Journal article
Iterative Solution of SPARK Methods Applied to DAEs
Numerical Algorithms, Vol.31(1), pp.171-191
12/2002
DOI: 10.1023/A:1021116800010
Abstract
In this article a broad class of systems of implicit differential–algebraic equations (DAEs) is considered, including the equations of mechanical systems with holonomic and nonholonomic constraints. Solutions to these DAEs can be approximated numerically by applying a class of super partitioned additive Runge–Kutta (SPARK) methods. Several properties of the SPARK coefficients, satisfied by the family of Lobatto IIIA-B-C-C*-D coefficients, are crucial to deal properly with the presence of constraints and algebraic variables. A main difficulty for an efficient implementation of these methods lies in the numerical solution of the resulting systems of nonlinear equations. Inexact modified Newton iterations can be used to solve these systems. Linear systems of the modified Newton method can be solved approximately with a preconditioned linear iterative method. Preconditioners can be obtained after certain transformations to the systems of nonlinear and linear equations. These transformations rely heavily on specific properties of the SPARK coefficients. A new truly parallelizable preconditioner is presented.
Details
- Title: Subtitle
- Iterative Solution of SPARK Methods Applied to DAEs
- Creators
- Laurent Jay - Department of Mathematics The University of Iowa 14 MacLean Hall Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Numerical Algorithms, Vol.31(1), pp.171-191
- DOI
- 10.1023/A:1021116800010
- ISSN
- 1017-1398
- eISSN
- 1572-9265
- Publisher
- Kluwer Academic Publishers; Dordrecht
- Language
- English
- Date published
- 12/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983985887102771
Metrics
27 Record Views