On two optimal control problems for magnetic fields

DOI10.1515/cmam-2014-0022zbMath1315.35226OpenAlexW2021249348MaRDI QIDQ481904

Simon Stingelin, Fredi Tröltzsch, Serge Nicaise

Publication date: 18 December 2014

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://digitalcollection.zhaw.ch/handle/11475/15840

zbMATH Keywords

optimal controlproper orthogonal decompositionmodel reductiondegenerate parabolic equationinduction lawevolution Maxwell equationvector potential formulations

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) PDEs in connection with optics and electromagnetic theory (35Q60) Degenerate parabolic equations (35K65) Electromagnetic theory (general) (78A25) Existence theories for optimal control problems involving partial differential equations (49J20) Integro-partial differential equations (35R09) PDEs in connection with control and optimization (35Q93) Model reduction in optics and electromagnetic theory (78M34)

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Uses Software

• MinRes
• NGSolve

Cites Work

• Optimal control of Maxwell's equations with regularized state constraints
• Computations of boundary optimal control problems for an electrically conducting fluid
• Boundary optimal control of MHD flows
• Analysis and discretization of an optimal control problem for the time-periodic MHD equations
• Optimal Control of Three-Dimensional State-Constrained Induction Heating Problems with Nonlocal Radiation Effects
• Optimal Control of a Semilinear PDE with Nonlocal Radiation Interface Conditions
• Optimal Control for a Stationary MHD System in Velocity‐Current Formulation
• Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
• Real-Time Computational Algorithm for Optimal Control of an MHD Flow System
• Optimization of semiconductor melts
• Galerkin proper orthogonal decomposition methods for parabolic problems