Analysis and comparison of two general sparse solvers for distributed memory computers
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)
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Parallel Computing - Parallel matrix algorithms and applications
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
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
MUMPS: A General Purpose Distributed Memory Sparse Solver
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
Domain Decomposition Solvers for Large Scale Industrial Finite Element Problems
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SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Impact of reordering on the memory of a multifrontal solver
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
Adapting a parallel sparse direct solver to architectures with clusters of SMPs
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
A parallel direct solver for large sparse highly unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Parallel and fully recursive multifrontal sparse Cholesky
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Adaptive grid refinement for a model of two confined and interacting atoms
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Parallel sparse LU factorization on second-class message passing platforms
Proceedings of the 19th annual international conference on Supercomputing
Constructing memory-minimizing schedules for multifrontal methods
ACM Transactions on Mathematical Software (TOMS)
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
An out-of-core sparse symmetric-indefinite factorization method
ACM Transactions on Mathematical Software (TOMS)
Deployment of parallel direct sparse linear solvers within a parallel finite element code
PDCN'06 Proceedings of the 24th IASTED international conference on Parallel and distributed computing and networks
Parallel sparse LU factorization on different message passing platforms
Journal of Parallel and Distributed Computing
SIPs: Shift-and-invert parallel spectral transformations
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Experiences of sparse direct symmetric solvers
ACM Transactions on Mathematical Software (TOMS)
Performance Optimization and Modeling of Blocked Sparse Kernels
International Journal of High Performance Computing Applications
Shape determination for deformed electromagnetic cavities
Journal of Computational Physics
Scaling performance of interior-point method on large-scale chip multiprocessor system
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Parallel scalability study of hybrid preconditioners in three dimensions
Parallel Computing
ACM Transactions on Mathematical Software (TOMS)
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Algorithmic performance studies on graphics processing units
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Analysis and Comparison of Reordering for Two Factorization Methods (LU and WZ) for Sparse Matrices
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Some preconditioning techniques for linear systems
WSEAS Transactions on Mathematics
C++ Bindings to External Software Libraries with Examples from BLAS, LAPACK, UMFPACK, and MUMPS
ACM Transactions on Mathematical Software (TOMS)
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Journal of Computational Physics
Adaptive grid refinement for a model of two confined and interacting atoms
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Parallelising a simulator for the analysis of electromagnetic radiation using MUMPS library
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
A parallel direct solver for the self-adaptive hp Finite Element Method
Journal of Parallel and Distributed Computing
Analysis of the solution phase of a parallel multifrontal approach
Parallel Computing
Towards a transparent data access model for the GridRPC paradigm
HiPC'07 Proceedings of the 14th international conference on High performance computing
Finite Elements in Analysis and Design
Sparse non-linear least squares optimization for geometric vision
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
An hybrid approach for the parallelization of a block iterative algorithm
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
A domain-decomposing parallel sparse linear system solver
Journal of Computational and Applied Mathematics
Scalable stochastic optimization of complex energy systems
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation
Journal of Computational Physics
Journal of Computational Physics
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
Design of a Multicore Sparse Cholesky Factorization Using DAGs
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Domain-Decomposition-Type Methods for Computing the Diagonal of a Matrix Inverse
SIAM Journal on Scientific Computing
Towards high performance discrete-event simulations of smart electric grids
Proceedings of the first international workshop on High performance computing, networking and analytics for the power grid
A preliminary out-of-core extension of a parallel multifrontal solver
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific 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
A sweeping preconditioner for time-harmonic Maxwell's equations with finite elements
Journal of Computational Physics
A static parallel multifrontal solver for finite element meshes
ISPA'06 Proceedings of the 4th international conference on Parallel and Distributed Processing and Applications
Advances in Engineering Software
Reflections on simultaneous impact
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Modal shape analysis beyond Laplacian
Computer Aided Geometric Design
Parallel coarse-grid treatment in AMG for coupled systems
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
ACM Transactions on Mathematical Software (TOMS)
A parallel two-level preconditioner for cosmic microwave background map-making
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Task scheduling for parallel multifrontal methods
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
A rapidly converging domain decomposition method for the Helmholtz equation
Journal of Computational Physics
Computers & Mathematics with Applications
Scalable domain decomposition preconditioners for heterogeneous elliptic problems
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Parallel design and performance of nested filtering factorization preconditioner
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
A three-dimensional numerical model for dense granular flows based on the µ(I) rheology
Journal of Computational Physics
Applying microprocessor analysis methods to river network modelling
Environmental Modelling & Software
Journal of Computational Physics
hp-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Parallel algebraic domain decomposition solver for the solution of augmented systems
Advances in Engineering Software
Computers & Mathematics with Applications
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In this paper, we analyze the main features and discuss the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project. The algorithms use a multifrontal approach and are especially designed to cover a large class of problems. The problems can be symmetric positive definite, general symmetric, or unsymmetric matrices, both possibly rank deficient, and they can be provided by the user in several formats. The algorithms achieve high performance by exploiting parallelism coming from the sparsity in the problem and that available for dense matrices. The algorithms use a dynamic distributed task scheduling technique to accommodate numerical pivoting and to allow the migration of computational tasks to lightly loaded processors. Large computational tasks are divided into subtasks to enhance parallelism. Asynchronous communication is used throughout the solution process to efficiently overlap communication with computation.We illustrate our design choices by experimental results obtained on an SGI Origin 2000 and an IBM SP2 for test matrices provided by industrial partners in the PARASOL project.