NEARLY ISOTROPIC PROPAGATION OF SPATIALLY DISCRETIZED WAVES

The effect of spatial discretization on the isotropy of propagating wa ves is investigated. A general criterion is given for minimizing the n umerical anisotropy and dispersion caused by spatial discretization, a nd specific discretizations in two and three space dimensions are deri ved which give, in a well-defined sense, optimally isotropic propagati on. We establish the group-theoretic connection between the properties of the spatial discretization and the symmetries of the underlying co mputational grid. The discretization technique, described here in the context of the scalar wave equation, may also be applied to other part ial differential equations containing the Laplacian or gradient operat ors.