Deployment of Parallel Direct Sparse Linear Solvers WITHIN a Parallel Finite Element Code

A.N.F. Klimowicz, M.D. Mihajlović, and M. Heil (UK)


finite element method, parallel sparse direct linear solvers, convection-diffusion equation.


In this paper we present and evaluate the performance of two different strategies for the deployment of parallel mul tifrontal and multiple frontal sparse linear solvers in the context of a parallel finite element code. Direct sparse lin ear solvers are based on sophisticated reorganisation of the standard Gaussian elimination algorithm with the aim of exploring matrix sparsity and reducing the amount of fill in. Such codes can be successfully applied to very large linear systems, and are especially effective when a sparse linear system needs to be solved for multiple right-hand sides. Unfortunately, many important applications, such as finite element solutions of non-linear, transient problems, require repeated factorisation of the coefficient matrix. In such cases the only way of achieving good performance is parallelisation of both the computation of the finite element matrices and the linear system solution phase. We have developed two different designs for deployment of paral lel multifrontal and multiple frontal sparse linear solvers in this context, each deploying three different strategies for the assembly of the global data. These designs are suitable for parallel and heterogeneous architectures. Experiments confirm high efficiency, low communication cost, and re duced initial memory requirements of our deployment de signs, compared to a standard deployment strategy.

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