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A grid free Monte Carlo algorithm for solving elliptic boundary value problem
by
Todor Gurov
Brooklyn College - CUNY and Bulgarian Academy of Sciences
Coauthors: Ivan Dimov (Bulgarian Academy of Sciences), Paula Whitlock (Brooklyn College - CUNY)
In order to generate random variables with the desired distribution, rejection techniques on two levels are used. The estimate of the averaged number of moves for reaching the \epsilon-strip of the boundary of the domain for the new random process is obtained. It is shown that the algorithm efficiency and the Monte Carlo solution depend on the radius of the maximal sphere (ball) lying inside the domain in which the problem is defined and on the parameters (advection and deposition) of the operator under consideration.
Varied numerical tests on a Sun Ultra Enterprise 4000 with 14 UltraSPARC processors were performed. The code which implemented the new algorithm was written in JAVA.
The numerical results show that the derived theoretical estimates can be used to predict the behavior of a wide class of elliptic boundary value problems.
Date received: February 3, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caen-00.