Implementing iterative solvers for irregular sparse matrix problems in high performance Fortran
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.
KeywordsHigh Performance Fortran Irregular Sparse Matrices Iterative Solvers
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- 1.S. T. Barnard and H. D. Simon. A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Technical Report RNR92-033, NASA Ames Research Center, Mail Stop T045-1, Moffet Field, CA 94035, USA, 1992.Google Scholar
- 2.E. De Sturler. Iterative Methods on, Distributed Memory Computers. PhD thesis, Delft University of Technology, Delft, The Netherlands, October 1994.Google Scholar
- 4.E. De Sturler and H. A. Van der Vorst. Communication cost reduction for Krylov methods on parallel computers. In W. Gentzsch and U. Harms, editors, HighPerformance Computing and Networking, Lecture Notes in Computer Science 797, pages 190–195, Berlin, Heidelberg, Germany, 1994. Springer-Verlag.Google Scholar
- 6.F. Nataf, F. Rogier, and E. De Sturler. Domain decomposition methods for fluid dynamics. In A. Sequeira, editor, Navier-Stokes Equations and Related Nonlinear Problems, New York, 1995. Plenum Press.Google Scholar
- 7.High Performance Fortran Forum. High Performance Fortran Language Specification, version 2.0 Rice University, 1997Google Scholar