Efficient Parallelization of the Preconditioned Conjugate Gradient Method

In this paper we present methods for efficient parallelization of the solution of pressure Poisson equation arising in 3D CFD forest fire modeling. The solution procedure employs the Conjugate Gradient method with implicit Modified ILU (MILU) preconditioner. The basic idea for parallelizing recursive incomplete-decomposition algorithms is to use a direct nested twisted approach in combination with a staircase method. Parallelization of MILU-CG solver is implemented in OpenMP environment for Non-uniform memory (NuMA) computer systems. Performance results of the parallelized algorithm are presented and analyzed for different number of processors (up to 16).

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