  We study 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. We demonstrate that this leads to
greater efficiency and parallelization and easier treatment of boundary
conditions compared to methods based on rectangular meshes. We develop a
variety of initial and boundary value treatments and present numerical evidence
of their performance. In all cases, the observed order of convergence is equal
to or greater than the number of stages of the underlying Runge--Kutta method.
