The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation

Authors:
L. Marin;D. Lesnic
Affiliations:
-;-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2005

Citing 3
Cited 2

The method of fundamental solutions for the numerical solution of the biharmonic equation

Journal of Computational Physics
A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer

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Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion

Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion

A meshless method for solving an inverse spacewise-dependent heat source problem

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Convergence analysis for the Cauchy problem of Laplace's equation by a regularized method of fundamental solutions

Advances in Computational Mathematics

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Abstract

In this paper, the application of the method of fundamental solutions to inverse problems associated with the two-dimensional biharmonic equation is investigated. The resulting system of linear algebraic equations is ill-conditioned and, therefore, its solution is regularized by employing the 0^t^h-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed.