Abstract
In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz collocation method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations. Unlike the traditional time discretization strategies, the proposed numerical scheme introduces the spatial–temporal radial Trefftz functions (STRTFs) as the basis functions for the spatial and temporal discretization of the transient wave equations. The STRTFs are constructed in the spatial–temporal domain, which is a combination of 3D Euclidean space and time into a 4D manifold. Moreover, since the initial and boundary conditions are imposed on the spatial–temporal domain boundaries, the original transient wave propagation problem can be converted to an inverse boundary value problem. To deal with the specified time-dependent sound source excitations, the composite multiple reciprocity technique is extended from the spatial domain to the spatial–temporal domain, which transforms the original problem with a source term into a high-order problem without a source term. By deriving the related STRTFs for the considered high-order problem, the proposed scheme only requires the node discretization on the spatial–temporal domain boundaries. The efficiency of the proposed method is numerically verified by four benchmark examples under 3D transient wave equations with specified time-dependent sound source excitation.
Highlights
The strong-form boundary meshless methods mainly include the wave superposition method [21,22], method of fundamental solutions (MFS) [23,24], regularized meshless method [25], boundary distributed source method [26], singular boundary method (SBM) [27–31], collocation Trefftz method (CTM) [32,33], and so on. Due to their simpler form, integral-free and easy-to-use merits, this study focused on the strong-form boundary meshless methods based on the semi-analytical basis functions
We present four benchmark examples of 3D transient wave propagation problems with specified sound source excitations to verify the efficiency of the proposed spatial–temporal radial Trefftz collocation method (STRTCM)
The particular solution can be obtained by using a linear combination of the related high-order spatial–temporal radial Trefftz functions
Summary
The phenomenon of wave propagation [1–7] widely exists in various areas of science and engineering, such as acoustics, elastodynamics, electromagnetics, and fluid dynamics. Traditional numerical methods [8–10], such as the finite difference method and finite element method (FEM), have been widely used in wave propagation analysis They usually have the problems of low computational efficiency and poor computational accuracy due to the use of universal polynomial functions. The strong-form boundary meshless methods mainly include the wave superposition method [21,22], method of fundamental solutions (MFS) [23,24], regularized meshless method [25], boundary distributed source method [26], singular boundary method (SBM) [27–31], collocation Trefftz method (CTM) [32,33], and so on. Due to their simpler form, integral-free and easy-to-use merits, this study focused on the strong-form boundary meshless methods based on the semi-analytical basis functions
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