Experiences with sparse matrix solvers in parallel ODE software
type: Item
instance of: scholarly article
title: Experiences with sparse matrix solvers in parallel ODE software
zbMATH Open document ID: 0859.65072
DOI: 10.1016/0898-1221(96)00041-7
publication date: 1997-04-07T00:00:00Z
full work available at URL: https://ir.cwi.nl/pub/1958
review text: For solving a stiff initial value problem, one of the most powerful methods is an implicit Runge-Kutta (RK) scheme. However, in such a method, since one has to solve a system of nonlinear equations of dimension \(sd\) in every time step, where \(s\) is the number of stages, this may require a lot of computational effort. On parallel computer architectures, the costs can be reduced significantly. In this paper, the authors focus on parallel software for ordinary differential equations (PSODE). PSODE is an implementation of a Radau IIA method with a Newton-type iteration process, which reduces the nonlinear systems to sequences of linear systems. For problems arising in practice it often occurs that the components of the derivative function only depend on a small number of variables. Such problems lead to linear systems of which the matrix is sparse. The goal of this paper is to reduce the linear algebra costs for such problems by using a sparse matrix solver like MA28 and Y12M. The numerical results presented give insight into the behaviour of these matrix solvers.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 915123
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: stiff system
zbMATH Keywords: parallel computation
zbMATH Keywords: numerical examples
zbMATH Keywords: parallel software for ordinary differential equations
zbMATH Keywords: Radau IIA method
zbMATH Keywords: Newton-type iteration process
zbMATH Keywords: sparse matrix solver
author: Jacques J. B. de Swart
author: J. G. Blom
describes a project that uses: Maple
describes a project that uses: Y12M
describes a project that uses: ODEPACK
describes a project that uses: MA28
MaRDI profile type: Publication
OpenAlex ID: W1984481827
cites work: Y12M. Solution of large and sparse systems of linear algebraic equations. Documentation of subroutines
cites work: Q4274999
cites work: Q3830493
cites work: Parallel ODE-solvers with stepsize control
cites work: Parallel methods for initial value problems
cites work: Parallel Runge-Kutta methods with real eigenvalues
cites work: Iterated Runge–Kutta Methods on Parallel Computers
cites work: Analysis of parallel diagonally implicit iteration of Runge-Kutta methods
cites work: The elimination form of the inverse and its application to linear programming
cites work: Q3740904
cites work: Q4002478
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 915123