A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Parallel algorithms for forward and back substitution in direct solution of sparse linear systems
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Introduction to Algorithms
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
An Accurate and Efficient Frontal Solver for Fully-Coupled Hygro-Thermo-Mechanical Problems
ICCS '02 Proceedings of the International Conference on Computational Science-Part I
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
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We present a static parallel implementation of the multifrontal method to solve unsymmetric sparse linear systems on distributed-memory architectures. We target Finite Element (FE) applications where numerical pivoting can be avoided, since an implicit minimum-degree ordering based on the FE mesh topology suffices to achieve numerical stability. Our strategy is static in the sense that work distribution and communication patterns are determined in a preprocessing phase preceding the actual numerical computation. To balance the load among the processors, we devise a simple model-driven partitioning strategy to precompute a high-quality balancing for a large family of structured meshes. The resulting approach is proved to be considerably more efficient than the strategies implemented by MUMPS and SuperLU_DIST, two state-of-the-art parallel multifrontal solvers.