Fast mass lumped multiscale wave propagation modelling

TL;DR

This paper presents a novel explicit multiscale wave propagation method combining mass lumping, leapfrog time stepping, and Localized Orthogonal Decomposition, achieving scale-independent convergence and improved computational efficiency.

Contribution

It introduces a mass lumping approach integrated with multiscale techniques for explicit wave simulation, ensuring convergence independent of material scale variations.

Findings

Second-order convergence in energy norm

Method's performance demonstrated through numerical experiments

Scale-independent accuracy in heterogeneous media

Abstract

In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme for the temporal discretisation with the multiscale technique known as Localized Orthogonal Decomposition for the spatial discretisation. 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 Localized Orthogonal Decomposition 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.