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Intel® Math Kernel Library Parallel Direct Sparse Solver for Clusters
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, EAGE Workshop on High Performance Computing for Upstream, Sep 2014, cp-426-00023
- ISBN: 978-94-6282-025-8
Abstract
Many of Oil and Gas modelling and simulation applications are using the solution of systems of linear algebraic equations underneath. The systems arise from approximations of a filtration problem in oil-source bed, thermo-chronological modelling of accretionary-collisional processes, etc. The solution of linear systems in such applications is usually the most time-consuming part of computations, so the solver requires a highly efficient implementation. The paper describes a direct method for solving the equation Ax=b with a sparse matrix A. The main idea of this method is to do a decomposition of the matrix A into a product of a lower-triangular, diagonal, and upper triangular matrices followed by solving resulted 3 subsystems computed. To achieve an efficient work balance on a large number of MPI processes on a cluster we propose an approach further referred to as "multifrontal" approach. This paper expands the previous results obtained by the authors. The proposed algorithm of tree balancing and symmetric multiprocessing (SMP) parallelization on each MPI process allows us to achieve better overall performance compared to the available open source software packages. The performance charts are presented in the Numerical Experiments section.