27 research outputs found
A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields
This paper is concerned with the analysis and numerical analysis for the
optimal control of first-order magneto-static equations. Necessary and
sufficient optimality conditions are established through a rigorous Hilbert
space approach. Then, on the basis of the optimality system, we prove
functional a posteriori error estimators for the optimal control, the optimal
state, and the adjoint state. 3D numerical results illustrating the theoretical
findings are presented.Comment: Keywords: Maxwell's equations, magneto statics, optimal control, a
posteriori error analysi
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Regularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions
A state-constrained optimal control problem with nonlocal radiation
interface conditions arising from the modeling of crystal growth processes is
considered. The problem is approximated by a Moreau-Yosida type
regularization. Optimality conditions for the regularized problem are derived
and the convergence of the regularized problems is shown. In the last part of
the paper, some numerical results are presented
Regularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions
A state-constrained optimal control problem with nonlocal radiation interface conditions arising from the modeling of crystal growth processes is considered. The problem is approximated by a Moreau-Yosida type regularization. Optimality conditions for the regularized problem are derived and the convergence of the regularized problems is shown. In the last part of the paper, some numerical results are presented
State-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions
We consider a control- and state-constrained optimal control problem
governed by a semilinear elliptic equation with nonlocal interface
conditions. These conditions occur during the modeling of diffuse-gray
conductive-radiative heat transfer. The nonlocal radiation interface
condition and the pointwise state-constraints represent the particular
features of this problem. To deal with the state-constraints, continuity of
the state is shown which allows to derive first-order necessary conditions.
Afterwards, we establish second-order sufficient conditions that account for
strongly active sets and ensure local optimality in an -neighborhood
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Optimal control of 3D state constrained induction heating problems with nonlocal radiation effects
The paper is concerned with a class of optimal heating problems in
semiconductor single crystal growth processes. To model the heating process,
time-harmonic Maxwell equations are considered in the system of the state.
Due to the high temperatures characterizing crystal growth, it is necessary
to include nonlocal radiation boundary conditions and a temperature-dependent
heat conductivity in the description of the heat transfer process. The first
goal of this paper is to prove the existence and uniqueness of the solution
to the state equation. The regularity analysis associated with the time
harmonic Maxwell equations is also studied. In the second part of the paper,
the existence and uniqueness of the solution to the corresponding linearized
equation is shown. With this result at hand, the differentiability of the
control-to-state mapping operator associated with the state equation is
derived. Finally, based on the theoretical results, first oder necessary
optimality conditions for an associated optimal control problem are
established