Vector and parallel methods for the direct solution of Poisson's equation

摘要

Recent developments in the area of fast direct Poisson solvers are examined in the context of parallel computing. The growing gap that exists between peak and actual performance of contemporary architectures is attributed to internal communication requirements that do not contribute to performance as measured in m flops. For this reason, we focus on algorithms for parallel communication as well as parallel computation. Parallel algorithms for transposition, binary-reflected orderings, and index permutations in support of parallel methods for fast direct solvers are discussed. Both fine and medium grain computations are considered for: the “complete” Fourier method, partial matrix decomposition, parallel cyclic reduction with partial fraction expansion, and parallel approximate cyclic reduction.