Numerical Modeling of Photovoltaic Cells with the Meshless Global Radial Basis Function Collocation Method

Murat Ispir and Tayfun Tanbay ()
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Murat Ispir: Department of Mechanical Engineering, Faculty of Engineering and Natural Sciences, Konya Technical University, Konya 42250, Türkiye
Tayfun Tanbay: Department of Mechanical Engineering, Faculty of Engineering and Natural Sciences, Bursa Technical University, Bursa 16310, Türkiye

Energies, 2025, vol. 18, issue 19, 1-22

Abstract: Accurate prediction of photovoltaic performance hinges on resolving the electron density in the P-region and the hole density in the N-region. Motivated by this need, we present a comprehensive assessment of a meshless global radial basis function (RBF) collocation strategy for the steady current continuity equation, covering a one-dimensional two-region P–N junction and a two-dimensional single-region problem. The study employs Gaussian (GA) and generalized multiquadric (GMQ) bases, systematically varying shape parameter and node density, and presents a detailed performance analysis of the meshless method. Results map the accuracy–stability–computation-time landscape: GA achieves faster convergence but over a narrower stability window, whereas GMQ exhibits greater robustness to shape-parameter variation. We identify stability plateaus that preserve accuracy without severe ill-conditioning and quantify the runtime growth inherent to dense global collocation. A utopia-point multi-objective optimization balances error and computation time to yield practical node-count guidance; for the two-dimensional case with equal weighting, an optimum of 19 intervals per side emerges, largely insensitive to the RBF choice. Collectively, the results establish global RBF collocation as a meshless, accurate, and systematically optimizable alternative to conventional mesh-based solvers for high-fidelity carrier-density prediction in P-N junctions, thereby enabling more reliable performance analysis and design of photovoltaic devices.

Keywords: photovoltaic cell; carrier continuity equation; meshless method; RBF collocation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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