Mixed Mode Programming for Sparse Linear Algebra

Sparse linear algebra algorithms, and especially algorithms for the iterative solution of sparse lineary systems, lie at the heart of many scientific computing applications, ranging from computational fluid dynamics to structural engineering and electromagnetic analysis. Their efficient implementation is thus a very important challenge for the numerical software community. The current trend in high performance computing architectures is to move towards clusters of shared memory multiprocessor machines; the advances in the hardware and system performance however have yet to be matched by corresponding advances in programming paradigms. In this paper we report on our experiments in implementing a hybrid programming model for sparse linear algebra computations. We have taken an existing library interface based on MPI [3] and reimplemented its kernels by using OpenMP parallelization for intra-node computations. We comment on the major points related to the parallelization of the various algorithms, and on the viability of the various operating environments, with respect to the computing, communication and compilation systems. Our aim in this work is to provide an interface for the convenient implementation of iterative methods for sparse linear systems on clusters of shared memory computers; such computing platforms include most currently available supercomputers such as the IBM SP machines, as well as networks of commodity workstations based on the Intel processor architecture. The field of sparse linear algebra has seen recently the emergence of a new standard proposed by Duff et al [1], which is a substantial update of the previous effort documented in [2]; our library is based on the same internals, and we are currently working at making the user-level interface compatible with the new standard.