Journal article
A parallelizable preconditioner for the iterative solution of implicit Runge–Kutta-type methods
Journal of computational and applied mathematics, Vol.111(1), pp.63-76
1999
DOI: 10.1016/S0377-0427(99)00132-6
Abstract
The main difficulty in the implementation of most standard implicit Runge–Kutta (IRK) methods applied to (stiff) ordinary differential equations (ODEs) is to efficiently solve the nonlinear system of equations. In this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit Euler method. The preconditioner is based on the W-transformation of the RK coefficient matrices discovered by Hairer and Wanner. For stiff ODEs the preconditioner is by construction asymptotically exact for methods with an invertible RK coefficient matrix. The methodology is particularly useful when applied to super partitioned additive Runge–Kutta (SPARK) methods. The nonlinear system can be solved by inexact simplified Newton iterations: at each simplified Newton step the linear system can be approximately solved by an iterative method applied to the preconditioned linear system.
Details
- Title: Subtitle
- A parallelizable preconditioner for the iterative solution of implicit Runge–Kutta-type methods
- Creators
- Laurent O Jay - Institute for Mathematics and its Applications, University of Minnesota, 514 Vincent Hall, 206 Church Street S.E., Minneapolis, MN 55455, USAThierry Braconnier - Université de la Réunion, IREMIA, Département de Mathématiques et Informatique, 15 Avenue René Cassin, BP 7151, 97715 Saint-Denis Messag, Cedex 9, La Réunion, France
- Resource Type
- Journal article
- Publication Details
- Journal of computational and applied mathematics, Vol.111(1), pp.63-76
- DOI
- 10.1016/S0377-0427(99)00132-6
- ISSN
- 0377-0427
- eISSN
- 1879-1778
- Publisher
- Elsevier B.V
- Language
- English
- Date published
- 1999
- Academic Unit
- Mathematics
- Record Identifier
- 9983985855502771
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