Communications in Mathematical Sciences

Volume 20 (2022)

Number 3

An optimal design of random surfaces in solar cells via mini-batch stochastic gradient approach

Pages: 747 – 762

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n3.a6

Authors

Dan Wang (College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, Heilongjiang, China)

Qiang Li (Department of Mathematics and Statistics, Auburn University, Auburn, Alabama, U.S.A.)

Jihong Shen (College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, Heilongjiang, China)

Abstract

A resultful way to increase the absorbing efficiency of solar cells is using random rough textures which can trap the optical light and increase the optical path of photons. In this paper, we consider the design problem for two-layer structure thin-film solar cells to find the optimal interface and bottom. We formulate the design problem as a random PDE constrained optimization problem and employ gradient-based methods for solving the problem numerically. To improve the time efficiency, mini-batch stochastic gradient method is used. Numerical examples are shown to test the efficiency of the proposed algorithm.

Keywords

surface optimal design, stochastic gradient method, solar cells

2010 Mathematics Subject Classification

65C20, 65K10

Received 21 April 2021

Received revised 20 August 2021

Accepted 29 August 2021

Published 21 March 2022