A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation

• DOI: 10.3390/math10060897
• Publication Date: 2022-03-11T17:58:36Z
• Authors: Lin Chen; Wenzhi Xu; Zhuojia Fu
• Keywords: Temporal discretization; Solver; Collocation (remote sensing); Transient (computer programming)

In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations. Unlike traditional time discretization strategies, numerical scheme introduces functions (STRTFs) as basis for spatial and temporal of equations. The STRTFs are constructed in domain, which combination Euclidean space into 4D manifold. Moreover, since initial boundary conditions imposed on domain boundaries, original propagation problem can be converted an inverse value problem. To deal time-dependent excitations, composite multiple reciprocity technique extended from transforms term high-order without term. By deriving related considered problem, only requires node boundaries. efficiency numerically verified by four benchmark examples under excitation.