Open Access

ARTICLE

A Hybrid Laplace Transform/Finite Difference Boundary Element Method for Diffusion Problems

A. J. Davies¹, D. Crann¹, S. J. Kane¹, C-H. Lai²

1 School of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, Herts. AL10 9AB, U.K.
2 School of Computing and Mathematical Sciences, University of Greenwich, London SE10 9LS, U.K.

Computer Modeling in Engineering & Sciences 2007, 18(2), 79-86. https://doi.org/10.3970/cmes.2007.018.079

Abstract

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution.

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