Impacto de estratégias combinatórias no precondicionador paralelo baseado no algoritmo híbrido SPIKE

Abstract

In this work, we use the parallel hybrid SPIKE algorithm as a preconditioner for a nonstationary iterative method combining distributed and shared memory architectures, MPI and OpenMP. In order to obtain a good preconditioner we apply a set of strategies modeled as combinatorial problems such as matching, reorderings to reduce matrix bandwidth, graph partitioning and the quadratic knapsack problem that perform permutations in the rows and columns of the matrix. Computational experiments demonstrate the efficiency of the parallel preconditioner and a great influence of each presented combinatorial strategies. In addition, the results show excellent scalability for up to 64 cores in finite element applications.