Geodesic
Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition
Applications of Mathematics, Tome 62 (2017) no. 4, pp. 297-317 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2017.0018-17
Classification : 31A30, 49M27, 65N80
Keywords: method of fundamental solutions; biharmonic equation; Almansi-type decomposition 
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     title = {Method of fundamental solutions for biharmonic equation based on {Almansi-type} decomposition},
     journal = {Applications of Mathematics},
     pages = {297--317},
     year = {2017},
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Sakakibara, Koya. Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition. Applications of Mathematics, Tome 62 (2017) no. 4, pp. 297-317. doi: 10.21136/AM.2017.0018-17

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