Extended Synchronous Variational Integrators for Wave Propagations on Non-Uniform Meshes

Abstract

This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform resolution. We extend the traditional asynchronous variational integrators (AVIs) method to higher order and couple different spatial elements to adapt to nonuniform meshes. We show that the extension of AVIs method is stable, convergent and may reduce the spurious inter-grid reflection across meshes with different sizes. Numerical experiments are provided to verify the stability and convergence of the extended AVIs. The total energy is numerically conserved in our experiments.