General Sparse Solver Research Articles

A Shared- and distributed-memory parallel general sparse direct solver

An important recent development in the area of solution of general sparse systems of linear equations has been the introduction of new algorithms that allow complete decoupling of symbolic and numerical phases of sparse Gaussian elimination with partial pivoting. This enables efficient solution of a series of sparse systems with the same nonzero pattern but different coefficient values, which is a fairly common situation in practical applications. This paper reports on a shared- and distributed-memory parallel general sparse solver based on these new symbolic and unsymmetric-pattern multifrontal algorithms.

Impact of the implementation of MPI point-to-point communications on the performance of two general sparse solvers

We examine the send and receive mechanisms of MPI and show how to implement message passing robustly so that performance is not significantly affected by changes to the MPI system. We discuss this within the context of two different parallel algorithms for sparse Gaussian elimination: a multifrontal solver ( MUMPS), and a supernodal one ( SuperLU). The performance of our initial strategies based on simple MPI point-to-point communication primitives is very sensitive to the MPI system, particularly the way MPI buffers are used. Using nonblocking communication primitives improves the performance and robustness, but at the cost of increased code complexity.

Analysis and comparison of two general sparse solvers for distributed memory computers

This paper provides a comprehensive study and comparison of two state-of-the-art direct solvers for large sparse sets of linear equations on large-scale distributed-memory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called superLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512-processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers.

The impact of an efficient linear solver on finite element analyses

Finite-element programs are commonly integrated with advanced software systems for computer-aided analysis and design. In this setting, we often see models for which the finite-element program is the bottleneck with respect to computer time and storage. In this paper, we show how this can be alleviated by integrating a general sparse solver into the finite-element program and demonstrate the effect with examples of analyses of ship and offshore structures.