A Parallel Laplace Transform Method For Diffusion Problems With Discontinuous Boundary Conditions
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A. J. Davies, D. Crann and J. Mushtaq
A parallel Laplace transform method for diffusion problems with discontinuous boundary conditions A. J. Davies, D. Crann and J. Mushtaq Department of Mathematics, University of Hertfordshire, UK. Abstract The Laplace transform method in the time variable provides an excellent alternative to the finite difference method for the solution of diffusion-type problems. Stehfest's numerical inversion process provides a stable and accurate method. The boundary-value problem in the transform space may be solved by a variety of methods and we shall use a finite difference approach leading to the usual five-point stencil for the Laplacian operator. The inversion via Stehfest's method may be effected for any value of the time variable and as such leads to a direct domain-decomposition in time. This inherent data-parallelism is well- suited to an implementation on an MIMD parallel environment. Such an implementation is of the SPMD type with the same program on each processor.