Explicit Computational Wave Propagation in Micro-Heterogeneous Media

TL;DR

This paper introduces a numerical homogenization approach using the Localized Orthogonal Decomposition method to enable explicit wave propagation simulations in micro-heterogeneous media with relaxed CFL conditions.

Contribution

It presents a novel application of the Localized Orthogonal Decomposition method for reducing spatial complexity in explicit wave simulations, allowing larger time steps.

Findings

Achieves convergence under weak regularity assumptions.

Reduces spatial complexity in micro-heterogeneous media.

Enables relaxation of the CFL condition for explicit schemes.

Abstract

Explicit time stepping schemes are popular for linear acoustic and elastic wave propagation due to their simple nature which does not require sophisticated solvers for the inversion of the stiffness matrices. However, explicit schemes are only stable if the time step size is bounded by the mesh size in space subject to the so-called CFL condition. In micro-heterogeneous media, this condition is typically prohibitively restrictive because spatial oscillations of the medium need to be resolved by the discretization in space. This paper presents a way to reduce the spatial complexity in such a setting and, hence, to enable a relaxation of the CFL condition. This is done using the Localized Orthogonal Decomposition method as a tool for numerical homogenization. A complete convergence analysis is presented with appropriate, weak regularity assumptions on the initial data.