Functional Random Walk on Spheres algorithm for biharmonic equation: optimization and error estimation
Karl K. Sabelfeld, E. V. Shkarupa · Monte Carlo Methods and Applications · 2003
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.