HPF-2 Support for Dynamic Sparse Computations

This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science. The final authenticated version is available online at: https://doi.org/10.1007/3-540-48319-5_15[Abstract] There is a class of sparse matrix computations, such as direct solvers of systems of linear equations, that change the fill-in (nonzero entries) of the coefficient matrix, and involve row and column operations (pivoting). This paper addresses the problem of the parallelization of these sparse computations from the point of view of the parallel language and the compiler. Dynamic data structures for sparse matrix storage are analyzed, permitting to efficiently deal with fill-in and pivoting issues. Any of the data representations considered enforces the handling of indirections for data accesses, pointer referencing and dynamic data creation. All of these elements go beyond current data-parallel compilation technology. We propose a small set of new extensions to HPF-2 to parallelize these codes, supporting part of the new capabilities on a runtime library. This approach has been evaluated on a Cray T3E, implementing, in particular, the sparse LU factorization.Ministerio de Educación y Ciencia; TIC96-1125-C03Xunta de Galicia; XUGA20605B96European Commision; BRITE-EURAM III BE95-1564European Commision; ERB4050P192166

Sparse LU Factorization on The Cray T3D

. The paper describes a parallel algorithm for the LU factorization of sparse matrices on distributed memory machines by using SPMD as programming model and PVM as message passing interface. We address all the difficulties arising in sparse codes, as the fill-in or the dynamic movement of data inside the matrix. The cyclic distribution has been used to evenly distribute the elements onto a mesh of processors, whereas two local storage schemes are proposed: A semi-ordered and two-dimensional linked list, which fulfils better the requirements of the algorithm, and a compressed storage by rows, which behaves better in the use of memory. The properties of the code are extensively analyzed and execution times on the CRAY T3D are presented to illustrate the overall efficiency achieved by our methods. 1 Introduction The solution of linear systems Ax = b, where the coefficient matrix A has a sparse sort and huge dimensions, plays a basic role in many fields of the science, engineering and eco..