Wave propagation using bases for bandlimited functions

We develop a two-dimensional solver for the acoustic wave equation with spatially varying coefficients. In what is a new approach, we use a basis of approximate prolate spheroidal wavefunctions and construct derivative operators that incorporate boundary and interface conditions. Writing the wave equation as a first-order system, we evolve the equation in time using the matrix exponential. Computation of the matrix exponential requires efficient representation of operators in two dimensions and for this purpose we use short sums of one-dimensional operators. We also use a partitioned low-rank representation in one dimension to further speed up the algorithm. We demonstrate that the method significantly reduces numerical dispersion and computational time when compared with a fourth-order finite difference scheme in space and an explicit fourth-order Runge-Kutta solver in time.