Multi-symplectic discretisation of wave map equations

Abstract

We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. When applied to the wave map equation, this numerical scheme is explicit, preserves the constraint and can be seen as a generalisation of the Shake algorithm for constrained mechanical systems. Furthermore, numerical experiments show excellent conservation properties of the numerical solutions.

References in corpus (7)

• Global regularity of wave maps II. Small energy in two dimensions
• Renormalization and blow up for charge one equivariant critical wave maps
• Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere
• Geometric Generalisations of SHAKE and RATTLE
• Singularity Formation in 2+1 Wave Maps
• Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map
• Reductions of Operator Pencils

Cited by in corpus (2)

• Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations
• A posteriori error estimates for wave maps into spheres