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

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Sabelfeld Karl & Shkarupa Elena, 2003. "Functional Random Walk on Spheres algorithm for biharmonic equation: optimization and error estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 9(1), pages 51-65, January.
    • Handle: RePEc:bpj:mcmeap:v:9:y:2003:i:1:p:51-65:n:5
    DOI: 10.1515/156939603322587461
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