This article describes results of an effort to improve the parallel efficiency of a solver for turbulent reacting flows on two computer architectures. The compact finite-difference scheme employed for the solution of the differential equations involves the inversion of multiple tridiagonal matrices at each time step. Detailed performance evaluation of the standard LU, parallel partition LU, and parallel diagonal dominant algorithms are presented. The speed-up and efficiencies of these parallel strategies are critically compared and evaluated based on both computation and communication complexities, on the CRAY XT4 and IBM Blue Gene/P architectures.
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