The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems
Abstract
:1. Introduction
2. The FEM-DBCI Method for Electrostatics
3. The FEM-DBCI Method for Skin Effect
4. Solution of the Global Algebraic System
- (1)
- Set a zero initial guess for the Dirichlet condition on ΓT;
- (2)
- Solve the FEM equation (by means of the CG) to find ;
- (3)
- Compute .
- (a)
- Given the array ;
- (b)
- Solve the FEM equation with k0 = 0 (by means of the CG) to find ;
- (c)
- Compute .
5. An Analytical Example
6. Numerical Examples
6.1. Capacitance of a Strip Line
6.2. Two-Wire Transmission Line
6.3. Capacitance of a Cube Conductor
6.4. Skin Effect in a Two Wire Transmission Line
6.5. Skin Effect in a Non-Symmetric Transmission Line
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Dirichet | Neumann | Robin | |
---|---|---|---|
ΓT ≠ ΓIE | FEM-DBCI (LF) | – | FEM-RBCI FEM-AABC (HF) |
ΓT ≡ ΓIE | FEM-SDBCI (LF) | FEM-BEM FEM-MoM (LF) (HF) | FEM-SRBCI (HF) |
Method | GMRES Steps | CPU Time | Error Indicator ζ | Capacitance c/ε0 |
---|---|---|---|---|
FEM-DBCI (a) | 6 | 1.00 | 7.45 × 10−3 | 5.048423 |
FEM-DBCI (b) | 6 | 1.02 | 6.71 × 10−3 | 5.047634 |
FEM-DBCI (c) | 6 | 1.02 | 6.82 × 10−3 | 5.047570 |
FEM-BEM | 8 | 2.01 | 2.19 × 10−3 | 5.047849 |
Method | GMRES Steps | CPU Time (ms) | Normalized Capacitance |
---|---|---|---|
FEM-DBCI | 4 | 161.7 | 0.662214 |
FEM-BEM | 18 | 1421.9 | 0.661590 |
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Aiello, G.; Alfonzetti, S.; Rizzo, S.A.; Salerno, N. The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems. Mathematics 2021, 9, 1968. https://doi.org/10.3390/math9161968
Aiello G, Alfonzetti S, Rizzo SA, Salerno N. The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems. Mathematics. 2021; 9(16):1968. https://doi.org/10.3390/math9161968
Chicago/Turabian StyleAiello, Giovanni, Salvatore Alfonzetti, Santi Agatino Rizzo, and Nunzio Salerno. 2021. "The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems" Mathematics 9, no. 16: 1968. https://doi.org/10.3390/math9161968
APA StyleAiello, G., Alfonzetti, S., Rizzo, S. A., & Salerno, N. (2021). The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems. Mathematics, 9(16), 1968. https://doi.org/10.3390/math9161968