Weighted graph based ordering techniques for preconditioned conjugate gradient methods
type: Item
instance of: scholarly article
title: Weighted graph based ordering techniques for preconditioned conjugate gradient methods
zbMATH Open document ID: 0839.65110
DOI: 10.1007/BF01732977
author: Simon S. Clift
author: Wei-Pai Tang
published in: BIT
publication date: 1996-06-02T00:00:00Z
review text: This work is a report about the results of seven new ordering techniques for improving the incomplete LU-factorization based preconditioned conjugate gradient solution of the Neumann problem of anisotropic partial differential equations of the form \[ \sum^n_{i= 1} {\partial\over \partial x_i} \Biggl(K_i {\partial u\over \partial x_i}\Biggr)= q,\quad x_i\in (0, 1),\quad i= 1,\dots, n, \] where \(K_i\), \(i= 1,\dots, n\) are different in magnitude. The ordering techniques suggested and analyzed are some modifications of the reverse Cuthill-McKee ordering algorithm; they are in some sense matrix coefficient sensitive algorithms. Numerical tests are given in tables showing that the idea of the construction works in the practice. The time required to perform ordering and the time required to perform PCG solver iteration vary significantly (factors are 1-4 and 0.5-- 3.4, respectively) depending on the ordering technique choosen.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 773822
zbMATH Keywords: numerical test
zbMATH Keywords: ordering techniques
zbMATH Keywords: incomplete LU-factorization
zbMATH Keywords: preconditioned conjugate gradient
zbMATH Keywords: Neumann problem
zbMATH Keywords: reverse Cuthill-McKee ordering algorithm
zbMATH Keywords: matrix coefficient sensitive algorithms
reviewed by: Gy. Molnárka
describes a project that uses: symrcm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 773822