A space-time sparse-grid method for the wave equation

Abstract

We develop a fast space-time numerical scheme for approximating solutions to the linear wave equation. The approach is based on the sparse-grid combination technique applied to a coercive space-time discretization. Designed for tensor-product space-time discretizations, the method enables efficient parallelization of the resulting solver. We provide a rigorous theoretical analysis establishing convergence rates and computational complexity estimates. Numerical experiments validate the theoretical estimates and demonstrate the efficiency of the proposed method.