Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
IEEE Transactions on Parallel and Distributed Systems
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
ACM Transactions on Mathematical Software (TOMS)
Parallel Computing - Parallel matrix algorithms and applications
Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Recent Progress in General Sparse Direct Solvers
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
An Experimental Comparison of some Direct Sparse Solver Packages
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Nested-Dissection Orderings for Sparse LU with Partial Pivoting
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
International Journal of Computational Fluid Dynamics - Mesoscopic Methods And Their Applications To CFD
Journal of Computational Physics
Applied Numerical Mathematics
A new version of the Improved Primal Simplex for degenerate linear programs
Computers and Operations Research
Scaling and pivoting in an out-of-core sparse direct solver
ACM Transactions on Mathematical Software (TOMS)
Reconstructing animated meshes from time-varying point clouds
SGP '08 Proceedings of the Symposium on Geometry Processing
Algorithm 907: KLU, A Direct Sparse Solver for Circuit Simulation Problems
ACM Transactions on Mathematical Software (TOMS)
Invited paper: Thermal modeling and analysis of 3D multi-processor chips
Integration, the VLSI Journal
A Numerical Scheme for a Viscous Shallow Water Model with Friction
Journal of Scientific Computing
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
A CPU-GPU hybrid approach for the unsymmetric multifrontal method
Parallel Computing
A shared- and distributed-memory parallel sparse direct solver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Technical section: Memory efficient light baking
Computers and Graphics
Asymptotic-preserving scheme for highly anisotropic non-linear diffusion equations
Journal of Computational Physics
Advances in Engineering Software
Parallel framework for topology optimization using the method of moving asymptotes
Structural and Multidisciplinary Optimization
Three-dimensional visco-acoustic modeling using a renormalized integral equation iterative solver
Journal of Computational Physics
Journal of Computational Physics
Advances in Engineering Software
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
Scientific Programming
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Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily on dense matrix kernels exists for matrices whose pattern is very unsymmetric. We address this deficiency and present a new unsymmetric-pattern multifrontal method based on dense matrix kernels. As in the classical multifrontal method, advantage is taken of repetitive structure in the matrix by factorizing more than one pivot in each frontal matrix, thus enabling the use of Level 2 and Level 3 BLAS. The performance is compared with the classical multifrontal method and other unsymmetric solvers on a CRAY C-98.