Journal ArticleDOI
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Pascal Hénon,Pierre Ramet,Jean Roman +2 more
- Vol. 28, Iss: 2, pp 301-321
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TLDR
The block partitioning and scheduling problem for sparse parallel factorization without pivoting is considered, and the scalability of the parallel solver and the compromise between memory overhead and efficiency are considered.Abstract:
Solving large sparse symmetric positive definite systems of linear equations is a crucial and time-consuming step, arising in many scientific and engineering applications. The block partitioning and scheduling problem for sparse parallel factorization without pivoting is considered. There are two major aims to this study: the scalability of the parallel solver, and the compromise between memory overhead and efficiency. Parallel experiments on a large collection of irregular industrial problems validate our approach.read more
Citations
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The FEniCS Project Version 1.5
Martin Sandve Alnæs,Jan Blechta,Johan Hake,August Johansson,Benjamin Kehlet,Anders Logg,Chris N. Richardson,Johannes Ring,Marie E. Rognes,Garth N. Wells +9 more
TL;DR: The FEniCS Project is a collaborative project for the development of innovative concepts and tools for automated scientific computing, with a particular focus on the solution of differential equations by finite element methods.
Journal ArticleDOI
Hybrid scheduling for the parallel solution of linear systems
TL;DR: This work considers the problem of designing a dynamic scheduling strategy that takes into account both workload and memory information in the context of the parallel multifrontal factorization and shows that a new scheduling algorithm significantly improves both the memory behaviour and the factorization time.
Journal ArticleDOI
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
TL;DR: CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems, updating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices.
Journal ArticleDOI
MHD stability in X-point geometry: simulation of ELMs
G.T.A. Huysmans,Olivier Czarny +1 more
TL;DR: A non-linear MHD code, named JOREK, is under development with the aim of studying the nonlinear evolution of the MHD instabilities thought to be responsible for edge localized modes (ELMs): external kink (peeling) and medium-n ballooning modes as discussed by the authors.
Journal ArticleDOI
A survey of direct methods for sparse linear systems
TL;DR: The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems.
References
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Journal ArticleDOI
Computer solution of large sparse positive definite systems
METIS: A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices
George Karypis,Vipin Kumar +1 more
TL;DR: Metis is copyrighted by the regents of the University of Minnesota as mentioned in this paper, and the content of which does not necessarily reflect the position or the policy of lhe government, and no official endorsement should be inferred.
Journal ArticleDOI
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
Iain S. Duff,John Reid +1 more
TL;DR: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps.
Journal ArticleDOI
Multifrontal parallel distributed symmetric and unsymmetric solvers
TL;DR: In this paper, a new parallel distributed memory multifrontal approach is described to handle numerical pivoting efficiently, a parallel asynchronous algorithm with dynamic scheduling of the computing tasks has been developed.
Journal ArticleDOI
An Approximate Minimum Degree Ordering Algorithm
TL;DR: An approximate minimum degree (AMD) ordering algorithm for preordering a symmetric sparse matrix prior to numerical factorization is presented and produces results that are comparable in quality with the best orderings from other minimum degree algorithms.