Elasto-acoustic wave propagation in geophysical media using hybrid high-order methods on general meshes

2025-05-21

AI Summary

This study addresses high-accuracy numerical simulation of elastic–acoustic wave propagation in geophysical fluid–solid coupled media. We propose the first systematic application of the hybrid high-order (HHO) method to the spatial semi-discretization of the elastic–acoustic coupling wave equation. To ensure computational efficiency while preserving geometric flexibility—including non-conforming meshes and hanging nodes—we design a block-diagonal static condensation strategy tailored for explicit and singly diagonally implicit Runge–Kutta (ERK/SDIRK) time integrators. Theoretically, we derive a CFL stability condition for ERK schemes. Numerical experiments on realistic 2D geophysical scenarios demonstrate that the method achieves accuracy comparable to spectral element methods and natively supports mixed triangular–quadrilateral meshes. Moreover, the SDIRK variant exhibits superior robustness in media with strong material contrasts and under large time-step sizes.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• 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
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Hybrid high-order (HHO) methods are numerical methods characterized by several interesting properties such as local conservativity, geometric flexibility and high-order accuracy. Here, HHO schemes are studied for the space semi-discretization of coupled elasto-acoustic waves in the time domain using a first-order formulation. Explicit and singly diagonal implicit Runge--Kutta (ERK&SDIRK) schemes are used for the time discretization. We show that an efficient implementation of explicit (resp. implicit) time schemes calls for a static condensation of the face (resp. cell) unknowns. Crucially, both static condensation procedures only involve block-diagonal matrices. Then, we provide numerical estimates for the CFL stability limit of ERK schemes and present a comparative study on the efficiency of explicit versus implicit schemes. Our findings indicate that implicit time schemes remain competitive in many situations. Finally, simulations in a 2D realistic geophysical configuration are performed, illustrating the geometrical flexibility of the HHO method: both hybrid (triangular and quadrangular) and nonconforming (with hanging nodes) meshes are easily handled, delivering results of comparable accuracy to a reference spectral element software based on tensorized elements.

Problem

• Modeling elasto-acoustic wave propagation in geophysical media
• Comparing explicit and implicit time discretization schemes
• Evaluating geometric flexibility of hybrid high-order methods

Innovation

• Hybrid high-order methods for elasto-acoustic waves
• Explicit and implicit Runge-Kutta time discretization
• Static condensation with block-diagonal matrices