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A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains

Chein-Shan Liu1
Department of Mechanical and Mechatronic Engineering, Department of Harbor and River Engineering, Taiwan Ocean University, Keelung, Taiwan. E-mail: csliu@mail.ntou.edu.tw.

Computer Modeling in Engineering & Sciences 2008, 35(2), 91-112. https://doi.org/10.3970/cmes.2008.035.091

Abstract

We consider the inverse Cauchy problems for Laplace equation in simply and doubly connected plane domains by recoverning the unknown boundary value on an inaccessible part of a noncircular contour from overspecified data. A modified Trefftz method is used directly to solve those problems with a simple collocation technique to determine unknown coefficients, which is named a modified collocation Trefftz method (MCTM). Because the condition number is small for the MCTM, we can apply it to numerically solve the inverse Cauchy problems without needing of an extra regularization, as that used in the solutions of direct problems for Laplace equation. So, the computational cost of MCTM is very saving. Numerical examples show the effectiveness of the new method in providing an excellent estimate of unknown boundary data, even by subjecting the given data to a large noise.

Keywords

Inverse Cauchy problem, Modified Trefftz method, Laplace equation, Modified collocation Trefftz method (MCTM).

Cite This Article

Liu, C. (2008). A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains. CMES-Computer Modeling in Engineering & Sciences, 35(2), 91–112.



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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