Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning

doi:10.1016/j.jpdc.2018.04.017

Title: Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning

Full Record
Other Related Research

Authors:: Chow, Edmond; Anzt, Hartwig; Scott, Jennifer; Dongarra, Jack

Publication Date:: 2018-09-01

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1582723

Grant/Contract Number:: SC-0016564; SC-0016513

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Journal of Parallel and Distributed Computing

Additional Journal Information:: Journal Name: Journal of Parallel and Distributed Computing Journal Volume: 119 Journal Issue: C; Journal ID: ISSN 0743-7315

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Citation Formats


                    Chow, Edmond, Anzt, Hartwig, Scott, Jennifer, and Dongarra, Jack. Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning.  United States: N. p., 2018. 
        Web.  doi:10.1016/j.jpdc.2018.04.017.

Copy to clipboard


                    Chow, Edmond, Anzt, Hartwig, Scott, Jennifer, & Dongarra, Jack. Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning.  United States.  doi:10.1016/j.jpdc.2018.04.017.

Copy to clipboard


                    Chow, Edmond, Anzt, Hartwig, Scott, Jennifer, and Dongarra, Jack. Sat .  
        "Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning".  United States.  doi:10.1016/j.jpdc.2018.04.017.

Copy to clipboard


                    
@article{osti_1582723,

  title        = {Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning},

  author       = {Chow, Edmond and Anzt, Hartwig and Scott, Jennifer and Dongarra, Jack},

  abstractNote = {},

  doi          = {10.1016/j.jpdc.2018.04.017},

  journal      = {Journal of Parallel and Distributed Computing},

  number       = C,

  volume       = 119,

  place        = {United States},

  year         = {2018},

  month        = {9}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Publisher's Version of Record
DOI: 10.1016/j.jpdc.2018.04.017

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 3 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

NSPCG (Nonsymmetric Preconditioned Conjugate Gradient) user's guide: Version 1. 0: A package for solving large sparse linear systems by various iterative methods

Technical Report Oppe, T C ; Joubert, W D ; Kincaid, D R

NSPCG (or Nonsymmetric Preconditioned Conjugate Gradient) is a computer package to solve the linear system Au = b by various iterative methods. The coefficient matrix A is assumed to be large and sparse with real coefficients. A wide selection of preconditioners and accelerators is available for both symmetric and nonsymmetric coefficient matrices. Several sparse matrix data structures are available to represent matrices whose structures range from highly structures to completely unstructured. 36 refs., 8 tabs.
Solving structures problems iteratively with a shifted incomplete Cholesky preconditioning

Conference Manteuffel, T A

A technique for solving the large sparse symmetric linear systems that arise from the application of finite element methods is described. The technique combines an incomplete factorization method called the shifted incomplete Cholesky factorization with the method of generalized conjugate gradients. The shifted incomplete Cholesky factorization produces a splitting of the matrix A that is dependent upon a parameter ..cap alpha... It is shown that, if A is positive definite, then there is some ..cap alpha.. for which this splitting is possible and that this splitting is at least as good as the Jacobi splitting. The method is shown tomore »« less
Incomplete block factorization preconditioning for indefinite elliptic problems

Conference Guo, Chun-Hua

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.
DOI: 10.1007/s002119900076

Full Text Available
Factors impacting performance of multithreaded sparse triangular solve.

Conference Wolf, Michael M ; Heroux, Michael Allen ; Boman, Erik Gunnar

As computational science applications grow more parallel with multi-core supercomputers having hundreds of thousands of computational cores, it will become increasingly difficult for solvers to scale. Our approach is to use hybrid MPI/threaded numerical algorithms to solve these systems in order to reduce the number of MPI tasks and increase the parallel efficiency of the algorithm. However, we need efficient threaded numerical kernels to run on the multi-core nodes in order to achieve good parallel efficiency. In this paper, we focus on improving the performance of a multithreaded triangular solver, an important kernel for preconditioning. We analyze three factors thatmore »« less
Iterative methods for the solution of linear equations based on incomplete block factorization of the matrix

Conference Meyerink, J A - Soc. Pet. Eng. AIME, Pap.; (United States)

This work presents a class of iterative methods for the solution of linear equations like those that arise in reservoir simulators. The methods are generalizations of the incomplete LU-factorization technique introduced earlier. It can be applied to equations generated by the usual 5- and 7-point finite difference approximations as well as to those generated by special 9-, 11-, 19- and 27-point approximations. Application of the method to equations where the band structure of the matrix has been spoiled is discussed and modifications for running efficiently on vector processors are given. Numeric examples for well-known test problems are presented and comparedmore »« less

Similar Records