Domain decomposition and multi-level type techniques for general sparse linear systems

1998 ◽  
pp. 174-190 ◽  
Author(s):  
Yousef Saad ◽  
Maria Sosonkina ◽  
Jun Zhang
Keyword(s):  
Domain Decomposition ◽  
Linear Systems ◽  
Sparse Linear Systems ◽  
Multi Level

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.

A Coarse Grid Correction to Domain Decomposition Based Preconditioners for Meso-Scale Simulation of Concrete

2012 ◽  
Vol 204-208 ◽  
pp. 4683-4687 ◽  
Author(s):  
Jian Ping Wu ◽  
Jun Qiang Song ◽  
Wei Min Zhang ◽  
Huai Fa Ma
Keyword(s):  
Linear System ◽  
Domain Decomposition ◽  
Linear Systems ◽  
Large Scale ◽  
Coarse Grid ◽  
Small Scale ◽  
Sparse Linear Systems ◽  
Incomplete Factorization ◽  
Coarse Grid Correction ◽  
Meso Scale

Meso-scale simulation is one of the important ways to study dynamic behaviors of concrete materials, while most of the simulation time is used to solve the sparse linear systems. Because the discrete grid is three dimensional and is of large scale, iterations are the best solutions. But the convergence depends on the distribution of the eigenvalues of the coefficient matrix, to make the eigenvalues distributed more closely each other, it is required to adopt preconditioning techniques. In this paper, with the characteristics of the sparse linear systems considered, there provides a coarse grid correction algorithm, which is based on domain decomposition preconditioners and aggregation of sub-domains, with each aggregated into a single super-node. A linear system with small scale size is formed, which contains the global information and the solution is used to correct the solution components of the original auxiliary linear system. For incomplete factorization preconditioner parallelized with block Jacobi, classic additive Schwarz, and factors combination techniques, the experiments show that the presented algorithm can improve the convergence rate and the efficiency.

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
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