Statistic modeling and Monte Carlo methods
We develop a new random walk method which is based on the following idea. The domain is approximated with a finite system of spheres and ellipsoids with a pair-wise overlapng property. In each sphere and ellipsoid the integral representation of the solution is used. For instance, in the case of Laplace equation the Poisson formula is used. This results in a system of integral equations which generally cannot be solved by the standard random walk on spheres method. For example, a system of Lame equations is such a case which is of our special interest. Thus we deal with a problem of construction of an effective iterative method for solving the above mentioned system of integral equations. For solving this problem we use a linear algebraic equation approximation. Then we extract spectral properties of this system numerically which allows us to construct the random walk algorithm.
Note. Abstracts are published in author's edition
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