# Optimal Control of Parameterized Maxwell's System: Reduced Basis, Convergence Analysis, and A Posteriori Error Estimates

arXiv: https://arxiv.org/abs/1908.08846 · HTML: https://mlsanity.com/paper/1908.08846/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [An Optimal Time Variable Learning Framework for Deep Neural Networks](https://mlsanity.com/paper/2204.08528/) (2022)

## Abstract (arXiv)

We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter set is assumed to be compact. We discretize the electric field by a finite element method and use variational discretization concept to discretize the control. We create a reduced basis method for the optimal control problem and establish uniform convergence of the reduced order solutions to that of the original high dimensional problem provided that the snapshot parameter sample is dense in the parameter set, with an appropriate parameter separability rule. Finally, we establish the absolute a posteriori error estimator for the reduced order solutions and the corresponding cost functions in terms of the state and adjoint residuals.