Multi-Symplectic Runge–Kutta Collocation Methods for Hamiltonian Wave Equations
✍ Scribed by Sebastian Reich
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 403 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
A number of conservative PDEs, like various wave equations, allow for a multisymplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplecticity under a symplectic method for Hamiltonian ODEs. We also discuss the issue of conservation of energy and momentum. Since time discretization by a Gauss-Legendre method is computational rather expensive, we suggest several semi-explicit multisymplectic methods based on Gauss-Legendre collocation in space and explicit or linearly implicit symplectic discretizations in time.