Direct methods for sparse matrices
Direct methods for sparse matrices
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The design of a new frontal code for solving sparse, unsymmetric systems
ACM Transactions on Mathematical Software (TOMS)
The design of MA48: a code for the direct solution of sparse unsymmetric linear systems of equations
ACM Transactions on Mathematical Software (TOMS)
A Load Balancing Method for a Parallel Application Based on a Domain Decomposition
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Reutilization of Partial LU Factorizations for Self-adaptive hp Finite Element Method Solver
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
A parallel direct solver for the self-adaptive hp Finite Element Method
Journal of Parallel and Distributed Computing
Journal of Computational Physics
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Many applications in science and engineering give rise to large sparse linear systems of equations that need to be solved as efficiently as possible. As the size of the problems of interest increases, it can become necessary to consider exploiting multiprocessors to solve these systems. We report on the design and development of parallel frontal solvers for the numerical solution of large sparse linear systems. Three codes have been developed for the mathematical software library HSL (www.cse.clrc.ac.uk/Activity/HSL). The first is for unsymmetric finite-element problems; the second is for symmetric positive definite finite-element problems; and the third is for highly unsymmetric linear systems such as those that arise in chemical process engineering. In each case, the problem is subdivided into a small number of loosely connected subproblems and a frontal method is then applied to each of the subproblems in parallel. We discuss how our software is designed to achieve the goals of portability, ease of use, efficiency, and flexibility, and illustrate the performance using problems arising from real applications.