A New Class of Grid-Free Monte Carlo Algorithms for Elliptic Boundary Value Problems

Authors:
R. J. Papancheva;Ivan Dimov;T. V. Gurov
Affiliations:
-;-;-
Venue:
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Year:
2002

Citing 1
Cited 1

A Grid Free Monte Carlo Algorithm for Solving Elliptic Boundary Value Problems

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications

Parallel realization of grid-free monte carlo algorithm for boundary value problems

LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing

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Abstract

In this paper we consider the following mathematical model: an elliptic boundary value problem, where the partial differential equation contains advection, diffusion, and deposition parts. A Monte Carlo (MC) method to solve this equation uses a local integral representation by the Green's function and a random process called "Walks on Balls"(WOB). A new class of grid free MC algorithms for solving the above elliptic boundary value problem is suggested and studied. We prove that the integral transformation kernel can be taken as a transition density function in the Markov chain in the case when the deposition part is equal to zero. An acceptance-rejection (AR) and an inversetransformation methods are used to sample the next point in the Markov chain. An estimate for the efficiency of the AR method is obtained.