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\iteman{io-port 01129756}
\itemau{Chen, C.S.; Golberg, M.A.}
\itemti{Las Vegas method for diffusion equations.}
\itemso{Frankel, J. I. (ed.) et al., Boundary element technology XII. BETECH 97. 12th international conference, Knoxville, TN (USA), April 1997. Southampton: Computational Mechanics Publications. 299-308 (1997).}
\itemab
Summary: The Laplace transform is applied to remove the time-dependent variable in diffusion problems. In Laplace space we then applied Atkinson's formulae to find a particular solution of the modified Helmholtz's equation. The quasi-Monte Carlo integration which alleviates the difficulty of domain integration has been implemented for computing particular solutions of the modified Helmholtz's equation. With the method of fundamental solutions, we find the solution of the homogeneous equation. The solution in the Laplace space is then inverted numerically to yield a solution in time domain. A numerical example is given to illustrate the effectiveness of our approach in solving diffusion-type PDEs.
\itemrv{~}
\itemcc{}
\itemut{Laplace transform; Atkinson's formulae; modified Helmholtz's equation; quasi-Monte Carlo integration; method of fundamental solutions; homogeneous equation; time domain}
\itemli{}
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