The multisymplectic diamond scheme

Abstract: We introduce a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge--Kutta method. The scheme advances in time by filling in each diamond locally, leading to greater efficiency and parallelization and easier treatment of boundary conditions compared to methods based on rectangular meshes.