Applications of Mathematics, Vol. 62, No. 4, pp. 297-317, 2017


Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition

Koya Sakakibara

Received January 30, 2017.  First published July 20, 2017.

Abstract:  The aim of this paper is to analyze mathematically the method of fundamental solutions applied to the biharmonic problem. The key idea is to use Almansi-type decomposition of biharmonic functions, which enables us to represent the biharmonic function in terms of two harmonic functions. Based on this decomposition, we prove that an approximate solution exists uniquely and that the approximation error decays exponentially with respect to the number of the singular points. We finally present results of numerical experiments, which verify the sharpness of our error estimate.
Keywords:  method of fundamental solutions; biharmonic equation; Almansi-type decomposition
Classification MSC:  65N80, 31A30, 49M27
DOI:  10.21136/AM.2017.0018-17


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Affiliations:   Koya Sakakibara, Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan, e-mail: ksakaki@ms.u-tokyo.ac.jp

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