TY - JOUR
T1 - A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells
AU - Li , Qiang
AU - Bao , Gang
AU - Cao , Yanzhao
AU - Lin , Junshan
JO - Communications in Computational Physics
VL - 5
SP - 1361
EP - 1390
PY - 2023
DA - 2023/12
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0142
UR - https://global-sci.org/intro/article_detail/cicp/22256.html
KW - Optimal design, random rough surface, solar cell, Helmholtz equation, stochastic gradient descent method.
AB - <p style="text-align: justify;">In this work, we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar cells. We formulate the design problems as random PDE-constrained optimization problems and seek
the optimal statistical parameters for the random surfaces. The optimizations at fixed
frequency as well as at multiple frequencies and multiple incident angles are investigated. To evaluate the gradient of the objective function, we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the computation.
The stochastic gradient descent method evaluates the gradient of the objective function
only at a few samples for each iteration, which reduces the computational cost significantly. Various numerical experiments are conducted to illustrate the efficiency of the
method and significant increases of the absorptance for the optimal random structures.
We also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions
for the random interfaces.</p>