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

Sabelfeld Karl and Shkarupa Elena
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Sabelfeld Karl: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D - 10117 Berlin, Germany.
Shkarupa Elena: Institute of Comput. Math. and Mathem. Geophysics, Lavrentiev str., 6, 630090 Novosibirsk, Russia.

Monte Carlo Methods and Applications, 2003, vol. 9, issue 1, 51-65

Abstract: 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.

Keywords: Random Walk on Spheres algorithm; global estimators; biharmonic equation; optimization and error estimation; multilinear interpolation (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1515/156939603322587461

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