Fast mass lumped multiscale wave propagation modelling

Abstract

Abstract In this paper we investigate the use of a mass lumped fully explicit time-stepping scheme for the discretization of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme for the temporal discretization with the multiscale technique known as localized orthogonal decomposition (LOD) for the spatial discretization. To speed up the method and to make it fully explicit, a special mass lumping approach is introduced that relies on an appropriate interpolation operator. This operator is also employed in the construction of the LOD and is a key feature of the approach. We prove that the method converges with second order in the energy norm, with a leading constant that does not depend on the scales at which the material parameters vary. We also illustrate the performance of the mass lumped method in a set of numerical experiments.