Direct and approximate algorithmic methods for solving self-adjoint elliptic PDEs in three-space dimensions
type: Item
instance of: scholarly article
title: Direct and approximate algorithmic methods for solving self-adjoint elliptic PDEs in three-space dimensions
zbMATH Open document ID: 0538.65071
DOI: 10.1016/0377-0427(83)90039-0
author: Elias A. Lipitakis
published in: Journal of Computational and Applied Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The finite difference discretization of a class of three-dimensional self-adjoint elliptic partial differential equations leads to the solution of a linear system of equations with a large sparse symmetric coefficient matrix which has seven occupied diagonals. After factorization into \(LDL^ T\) with L lower unit triangular and D diagonal the system can be solved by forward-backward substitution. The exact factorization can be considered as a special case of a described approximate factorization where the amount of fill in within the envelope is prescribed for the factor L. Two FORTRAN routines are given, LDL 3D for the factorization and FBS 3D for the computation of the solution. A numerical example is reported on.
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15-04
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 3856343
zbMATH Keywords: FORTRAN routines
zbMATH Keywords: incomplete factorization
zbMATH Keywords: forward-backward substitution
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: 0377-0427(83)90039-0
OpenAlex ID: W1965977433
cites work: Q4134790
cites work: Approximate root-free factorization techniques for solving elliptic difference equations in three space variables
description: scientific article; zbMATH DE number 3856343