A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems
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 chal...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/8/1249 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850144763107344384 |
|---|---|
| author | Hao Chang Fajie Wang Xingxing Yue Lin Qiu Linlin Sun |
| author_facet | Hao Chang Fajie Wang Xingxing Yue Lin Qiu Linlin Sun |
| author_sort | Hao Chang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-20d9ccbd7f0347158e87f20caaf4ce3b |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-20d9ccbd7f0347158e87f20caaf4ce3b2025-08-20T02:28:15ZengMDPI AGMathematics2227-73902025-04-01138124910.3390/math13081249A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation ProblemsHao Chang0Fajie Wang1Xingxing Yue2Lin Qiu3Linlin Sun4College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, ChinaCollege of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, ChinaCollege of Materials Science and Engineering, Qingdao University, Qingdao 266071, ChinaCollege of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, ChinaSchool of Science, Nantong University, Nantong 226019, ChinaThe 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.https://www.mdpi.com/2227-7390/13/8/1249elastic wave propagationmeshless methodgeneralized finite difference method2.5D techniqueslongitudinally invariant structures |
| spellingShingle | Hao Chang Fajie Wang Xingxing Yue Lin Qiu Linlin Sun A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems Mathematics elastic wave propagation meshless method generalized finite difference method 2.5D techniques longitudinally invariant structures |
| title | A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems |
| title_full | A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems |
| title_fullStr | A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems |
| title_full_unstemmed | A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems |
| title_short | A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems |
| title_sort | 2 5d generalized finite difference method for elastic wave propagation problems |
| topic | elastic wave propagation meshless method generalized finite difference method 2.5D techniques longitudinally invariant structures |
| url | https://www.mdpi.com/2227-7390/13/8/1249 |
| work_keys_str_mv | AT haochang a25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT fajiewang a25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT xingxingyue a25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT linqiu a25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT linlinsun a25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT haochang 25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT fajiewang 25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT xingxingyue 25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT linqiu 25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems AT linlinsun 25dgeneralizedfinitedifferencemethodforelasticwavepropagationproblems |