PARALLEL FINITE ELEMENT LAPLACE TRANSFORM METHOD FOR THE NON-EQUILIBRIUM GROUNDWATER TRANSPORT EQUATION

Groundwater transport of contaminants undergoing rate-limited or non-equilibrium sorption onto the solid matrix is often described by the dual-porosity or two-domain model, whereby the rate-limited reaction occurs between a mobile and an immobile region. When the sorption reaction is represented by a rst- order kinetic relationship, the equation takes the form of a convection{dispersion partial di erential equation with an integral term describing the mass transfer between the two regions. An e cient solution algo- rithm for this type of problems consists in the transformation of the original equation into the Laplace space and subsequent numerical solution of the resulting steady-state equation in the complex space. The exploitation of the Laplace transform to solve the time dependency restricts the application of the tech- nique to linear advection and dispersion terms, while non-linear reactions can be accommodated in partic- ular cases only. This approach has the advantage that it is easily parallelizable, and is therefore proposed in this paper as an e cient algorithm for the parallelization in time of these types of integrodi erential equations. The parallel e ciency of PFELT has been tested on a Cray T3D parallel computer for three sample problems of size N =1071, 3721, and 15 275, respectively, where N is the number of nodal mesh points. The speed-ups obtained vary from 1 98, with two processors, to 39 93 with 64 processors, for the most favorable case. This corresponds to a percentage of parallel work greater than 98 per cent, and a parallel e ciency of more than 60 per cent in the best case, showing the good performance achievable with this algorithm.