Parallel finite elements and Laplace transforms for reactive transport in sorbing porous media

The integro-differential equation controlling transport and non-ideal sorption of a reactive contaminant in a porous mediim can be first Laplace transformed to eliminate time, then solved in the Laplace space by finite elements and finally recovered back to the time domain by a numerical inversion procedure. This approach appears to be particularly attractive on parallel supercomputers where the Laplace transformed equation can be solved concurrently on several processors for different values of the Laplace parameter and back transformed again independently for the desired times of the desired nodes of the spatial finite element grid. The performance of this method is tested on two supercomputers, the CRAY T3D and the IBM SP2, using sample problems of increasing size N=15275. The results show that the algorithm is higly parallelizable, especially on the CRAY T3D, with the largest parallel efficiency achieved for larger problem sets.