On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations

In this paper, it is proved that the two approaches, known in the literature as the method of fundamental solutions (MFS) and the Trefftz method, are mathematically equivalent in spite of their essentially minor and apparent differences in formulation. In deriving the equivalence of the Trefftz meth...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2007-03, Vol.53 (6), p.851-879
Main Authors: Chen, J.T., Wu, C.S., Lee, Y.T., Chen, K.H.
Format: Article
Language:English
Subjects:
Accuracy
Biharmonic equations
Circulant
Condition number
Degenerate scale
Equivalence
Kernels
Mathematical analysis
Mathematical models
Method of fundamental solutions
Trefftz method
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Summary:In this paper, it is proved that the two approaches, known in the literature as the method of fundamental solutions (MFS) and the Trefftz method, are mathematically equivalent in spite of their essentially minor and apparent differences in formulation. In deriving the equivalence of the Trefftz method and the MFS for the Laplace and biharmonic problems, it is interesting to find that the complete set in the Trefftz method for the Laplace and biharmonic problems are embedded in the degenerate kernels of the MFS. The degenerate scale appears using the MFS when the geometrical matrix is singular. The occurring mechanism of the degenerate scale in the MFS is also studied by using circulant. The comparison of accuracy and efficiency of the two methods was addressed.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2005.02.021