Numerical Modeling of Photovoltaic Cells with the Meshless Global Radial Basis Function Collocation Method
Abstract
1. Introduction
- (1)
- A side-by-side comparison of GA and GMQ bases across wide shape parameter and node density ranges;
- (2)
- Stability windows and near-optimal plateaus that practitioners can use to select basis/parameter pairs that preserve accuracy in the P- and N-region QNRs without incurring ill-conditioning;
- (3)
- A multi-objective optimization framework that balances error against central processing unit (CPU) time and yields practical node-count guidelines;
- (4)
- Actionable best-practice recommendations (basis selection, shape-parameter tuning, and conditioning strategies) that translate directly to PV modeling workflows.
2. Current Continuity Equations for a PV Cell
3. Radial Basis Function Collocation Method
4. Results and Discussion
4.1. One-Dimensional Two-Region Problem
4.2. Two-Dimensional Single Region Problem
5. Conclusions
- The global RBF collocation method accurately reproduces carrier distributions in one-dimensional P-N junctions and two-dimensional domains, confirming its suitability for semiconductor device modeling.
- Basis selection matters: GA basis typically exhibits faster convergence and lower errors at comparable node counts but over a narrower stability window; GMQ variants are more robust to shape-parameter variation, albeit with slightly slower convergence.
- Shape parameter critically affects both error and conditioning; stable plateaus exist where accuracy is near-optimal without severe ill-conditioning, while an overly large shape parameter can destabilize GA in particular.
- Because the collocation matrix is dense, CPU time rises rapidly with node count. A utopia-point multi-objective optimization that balances error and runtime yields practical design guidance: for the 2D problem considered, an optimum of 19 intervals per side (equal weights on accuracy and CPU time) gives a near-Pareto solution, largely insensitive to the specific RBF choice.
- Physically, the meshless solver captures the expected sensitivities of carrier densities to surface recombination velocity, diffusion length, and absorption coefficient, aligning with analytical trends and reinforcing the model’s predictive value.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
CPU | Central processing unit |
FEM | Finite element method |
GA | Gaussian |
GMQ | Generalized multiquadric |
IMQ | Inverse multiquadric |
MQ | Multiquadric |
PV | Photovoltaic |
QNR | Quasi-neutral region |
RBF | Radial basis function |
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RBF | Limit | |||||
---|---|---|---|---|---|---|
18 | ||||||
18 | ||||||
18 | ||||||
18 | ||||||
17 | ||||||
11 | ||||||
0.6 |
RBF | |||||||||
---|---|---|---|---|---|---|---|---|---|
MQ | 0.1 | 11 | 0.1136 | 9 | 0.1154 | 10 | 0.1155 | 11 | 0.1152 |
0.3 | 15 | 0.2599 | 14 | 0.2707 | 15 | 0.2635 | 15 | 0.2555 | |
0.5 | 19 | 0.3981 | 19 | 0.4000 | 19 | 0.3931 | 19 | 0.3852 | |
0.7 | 25 | 0.5021 | 25 | 0.4926 | 25 | 0.4859 | 25 | 0.4799 | |
0.9 | 33 | 0.5551 | 33 | 0.5419 | 33 | 0.5328 | 33 | 0.5254 | |
IMQ | 0.1 | 8 | 0.1054 | 10 | 0.1142 | 9 | 0.1154 | 9 | 0.1147 |
0.3 | 14 | 0.2783 | 14 | 0.2680 | 14 | 0.2675 | 14 | 0.2669 | |
0.5 | 18 | 0.4151 | 19 | 0.3940 | 19 | 0.3904 | 19 | 0.3886 | |
0.7 | 26 | 0.5074 | 25 | 0.4817 | 25 | 0.4749 | 25 | 0.4713 | |
0.9 | 36 | 0.5370 | 33 | 0.5265 | 32 | 0.5184 | 32 | 0.5121 | |
GA | 0.1 | 6 | 0.0848 | 8 | 0.1103 | 8 | 0.1025 | 9 | 0.1182 |
0.3 | 14 | 0.2731 | 15 | 0.2633 | 14 | 0.2622 | 15 | 0.2581 | |
0.5 | 19 | 0.3631 | 19 | 0.3449 | 19 | 0.3481 | 20 | 0.3448 | |
0.7 | 26 | 0.3950 | 25 | 0.3763 | 25 | 0.3812 | 25 | 0.3851 | |
0.9 | 32 | 0.3824 | 31 | 0.3685 | 31 | 0.376 | 31 | 0.3855 | |
GMQ | 0.1 | 10 | 0.1049 | 9 | 0.1033 | 10 | 0.1058 | 10 | 0.1151 |
0.3 | 14 | 0.2666 | 14 | 0.2678 | 15 | 0.2617 | 15 | 0.2635 | |
0.5 | 19 | 0.4054 | 19 | 0.4010 | 19 | 0.3833 | 19 | 0.3799 | |
0.7 | 26 | 0.5031 | 26 | 0.4889 | 25 | 0.4650 | 25 | 0.4570 | |
0.9 | 37 | 0.5290 | 36 | 0.5063 | 33 | 0.5013 | 32 | 0.4942 | |
GMQ | 0.1 | 11 | 0.0868 | 9 | 0.1112 | 11 | 0.1134 | 7 | 0.1024 |
0.3 | 15 | 0.2509 | 14 | 0.2666 | 15 | 0.2514 | 14 | 0.2755 | |
0.5 | 19 | 0.3885 | 19 | 0.3850 | 19 | 0.3673 | 19 | 0.3905 | |
0.7 | 25 | 0.4852 | 25 | 0.4644 | 25 | 0.4483 | 25 | 0.4637 | |
0.9 | 33 | 0.5273 | 31 | 0.5085 | 30 | 0.4961 | 32 | 0.5011 | |
GMQ | 0.1 | 12 | 0.1071 | 8 | 0.0985 | 11 | 0.1112 | 9 | 0.1104 |
0.3 | 15 | 0.2543 | 14 | 0.2753 | 15 | 0.2562 | 14 | 0.2730 | |
0.5 | 19 | 0.3996 | 18 | 0.4133 | 19 | 0.3936 | 19 | 0.4038 | |
0.7 | 25 | 0.5119 | 25 | 0.5074 | 25 | 0.4953 | 26 | 0.4940 | |
0.9 | 33 | 0.5724 | 33 | 0.556 | 33 | 0.5447 | 34 | 0.5355 | |
GMQ | 0.1 | 10 | 0.1139 | 8 | 0.1024 | 9 | 0.1112 | 9 | 0.1150 |
0.3 | 14 | 0.2700 | 13 | 0.2806 | 14 | 0.2724 | 14 | 0.2728 | |
0.5 | 18 | 0.4147 | 18 | 0.4197 | 19 | 0.4084 | 19 | 0.4064 | |
0.7 | 25 | 0.5267 | 25 | 0.5176 | 26 | 0.5068 | 26 | 0.5009 | |
0.9 | 34 | 0.5886 | 34 | 0.5669 | 34 | 0.5515 | 35 | 0.5393 |
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Ispir, M.; Tanbay, T. Numerical Modeling of Photovoltaic Cells with the Meshless Global Radial Basis Function Collocation Method. Energies 2025, 18, 5267. https://doi.org/10.3390/en18195267
Ispir M, Tanbay T. Numerical Modeling of Photovoltaic Cells with the Meshless Global Radial Basis Function Collocation Method. Energies. 2025; 18(19):5267. https://doi.org/10.3390/en18195267
Chicago/Turabian StyleIspir, Murat, and Tayfun Tanbay. 2025. "Numerical Modeling of Photovoltaic Cells with the Meshless Global Radial Basis Function Collocation Method" Energies 18, no. 19: 5267. https://doi.org/10.3390/en18195267
APA StyleIspir, M., & Tanbay, T. (2025). Numerical Modeling of Photovoltaic Cells with the Meshless Global Radial Basis Function Collocation Method. Energies, 18(19), 5267. https://doi.org/10.3390/en18195267