A hybrid numerical method for multi-domain wave propagation problems

Abstract

This study introduces a hybrid numerical methodology designed to address multi-domain wave propagation problems. The temporal discretization is achieved using the Houbolt scheme, a finite-difference-based approach known for its robust stability in time-dependent simulations. Spatially, the computational domain is partitioned into subdomains via a domain decomposition strategy, with continuity and equilibrium constraints imposed along the interfaces to ensure physical fidelity. Within each subdomain, the meshless generalized finite difference method (GFDM) is employed, thereby avoiding the complexity of mesh generation. Through the integration of Taylor series expansion and moving least squares (MLS) approximation, explicit formulations of partial derivatives are constructed. Numerical experiments confirm that the proposed hybrid method provides high accuracy and stability in simulating multi-domain wave propagation phenomena.