Analytical Approach for Sharp Corner Reconstruction in the Kernel Free Boundary Integral Method during Magnetostatic Analysis for Inductor Design
Abstract
:1. Introduction
2. The C-core Problem
2.1. The Dimensions of C-core
2.2. PDEs and BCs for Magnetostatic Analysis
2.3. Inductance Calculation
3. KFBIM Framework for Single Boundary Magnetostatic Problems
4. Boundary Reconstruction and Implementation of the Kernel Free Boundary Integral Method
4.1. Boundary Reconstruction
4.2. Implementation of KFBIM
5. Results and Discussion of KFBIM
5.1. Numerical Example
5.2. Comparison between KFBIM and FEM on Magnetostatic Analysis
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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FEM | BEM/BIM | KFBIM |
---|---|---|
Body fitted mesh | Body fitted mesh | Unstructured mesh |
High computational time | Lowest computational time | Low computational time |
Differential method | Integral method | Integral method |
/ | Analytic expression of Green’s functions required | Analytic expression of Green’s functions is not required |
Adaptable to nonlinear | Nonlinear difficult | Adaptable to nonlinear |
Adaptable to complex geometry with sharp corners | Sharp corner difficulty | Sharp corner difficulty |
Symmetric, banded large, sparse discrete system | Well-conditioned small dense discrete system | Well-conditioned discrete system |
Region | Dimensions |
---|---|
Rectangular domain box (cm2) | 20 × 20 |
Center of rectangular box (cm) | (0,0) |
The inner radius of C-core (cm) | 4.5 |
The outer radius of C-core (cm) | 6.5 |
Center of C-core (cm) | (0,0) |
The radius of coils (cm) | 1.4 |
Center of the left coil (cm) | (−2.7, 0) |
Center of the right coil (cm) | (−8.3, 0) |
Current (A) | 100 |
Boundary | ||
---|---|---|
Original Boundary (sharp corner) | 2.47 × 10−4 | 2.21 × 10−3 |
Reconstructed Boundary | 9.00 × 10−5 | 4.23 × 10−4 |
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Jin, Z.; Cao, Y.; Li, S.; Ying, W.; Krishnamurthy, M. Analytical Approach for Sharp Corner Reconstruction in the Kernel Free Boundary Integral Method during Magnetostatic Analysis for Inductor Design. Energies 2023, 16, 5420. https://doi.org/10.3390/en16145420
Jin Z, Cao Y, Li S, Ying W, Krishnamurthy M. Analytical Approach for Sharp Corner Reconstruction in the Kernel Free Boundary Integral Method during Magnetostatic Analysis for Inductor Design. Energies. 2023; 16(14):5420. https://doi.org/10.3390/en16145420
Chicago/Turabian StyleJin, Zichao, Yue Cao, Shuwang Li, Wenjun Ying, and Mahesh Krishnamurthy. 2023. "Analytical Approach for Sharp Corner Reconstruction in the Kernel Free Boundary Integral Method during Magnetostatic Analysis for Inductor Design" Energies 16, no. 14: 5420. https://doi.org/10.3390/en16145420
APA StyleJin, Z., Cao, Y., Li, S., Ying, W., & Krishnamurthy, M. (2023). Analytical Approach for Sharp Corner Reconstruction in the Kernel Free Boundary Integral Method during Magnetostatic Analysis for Inductor Design. Energies, 16(14), 5420. https://doi.org/10.3390/en16145420