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(14)
Boundary Value Problem
Density Functional
Elliptic Boundary Value Problem
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Green's function Monte Carlo algorithms for elliptic problems
Green's function Monte Carlo algorithms for elliptic problems,10.1016/S03784754(03)000946,Mathematics and Computers in Simulation,Ivan Todor Dimov,R
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Green's function Monte Carlo algorithms for elliptic problems
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Citations: 1
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Ivan Todor Dimov
,
R. Y. Papancheva
In many largescale problems, one is interested to obtain directly an approximate value of a functional of the solution. Here, we consider a special class of gridfree
Monte Carlo
algorithms for direct computing of
linear functionals
of the solution of an elliptic boundaryvalue problem. Such kind of problems appear in environmental sciences, computational physics and financial mathematics. To create the algorithms, we use the Green's function analysis and define the conditions under which the integral transformation kernel of the
integral representation
for the boundaryvalue problem under consideration is nonnegative. This analysis is done for a possible set of densities, and it is used to generate three different gridfree
Monte Carlo
algorithms based on different choices of the density of the radius of the balls used in
Monte Carlo
simulation. Only one of the generated algorithms was known before. We shall call it Sipin's algorithm. It was proposed and studied by Sipin. The aim of this work is to study the two new algorithms proposed here and based on two other (than in Sipin's algorithm) possible choices of the densities. The algorithms are described and analyzed. The performed numerical tests show that the efficiency of one of the new algorithms, which is based on a constant density is higher than the efficiency of Sipin's algorithm. © 2003 IMACS. Published by Elsevier B.V. All rights reserved.
Journal:
Mathematics and Computers in Simulation
, vol. 63, no. 6, pp. 587604, 2003
DOI:
10.1016/S03784754(03)000946
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Citation Context
(1)
...It is proved in [
4
] that p(x;y) 0, when the following...
...using an acceptancerejection (AR) technique [
4
, 10]...
R. J. Papancheva
,
et al.
Monte Carlo study of particle transport problem in air pollution
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,
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,
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Journal:
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, vol. 9, no. 12, pp. 3965, 1996
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(
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Published in 1995.
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(
Citations: 227
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C. Miranda
Published in 1970.
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Citations
(1)
Monte Carlo study of particle transport problem in air pollution
(
Citations: 1
)
R. J. Papancheva
,
T. V. Gurov
,
I. T. Dimov