Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source
Abstract
:1. Introduction
2. Governing Equations and Boundary Conditions
3. Numerical Methods
4. Numerical Results and Comparisons
4.1. Case 1
4.2. Case 2
4.3. Case 3
4.4. Case 4
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Mode | LMFS P = 15 | LMFS P = 20 | LMFS P = 30 | MFS-SVD [1] | MFS-ES [28] | RBFCM [15] | Analytical Solution |
---|---|---|---|---|---|---|---|
1 | 1.4906 | 1.4906 | 1.4906 | 1.4908 | 1.4906 | 1.4906 | 1.4906 |
2 | 1.1607 | 1.1607 | 1.1607 | 1.1607 | 1.1607 | 1.1607 | 1.1607 |
3 | 0.9375 | 0.9375 | 0.9375 | 0.9375 | 0.9375 | 0.9376 | 0.9375 |
4 | 0.8093 | 0.8093 | 0.8093 | 0.8093 | 0.8093 | 0.8093 | 0.8093 |
5 | 0.7803 | 0.7803 | 0.7803 | 0.7799 | 0.7803 | 0.7804 | 0.7803 |
6 | 0.7083 | 0.7083 | 0.7083 | 0.7071 | 0.7083 | 0.7083 | 0.7083 |
Mode | LMFS P= 20 | LMFS P = 25 | LMFS P= 35 | MFS-SVD [1] | MFS-ES [28] | RBFCM [15] | Analytical Solution |
1 | 3.3482 | 3.3482 | 3.3482 | 3.3481 | 3.3482 | 3.3479 | 3.3482 |
2 | 1.8287 | 1.8287 | 1.8287 | 1.8287 | 1.8287 | 1.8284 | 1.8287 |
3 | 1.5649 | 1.5649 | 1.5649 | 1.5649 | 1.5650 | 1.5650 | 1.5650 |
4 | 1.2654 | 1.2654 | 1.2654 | 1.2654 | 1.2654 | 1.2656 | 1.2654 |
5 | 1.2292 | 1.2292 | 1.2292 | 1.2292 | 1.2292 | 1.2293 | 1.2292 |
6 | 0.9986 | 0.9986 | 0.9986 | 0.9986 | 0.9986 | 0.9984 | 0.9986 |
Mode | LMFS P = 20 | LMFS P = 30 | LMFS P = 50 | LSTM [29] | MFS-DDSM [36] | Analytical Solution |
---|---|---|---|---|---|---|
1 | 3.0650 | 3.0650 | 3.0650 | 3.0650 | 3.0650 | 3.0650 |
2 | 2.8254 | 2.8253 | 2.8254 | 2.8302 | 2.8302 | 2.8176 |
3 | 2.3621 | 2.3621 | 2.3621 | 2.3621 | 2.3621 | 2.3621 |
4 | 1.9574 | 1.9574 | 1.9574 | 1.9574 | 1.9574 | 1.9574 |
5 | 1.6535 | 1.6535 | 1.6535 | 1.6535 | 1.6535 | 1.6535 |
Mode | LMFS P = 10 | LMFS P = 20 | LMFS P = 30 | MFS-ES [28] | Lin et al. [37] | Kuttler [38] |
---|---|---|---|---|---|---|
1 | 1.3061 | 1.3061 | 1.3061 | 1.3061 | 1.3054 | 1.3057 |
2 | 1.14 | 1.14 | 1.14 | 1.14 | 1.1371 | 1.1398 |
3 | 1.0179 | 1.0179 | 1.0179 | 1.018 | 1.0118 | 1.0177 |
4 | 0.9241 | 0.9241 | 0.9241 | 0.9241 | 0.9189 | 0.9239 |
5 | 0.8497 | 0.8497 | 0.8497 | 0.8497 | 0.842 | 0.8495 |
Mode | LMFS P= 15 | LMFS P= 25 | LMFS P= 35 | MFS-ES [28] | Lin et al. [37] | Kuttler [38] |
1 | 4.6466 | 4.6466 | 4.6466 | 4.6421 | 4.6152 | 4.6466 |
2 | 4.4628 | 4.4628 | 4.4628 | 4.4586 | 4.4492 | 4.4571 |
3 | 2.341 | 2.341 | 2.341 | 2.3399 | 2.3138 | 2.3409 |
4 | 2.3391 | 2.3391 | 2.3392 | 2.338 | 2.2989 | 2.339 |
5 | 1.599 | 1.5989 | 1.599 | 1.5984 | 1.5817 | 1.5988 |
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Sun, K.; Ding, S.; Zhang, J.; Liu, Y.-C. Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source. Mathematics 2022, 10, 1128. https://doi.org/10.3390/math10071128
Sun K, Ding S, Zhang J, Liu Y-C. Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source. Mathematics. 2022; 10(7):1128. https://doi.org/10.3390/math10071128
Chicago/Turabian StyleSun, Ke, Shuang Ding, Junli Zhang, and Yan-Cheng Liu. 2022. "Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source" Mathematics 10, no. 7: 1128. https://doi.org/10.3390/math10071128
APA StyleSun, K., Ding, S., Zhang, J., & Liu, Y.-C. (2022). Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source. Mathematics, 10(7), 1128. https://doi.org/10.3390/math10071128