Multi-scale methods for wave propagation in heterogeneous media

TL;DR

This paper introduces a new multi-scale numerical method for wave propagation in heterogeneous media, significantly reducing computational costs by coupling macro- and micro-scale simulations, and demonstrates its effectiveness through theoretical analysis and numerical experiments.

Contribution

The paper develops and analyzes a novel multi-scale method that efficiently solves wave propagation problems with rapidly oscillating coefficients, with proven convergence and broad applicability.

Findings

Computational complexity is significantly reduced compared to traditional methods.

The method converges for periodic and non-periodic problems.

Effective for long time simulations with dispersive effects.

Abstract

Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multi-scale wave propagation in the framework of heterogeneous multi-scale method. The numerical methods couples simulations on macro- and micro-scales for problems with rapidly oscillating coefficients. We show that the complexity of the new method is significantly lower than that of traditional techniques with a computational cost that is essentially independent of the micro-scale. A convergence proof is given and numerical results are presented for periodic problems in one, two and three dimensions. The method is also successfully applied to non-periodic problems and for long time integration where dispersive effects occur.