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The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations

✍ Scribed by C. S. Chen; M. A. Golberg; Y. C. Hon

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 131 KB
Volume: 43
Category: Article
ISSN: 0029-5981
DOI: 10.1002/(sici)1097-0207(19981230)43:8<1421::aid-nme476>3.0.co;2-v

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✦ Synopsis

The Laplace transform is applied to remove the time-dependent variable in the di usion equation. For nonharmonic initial conditions this gives rise to a non-homogeneous modiÿed Helmholtz equation which we solve by the method of fundamental solutions. To do this a particular solution must be obtained which we ÿnd through a method suggested by Atkinson. 17 To avoid costly Gaussian quadratures, we approximate the particular solution using quasi-Monte-Carlo integration which has the advantage of ignoring the singularity in the integrand. The approximate transformed solution is then inverted numerically using Stehfest's algorithm. 13 Two numerical examples are given to illustrate the simplicity and e ectiveness of our approach to solving di usion equations in 2-D and 3-D. ? 1998 John

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