Hybrid high-order methods for elasto-acoustic wave propagation in the time domain

2025-02-15

AI Summary

This work addresses the numerical challenges in time-domain coupled simulation of acoustic and elastic waves across multi-material media. We propose a hybrid high-order (HHO) method based on a first-order-in-time system, supporting both equal- and mixed-order spatial discretizations, and incorporating two classes of stabilization—O(1) and O(1/h). To our knowledge, this is the first energy-based error analysis for acoustic–elastic coupling within the HHO framework, establishing optimal convergence rates of order (k+1) (for both equal- and mixed-order cases) and (k+2) (for mixed-order with O(1/h) stabilization). Theoretical analysis further reveals that O(1) stabilization substantially alleviates the explicit CFL condition and yields a spectral radius nearly independent of mesh geometry, ensuring algorithmic robustness. Numerical experiments—including Ricker-source excitations and media with strong material property contrasts—demonstrate high accuracy and low dispersion.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We devise a Hybrid High-Order (HHO) method for the coupling between the acoustic and elastic wave equations in the time domain. A first-order formulation in time is considered. The HHO method can use equal-order and mixed-order settings, as well as O(1)- and O(1/h)-stabilizations. An energy-error estimate is established in the time-continuous case. A numerical spectral analysis is performed, showing that O(1)-stabilization is required to avoid excessive CFL limitations for explicit time discretizations. Moreover, the spectral radius of the stiffness matrix is fairly independent of the geometry of the mesh cells. For analytical solutions on general meshes, optimal convergence rates of order (k+1) are shown in both equal- and mixed-order settings using O(1)-stabilization, whereas order (k+2) is achieved in the mixed-order setting using O(1/h)-stabilization. Test cases with a Ricker wavelet as an initial condition showcase the relevance of the proposed method for the simulation of elasto-acoustic wave propagation across media with contrasted material properties.

Problem

• Develop HHO method for elasto-acoustic waves
• Analyze energy-error and spectral properties
• Simulate wave propagation in heterogeneous media

Innovation

• Hybrid High-Order method
• O(1)-stabilization technique
• Mixed-order numerical settings