundary element method (IGA-DBEM) to solve the potential problem with a degenerate boundary. The non-uniform rational B-Spline (NURBS) based functions are employed to interpolate the geometry and physical function. To deal with the rank-deficiency problem due to the degenerate boundary, the hypersingular integral equation is introduced to promote the full rank for the influence matrix in the dual BEM. Finally, three numerical examples are given to verify the accuracy of our proposed method. Both circular and square domains subjected to the Dirichlet boundary condition are considered. The engineering problem containing a degenerate boundary is considered, e.g., a seepage flow problem with a sheet pile. Numerical results of the IGA-DBEM agree well with these of the exact solution and the original dual boundary element method.
ISSN:1727-7191
1811-8216
DOI:10.1017/jmech.2019.18