The Improved Element-Free Galerkin Method for 3D Helmholtz Equations
Abstract
:1. Introduction
2. The IMLS Approximation
3. The IEFG Method for 3D Helmholtz Equations
4. Numerical Examples
- (1)
- Weight function
- (2)
- Scale parameter
- (3)
- Penalty factor
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Nodes | Relative Error | Time (s) | ||
---|---|---|---|---|
IEFG | EFG | IEFG | EFG | |
7 × 7 × 7 | 4.3092% | 4.3092% | 5.5 | 5.8 |
11 × 11 × 11 | 1.3234% | 1.3234% | 26.7 | 28.5 |
13 × 13 × 13 | 0.8832% | 0.8832% | 49.9 | 53.1 |
15 × 15 × 15 | 0.6296% | 0.6296% | 92.1 | 98.0 |
17 × 17 × 17 | 0.4706% | 0.4706% | 152.0 | 161.9 |
21 × 21 × 21 | 0.2905% | 0.2905% | 384.5 | 398.6 |
25 × 25 × 25 | 0.1967% | 0.1967% | 903.3 | 940.2 |
29 × 29 × 29 | 0.1520% | 0.1520% | 1907.2 | 1937.1 |
33 × 33 × 33 | 0.1075% | 0.1075% | 4287.2 | 4408.3 |
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Cheng, H.; Peng, M. The Improved Element-Free Galerkin Method for 3D Helmholtz Equations. Mathematics 2022, 10, 14. https://doi.org/10.3390/math10010014
Cheng H, Peng M. The Improved Element-Free Galerkin Method for 3D Helmholtz Equations. Mathematics. 2022; 10(1):14. https://doi.org/10.3390/math10010014
Chicago/Turabian StyleCheng, Heng, and Miaojuan Peng. 2022. "The Improved Element-Free Galerkin Method for 3D Helmholtz Equations" Mathematics 10, no. 1: 14. https://doi.org/10.3390/math10010014
APA StyleCheng, H., & Peng, M. (2022). The Improved Element-Free Galerkin Method for 3D Helmholtz Equations. Mathematics, 10(1), 14. https://doi.org/10.3390/math10010014