A hybrid parallel algorithm for large sparse linear systems

2018 ◽  
Vol 25 (6) ◽  
pp. e2210
Author(s):  
S. Chandra Sekhara Rao ◽  
Rabia Kamra
Keyword(s):  
Parallel Algorithm ◽  
Linear Systems ◽  
Sparse Linear Systems

Parallel algorithm for solving sparse linear systems

1996 ◽  
Vol 32 (19) ◽  
pp. 1766
Author(s):  
K.N. Balasubramanya Murthy ◽  
C. Siva Ram Murthy
Keyword(s):  
Parallel Algorithm ◽  
Linear Systems ◽  
Sparse Linear Systems

scholarly journals A parallel algorithm for direct solution of large sparse linear systems, well suitable to domain decomposition methods

2009 ◽  
pp. 589-605
Author(s):  
Ibrahima Gueye ◽  
Xavier Juvigny ◽  
Frédéric Feyel ◽  
François-Xavier Roux ◽  
Georges Cailletaud
Keyword(s):  
Domain Decomposition ◽  
Parallel Algorithm ◽  
Linear Systems ◽  
Decomposition Methods ◽  
Computational Effort ◽  
Direct Solution ◽  
Sparse Linear Systems ◽  
Domain Decomposition Methods ◽  
Direct Solver ◽  
Upper Level

The goal of this paper is to develop a parallel algorithm for the direct solution of large sparse linear systems and integrate it into domain decomposition methods. The computational effort for these linear systems, often encountered in numerical simulation of structural mechanics problems by finite element codes, is very significant in terms of run-time and memory requirements.In this paper, a two-level parallelism is exploited. The exploitation of the lower level of parallelism is based on the development of a parallel direct solver with a nested dissection algorithm and to introduce it into the FETI methods. This direct solver has the advantage of handling zero-energy modes in floating structures automatically and properly. The upper level of parallelism is a coarse-grain parallelism between substructures of FETI. Some numerical tests are carried out to evaluate the performance of the direct solver.

Discretisation of sparse linear systems: An optimisation approach

2015 ◽  
Vol 80 ◽  
pp. 42-49 ◽  
Author(s):  
M. Souza ◽  
J.C. Geromel ◽  
P. Colaneri ◽  
R.N. Shorten
Keyword(s):  
Linear Systems ◽  
Sparse Linear Systems

scholarly journals Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

2012 ◽  
Vol 20 (3) ◽  
pp. 241-255 ◽  
Author(s):  
Eric Bavier ◽  
Mark Hoemmen ◽  
Sivasankaran Rajamanickam ◽  
Heidi Thornquist
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Direct Methods ◽  
Iterative Solvers ◽  
Software Project ◽  
Sparse Linear Systems ◽  
Scalar Type ◽  
Mixed Precision

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

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