We explore the use of PDE constrained nonlinear optimization techniques to optimize and design electromagnetic crystals which exhibit frozen mode behavior. This is characterized by the association with Van Hove singularities in the dispersion relation, e.g., stationary reflection points and degenerate band edge points. Hence, the optimization process modifies the dispersion relation by adjustin...

This thesis is mainly concerned with the efficient numerical solution of optimization problems subject to linear PDE-constraints, with particular focus on robust preconditioners and diffuse domain methods. Associated with such constrained optimization problems are the famous first-order KarushKuhn-Tucker (KKT) conditions. For certain minimization problems, the functions satisfying the KKT condi...

Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the opt...

This paper deals with an alternative approach for solving the PDE-constrained optimization problems. For this purpose, the problem has been discretized with the help of finite difference method. Then the reduced problem has been solved by advanced real coded genetic algorithm with ranking selection, whole-arithmetic crossover and non uniform mutation. The proposed approach has been illustrated ...

This paper describes an algorithm for PDE-constrained optimization that controls numerical errors using error estimates and grid adaptation. A key aspect of the algorithm is the use of adjoint variables to estimate errors in the first-order optimality conditions. Multilevel optimization is used to drive the optimality conditions and their estimated errors below a specified tolerance. The error ...

We present a class of inexact adaptive multilevel trust-region SQP-methods for the efficient solution of optimization problems governed by nonlinear partial differential equations. The algorithm starts with a coarse discretization of the underlying optimization problem and provides during the optimization process 1) implementable criteria for an adaptive refinement strategy of the current discr...