Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Statistic modeling and Monte Carlo methods

"Walk by Spheres and Balls" Estimation of the Gradient of a Solution to the Stationary Diffusion Equation in the Multidimensional Case

Burmistrov A.V.

ICM&MG SB RAS (Novosibirsk)

For the isotropic k-dimensional diffusion we consider the representation of the weighted trajectory concentration as well as its spatial derivatives in the form of combined integral equations (with some weights) of the solution to the corresponding boundary-value problem and its directional derivative along the convective velocity. This representation under some conditions (the most significant of which is the degeneracy of a convective velocity nearby the domain boundary) enables us to construct effective "walk by spheres and balls" algorithm for simultaneous estimation both the solution to the boundary-value problem and its spatial derivatives.

Note. Abstracts are published in author's edition

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