Stochastic simulation algorithm for solving the system of Lame equations for twoand three-dimensional domains by combining the Slobodianskii representation, the method of fundamental solutions and a random projection method
K.K. Sabelfeld, D.D. Smirnov
Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
Keywords: Lame equation, Slobodianskii representation, stochastic projection method, the method of fundamental solutions
Abstract
In this paper, a new stochastic algorithm for solving the system of Lame equations based on the Slobodianskii representation is proposed, in which the recovery of boundary conditions for the harmonic functions involved is carried out implicitly using the method of fundamental solutions, while the unknown coefficients in this method are calculated using a stochastic projection method. Results of numerical experiments for several examples of two- and three-dimensional boundary value problems are presented, which demonstrate the high efficiency of the proposed method.
|
