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VOL. 37 | 1999 A parallel matrix-free implementation of a Runge-Kutta code
Kevin Burrage, Craig Eldershaw, Roger Sidje

Editor(s) Tim Cranny, Bevan Thompson


It is known that matrix-free numerical implementations for solving stiff ordinary differential equations (ODEs) can be considerably more effective than implementations which rely on direct linear algebra techniques to solve the implicit equations governing the stage values. In this paper it will be shown how fully implicit, high order Runge-Kutta methods can be efficiently implemented in a matrix-free, parallel environment. The advantage of this is that no new parallel algorithms need be developed and that existing sequential methods that are adpated using these techniques need have no special structure (such as singly implicitness). This is demonstrated by the conversion of an existing Radau IIA method (RADAU5) to a matrix-free implementation using a dynamically pre-conditioned GMRES algorithm to solve the appropriate linear systems. Numerical results are presented for an implementation on a shared memory SGI Power Challenge and show the efficacy of this approach.


Published: 1 January 1999
First available in Project Euclid: 18 November 2014

zbMATH: 1193.65118

Rights: Copyright © 1999, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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