A coupled HDG discretization for the interaction between acoustic and elastic waves

TL;DR

This paper introduces a hybridizable discontinuous Galerkin (HDG) scheme for modeling the interaction between acoustic and elastic waves in the Laplace domain, with proven convergence and optimal numerical performance.

Contribution

It develops a novel coupled HDG discretization that weakly enforces stress tensor symmetry and demonstrates its convergence and superconvergence properties.

Findings

The method achieves optimal order of convergence.

Numerical results confirm superconvergence of traces.

The scheme effectively models acoustic-elastic wave interactions.

Abstract

We propose and analyze an HDG scheme for the Laplace-domain interaction between a transient acoustic wave and a bounded elastic solid embedded in an unbounded fluid medium. Two mixed variables (the stress tensor and the velocity of the acoustic wave) are included while the symmetry of the stress tensor is imposed weakly by considering the antisymmetric part of the strain tensor (the spin or vorticity tensor) as an additional unknown. Convergence of the method is demonstrated and theoretical rates are obtained; numerical results suggesting optimal order of convergence and superconvergence of the traces are presented.