TY - JOUR
T1 - An Alternating Direction Method of Multipliers for the Optimization Problem Constrained with a Stationary Maxwell System
JO - Communications in Computational Physics
VL - 5
SP - 1435
EP - 1454
PY - 2018
DA - 2018/06
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0117
UR - https://global-sci.org/intro/article_detail/cicp/12484.html
KW - Optimal control problem, stationary Maxwell's equations, Nédélec element, ADMM.
AB - <p style="text-align: justify;">This paper mainly focuses on an efficient numerical method for the optimization
problem constrained with a stationary Maxwell system. Following the idea
of [32], the edge element is applied to approximate the state variable and the control
variable, then the continuous optimal control problem is discretized into a finite dimensional
one. The novelty of this paper is the approach for solving the discretized
system. Based on the separable structure, an alternating direction method of multipliers
(ADMM) is proposed. Furthermore, the global convergence analysis is established
in the form of the objective function error, which includes the discretization error by
the edge element and the iterative error by ADMM. Finally, numerical simulations are
presented to demonstrate the efficiency of the proposed algorithm.</p>