Multi-symplectic discretisation of wave map equations
This work provides a new numerical method for wave map equations, benefiting researchers in computational PDEs and geometric integration.
The paper introduces a multi-symplectic formulation for constrained Hamiltonian PDEs and applies it to wave map equations, resulting in an explicit numerical scheme that preserves constraints and shows excellent conservation properties in experiments.
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.