A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems

Hao Chang, Fajie Wang (), Xingxing Yue, Lin Qiu and Linlin Sun ()
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Hao Chang: College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
Fajie Wang: College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
Xingxing Yue: College of Materials Science and Engineering, Qingdao University, Qingdao 266071, China
Lin Qiu: College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
Linlin Sun: School of Science, Nantong University, Nantong 226019, China

Mathematics, 2025, vol. 13, issue 8, 1-36

Abstract: The analysis of elastic wave propagation is a critical problem in both science and engineering, with applications in structural health monitoring and seismic wave analysis. However, the efficient and accurate numerical simulation of large-scale three-dimensional structures has posed significant challenges to traditional methods, which often struggle with high computational costs and limitations. This paper presents a novel two-and-a-half-dimensional generalized finite difference method (2.5D GFDM) for efficient simulation of elastic wave propagation in longitudinally invariant structures. The proposed scheme integrates GFDM with 2.5D technology, reducing 3D problems to a series of 2D problems in the wavenumber domain via Fourier transforms. Subsequently, the solutions to the original 3D problems can be recovered by performing inverse Fourier transforms on the solutions obtained from the 2D problems. The 2.5D GFDM avoids the inherent challenge of mesh generation in traditional methods like FEM and FVM, offering a meshless solution for complex 3D problems. By employing sparse coefficient matrices, it offers significantly improved computational efficiency. The new approach achieves significant computational advantages while maintaining high accuracy, as validated through three representative examples, making it a promising tool for solving large-scale elastic wave propagation problems in longitudinally invariant structures.

Keywords: elastic wave propagation; meshless method; generalized finite difference method; 2.5D techniques; longitudinally invariant structures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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