A set of level 3 basic linear algebra subprograms
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 Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Stabilized bordered block diagonal forms for parallel sparse solvers
Parallel Computing
Stabilized bordered block diagonal forms for parallel sparse solvers
Parallel Computing
Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization
SIAM Journal on Scientific Computing
Parallel distributed-memory simplex for large-scale stochastic LP problems
Computational Optimization and Applications
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The need to solve large sparse linear systems of equations efficiently lies at the heart of many applications in computational science and engineering. For very large systems when using direct factorization methods of solution, it can be beneficial and sometimes necessary to use multiple processors, because of increased memory availability as well as reduced factorization time. We report on the development of a new parallel code that is designed to solve linear systems with a highly unsymmetric sparsity structure using a modest number of processors (typically up to about 16). The problem is first subdivided into a number of loosely connected subproblems and a variant of sparse Gaussian elimination is then applied to each of the subproblems in parallel. An interface problem in the variables on the boundaries of the subproblems must also be factorized. We discuss how our software is designed to achieve the goals of portability, ease of use, efficiency, and flexibility, and illustrate its performance on an SGI Origin 2000, a Cray T3E, and a 2-processor Compaq DS20, using problems arising from real applications.