# A hybrid Laplace transform/finite difference boundary element method for diffusion problems

Davies, A.J., Crann, Diane, Kane, S.J. and Lai, Choi-Hong
(2007)
*A hybrid Laplace transform/finite difference boundary element method for diffusion problems.*
Computer Modelling in Engineering and Sciences, 18 (2).
pp. 79-86.
ISSN 1526-1492

## 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

Item Type: | Article |
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Uncontrolled Keywords: | boundary element method, finite difference method, diffusion problem |

Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science T Technology > TA Engineering (General). Civil engineering (General) |

Pre-2014 Departments: | School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering Group |

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Last Modified: | 14 Oct 2016 09:03 |

URI: | http://gala.gre.ac.uk/id/eprint/1145 |

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