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A Meshless Method for the Laplace and Biharmonic Equations Subjected to Noisy Boundary Data

B. Jin1,2
Center for Engineering and Scientific Computation, Zhejiang University, Hangzhou, Zhejiang, 310027, P.R. China.
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, P.R. China.

Computer Modeling in Engineering & Sciences 2004, 6(3), 253-262. https://doi.org/10.3970/cmes.2004.006.253

Abstract

In this paper, we propose a new numerical scheme for the solution of the Laplace and biharmonic equations subjected to noisy boundary data. The equations are discretized by the method of fundamental solutions. Since the resulting matrix equation is highly ill-conditioned, a regularized solution is obtained using the truncated singular value decomposition, with the regularization parameter given by the L-curve method. Numerical experiments show that the method is stable with respect to the noise in the data, highly accurate and computationally very efficient.

Keywords

The method of fundamental solutions, truncated singular value decomposition, L-curve method, Laplace equation, biharmonic equation.

Cite This Article

Jin, B. (2004). A Meshless Method for the Laplace and Biharmonic Equations Subjected to Noisy Boundary Data. CMES-Computer Modeling in Engineering & Sciences, 6(3), 253–262.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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