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Karl Sabelfeld, Elena Shkarupa

Functional Random Walk on Spheres algorithm for biharmonic equation: optimization and error estimation

Keywords: Random Walk on Spheres algorithm, global estimators, biharmonic equation, optimization and error estimation, multilinear interpolation

The global algorithm of Random Walk on Spheres suggested in [Sabelfeld K.K. Monte Carlo methods in boundary problems. Springer-Verlag, Heidelberg - Berlin - New York, 1991.] is analyzed and a kind of optimization strategy is suggested. The algorithm is applied here to construct a functional version of this method which uses a multilinear interpolation. As an example we have chosen the biharmonic equation governing the bending of a thin elastic plate with the simply supported boundary, however generalizations to other equations can be carried out.

Monte Carlo Methods and Applications, Walter de Gruyter

Print ISSN: 0929-9629
Volume: 9, 01/2003
Pages: 51 - 65

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