Parallel Laplace transform boundary element methods for diffusion problems

The Laplace transform method in time has been used, together with the boundary element method, by a number of authors for the solution of diffusion problems. The major problem associated with the use of the Laplace transform is the development of a numerical inversion. There is a variety of numerical techniques available and the most attractive are those based on real arithmetic. One technique, Stehfest's method, based on a statistically calculated sample, has been the numerical inversion process chosen by all authors so far. The procedure has been successfully implemented on a distributed memory architecture. An alternative technique, based on shifted Legendre polynomials, has been used together with the finite element method for the solution of the wave equation and is a possible alternative to Stehfest's method. The method is also suitable for solution in a distributed memory environment. The two methods are compared using the 'Single Program Multiple Data' paradigm on a sixty-four processor nCUBE machine arranged in a hypercube configuration.