Implementing iterative solvers for irregular sparse matrix problems in high performance Fortran

Abstract

Writing efficient iterative solvers for irregular, sparse matrices in HPF is hard. The locality in the computations is unclear, and for efficiency we use storage schemes that obscure any structure in the matrix. Moreover, the limited capabilities of HPF to distribute and align data structures make it hard to implement the desired distributions, or to indicate these such that the compiler recognizes the efficient implementation.

We propose techniques to handle these problems. We combine strategies that have become popular in message-passing parallel programming, like mesh partitioning and splitting the matrix in local submatrices, with the functionality of HPF and HPF compilers, like the implicit handling of communication and distribution. The implementation of these techniques in HPF is not trivial, and we describe in detail how we propose to solve the problems. Our results demonstrate that efficient implementations are possible. We indicate how some of the ‘approved extensions’ of HPF-2.0 can be used, but they do not solve all problems. For comparison we show results for regular, sparse matrices.