Direct methods for sparse matrices
Direct methods for sparse matrices
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
A mapping algorithm for parallel sparse Cholesky factorization
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Node Selection Strategies for Bottom-Up Sparse Matrix Ordering
SIAM Journal on Matrix Analysis and Applications
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Performance of Greedy Ordering Heuristics for Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
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
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Parallel Computing - Parallel matrix algorithms and applications
Sparse Matrix Ordering with SCOTCH
HPCN Europe '97 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
LAPACK Working Note 95: ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers -- Design Issues and Performance
Task Scheduling in an Asynchronous Distributed Memory Multifrontal Solver
SIAM Journal on Matrix Analysis and Applications
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Partitioning and blocking issues for a parallel incomplete factorization
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Applying parallel direct solver techniques to build robust high performance preconditioners
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
A parallel solution of large-scale heat equation based on distributed memory hierarchy system
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
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We consider the direct solution of general sparse linear systems baseds on a multifrontal method. The approach combines partial static scheduling of the task dependency graph during the symbolic factorization and distributed dynamic scheduling during the numerical factorization to balance the work among the processes of a distributed memory computer. We show that to address clusters of Symmetric Multi-Processor (SMP) architectures, and more generally non-uniform memory access multiprocessors, our algorithms for both the static and the dynamic scheduling need to be revisited to take account of the non-uniform cost of communication. The performance analysis on an IBM SP3 with 16 processors per SMP node and up to 128 processors shows that we can significantly reduce both the amount of inter-node communication and the solution time.