Journal article
Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods
SIAM Journal of Scientific Computing, Vol.20(2), pp.416-446
1998
DOI: 10.1137/S1064827595293223
Abstract
A broad class of partitioned differential equations with possible algebraic constraints is considered, including Hamiltonian and mechanical systems with holonomic constraints. For mechanical systems a formulation eliminating the Coriolis forces and closely related to the Euler-Lagrange equations is presented. A new class of integrators is defined: the super partitioned additive Runge-Kutta (SPARK) methods. This class is based on the partitioning of the system into different variables and on the splitting of the differential equations into different terms. A linear stability and convergence analysis of these methods is given. SPARK methods allowing the direct preservation of certain properties are characterized. Different structures and invariants are considered: the manifold of constraints, symplecticness, reversibility, contractivity, dilatation, energy, momentum, and quadratic invariants. With respect to linear stability and structure-preservation, the class of s-stage Lobatto IIIA-B-C-CSPARK methods is of special interest. Controllable numerical damping can be introduced by the use of additional parameters. Some issues related to the implementation of a reversible variable stepsize strategy are discussed.
Details
- Title: Subtitle
- Structure preservation for constrained dynamics with super partitioned additive Runge-Kutta methods
- Creators
- Laurent O Jay
- Resource Type
- Journal article
- Publication Details
- SIAM Journal of Scientific Computing, Vol.20(2), pp.416-446
- DOI
- 10.1137/S1064827595293223
- ISSN
- 1064-8275
- eISSN
- 1095-7197
- Language
- English
- Date published
- 1998
- Academic Unit
- Mathematics
- Record Identifier
- 9983985942502771
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