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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2007, Volume 10, Number 2, Pages 209–220
(Mi sjvm78)
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This article is cited in 3 scientific papers (total in 3 papers)
Random walk-on-spheres algorithms for solving mixed and Neumann boundary-value problems
N. A. Simonov Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
Abstract:
We propose a new approach to constructing Monte Carlo methods for solving mixed boundary value problems for elliptic equations with constant coefficients. We derived a mean-value relation for point values of the solution. As a consequence, the walk-on-spheres algorithm can still be used even after a trajectory hits the reflecting boundary. Such an approach is significantly more efficient than the standard one.
Key words:
Monte Carlo, random walk, walk-on-spheres, mixed boundary-value problem, Poisson equation, mean value theorem.
Received: 06.12.2005 Revised: 28.04.2006
Citation:
N. A. Simonov, “Random walk-on-spheres algorithms for solving mixed and Neumann boundary-value problems”, Sib. Zh. Vychisl. Mat., 10:2 (2007), 209–220
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https://www.mathnet.ru/eng/sjvm78 https://www.mathnet.ru/eng/sjvm/v10/i2/p209
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Abstract page: | 765 | Full-text PDF : | 419 | References: | 61 |
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