Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations (Communications in Computational Physics, 2010)
An energy conserving discretization of the elastic wave equation in secondorder formulation is developed for a composite grid, consisting of a set of structuredrectangular component grids with hanging nodes on the grid refinement interface. Previouslydeveloped summation-by-parts properties are generalized to devise a stablesecond order accurate coupling of the solution across mesh refinement interfaces. Thediscretization of singular source terms of point force and point moment tensor type arealso studied. Based on enforcing discrete moment conditions that mimic properties ofthe Dirac distribution and its gradient, previous single grid formulas are generalizedto work in the vicinity of grid refinement interfaces. These source discretization formulasare shown to give second order accuracy in the solution, with the error beingessentially independent of the distance between the source and the grid refinementboundary. Several numerical examples are given to illustrate the properties of the proposedmethod.