Comparison of some parallel krylov solvers for large scale ground-water contaminant transport simulations

摘要

SOme popular iterative solvers for non-symmetric systems arising from the finite-element discretization of three-dimensional groundwater contaminant transport problem are implemented and compared on distributed memory parallel platforms. This paper attempts to determine which solvers are most suitable for the contaminant transport problem under varied conditions for large scale simulations on distributed parallel platforms. The original parallel implementation was targeted for the 1024 node Intel Paragon platform using explicit message pasing with the NX library. Thids code was then proted to SGI Power Challenge Array, Convex Exemplar, and Origin 2000 machines using an MPI implementation. The performance of these solvers is studied for increasing problem size, roughness of the coefficients, and selected problem scenarios. These conditions affect the properties of the matrix and hence the difficulty level of the solution process. Performance is analyzed in terms of convergence behavior, overall time, parallel efficiency, and scalability. The solvers that are presented ar BiCGSTAB, GMRES, ORTHOMIN, and CGS. A simple diagonal preconditioner is used in this parallel implementation for all the metods. Our results indicate that all methods are comparable in performance with BiCGSTAB slightly outperforming the other methods for most problems. We achieved very good scalability in all the methods up to 1024 processors of the Intel Paragon XPS/150. We demonstrate scalability by solving 100 time steps of a 40 million element problem in about 5 minutes using either BiCGSTAB or GMRES.