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Optimal control of magnetic fields in flow measurement
1. | Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, F-59313 - Valenciennes Cedex 9 |
2. | ZHAW School of Engineering, Institut fur Angewandte Mathematik und Physik (IAMP), Technikumstrasse 9, Postfach, CH-8401 Winterthur, Switzerland |
3. | Technische Universität Berlin, Institut für Mathematik, Str. des 17. Juni 136, Sekr. MA 4-5, D-10623 Berlin, Germany |
References:
[1] |
K. Afanasiev and M. Hinze, Adaptive control of a wake flow using proper orthogonal decomposition, in Shape Optimization & Optimal Design, Lect. Notes in Pure and Appl. Math., 216 (2001), 317-332. |
[2] |
K. Altmann, Numerische Verfahren der Optimalsteuerung von Magnetfeldern, Phd thesis, Technical University of Berlin, 2013. |
[3] |
K. Altmann, S. Stingelin and F. Tröltzsch, On some optimal control problems for electric circuits, International Journal of Circuit theory, 42 (2014), 808-830.
doi: 10.1002/cta.1889. |
[4] |
F. Bachinger, U. Langer and J. Schöberl, Numerical analysis of nonlinear multiharmonic eddy current problems, Numer. Math., 100 (2005), 593-616.
doi: 10.1007/s00211-005-0597-2. |
[5] |
G. Bärwolff and M. Hinze, Optimization of semiconductor melts, ZAMM Z. Angew. Math. Mech., 86 (2006), 423-437.
doi: 10.1002/zamm.200410247. |
[6] |
P. E. Druet, O. Klein, J. Sprekels, F. Tröltzsch and I. Yousept, Optimal control of three-dimensional state-constrained induction heating problems with nonlocal radiation effects, SIAM J. Control Optim., 49 (2011), 1707-1736.
doi: 10.1137/090760544. |
[7] |
R. Griesse and K. Kunisch, Optimal control for a stationary MHD system in velocity-current formulation, SIAM J. Control Optim., 45 (2006), 1822-1845.
doi: 10.1137/050624236. |
[8] |
M. Gunzburger and C. Trenchea, Analysis and discretization of an optimal control problem for the time-periodic MHD equations, J. Math. Anal. Appl., 308 (2005), 440-466.
doi: 10.1016/j.jmaa.2004.11.022. |
[9] |
M. Hinze, Control of weakly conductive fluids by near wall Lorentz forces, GAMM-Mitt., 30 (2007), 149-158.
doi: 10.1002/gamm.200790004. |
[10] |
M. Hinze and S. Volkwein, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, in Dimension reduction of large-scale systems, Lect. Notes Comput. Sci. Eng.Berlin, Springer, 45 (2005), 261-306.
doi: 10.1007/3-540-27909-1_10. |
[11] |
D. Hömberg and J. Sokołowski, Optimal shape design of inductor coils for surface hardening, Numer. Funct. Anal. Optim., 42 (2003), 1087-1117.
doi: 10.1137/S0363012900375822. |
[12] |
L. S. Hou and A. J. Meir, Boundary optimal control of MHD flows, Appl. Math. Optim., 32 (1995), 143-162.
doi: 10.1007/BF01185228. |
[13] |
L. S. Hou and S. S. Ravindran, Computations of boundary optimal control problems for an electrically conducting fluid, J. Comput. Phys., 128 (1996), 319-330.
doi: 10.1006/jcph.1996.0213. |
[14] |
D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. |
[15] |
M. Kolmbauer, The Multiharmonic Finite Element and Boundary Element Method for Simulation and Control of Eddy Current Problems, Phd thesis, 2012. |
[16] |
M. Kolmbauer and U. Langer, A Robust Preconditioned MinRes Solver for Distributed Time-Periodic Eddy Current Optimal Control Problems, SIAM J. Sci. Comput., 34 (2012), B785-B809.
doi: 10.1137/110842533. |
[17] |
K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems, Numer. Math., 90 (2001), 117-148.
doi: 10.1007/s002110100282. |
[18] |
K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, SIAM J. Numerical Analysis, 40 (2002), 492-515.
doi: 10.1137/S0036142900382612. |
[19] |
C. Meyer, P. Philip and F. Tröltzsch, Optimal control of a semilinear {PDE} with nonlocal radiation interface conditions, SIAM J. Control Optimization, 45 (2006), 699-721.
doi: 10.1137/040617753. |
[20] |
S. Nicaise, S. Stingelin and F. Tröltzsch, On two optimal control problems for magnetic fields, To appear in Computational Methods in Applied Mathematics, (2014).
doi: 10.1515/cmam-2014-0022. |
[21] |
S. Nicaise and F. Tröltzsch, A coupled Maxwell integrodifferential model for magnetization processes. Mathematische Nachrichten, 287 (2014), 432-452.
doi: 10.1002/mana.201200206. |
[22] |
S. S. Ravindran, Real-time computational algorithm for optimal control of an MHD flow system, SIAM J. Sci. Comput., 26 (2005), 1369-1388 (electronic).
doi: 10.1137/S1064827502400534. |
[23] |
F. Tröltzsch, Optimal Control of Partial Differential Equations. Theory, Methods and Applications, 112, American Math. Society, Providence, 2010. |
[24] |
S. Volkwein, Model Reduction Using Proper Orthogonal Decomposition, Lecture notes, Institute of Mathematics and Scientific Computing, University of Graz, 2007. |
[25] |
I. Yousept, Optimal control of Maxwell's equations with regularized state constraints, Comput. Optim. Appl., 52 (2012), 559-581.
doi: 10.1007/s10589-011-9422-2. |
[26] |
I. Yousept and F. Tröltzsch., PDE-constrained optimization of time-dependent 3d electromagnetic induction heating by alternating voltages. ESAIM M2AN, 46 (2012), 709-729.
doi: 10.1051/m2an/2011052. |
show all references
References:
[1] |
K. Afanasiev and M. Hinze, Adaptive control of a wake flow using proper orthogonal decomposition, in Shape Optimization & Optimal Design, Lect. Notes in Pure and Appl. Math., 216 (2001), 317-332. |
[2] |
K. Altmann, Numerische Verfahren der Optimalsteuerung von Magnetfeldern, Phd thesis, Technical University of Berlin, 2013. |
[3] |
K. Altmann, S. Stingelin and F. Tröltzsch, On some optimal control problems for electric circuits, International Journal of Circuit theory, 42 (2014), 808-830.
doi: 10.1002/cta.1889. |
[4] |
F. Bachinger, U. Langer and J. Schöberl, Numerical analysis of nonlinear multiharmonic eddy current problems, Numer. Math., 100 (2005), 593-616.
doi: 10.1007/s00211-005-0597-2. |
[5] |
G. Bärwolff and M. Hinze, Optimization of semiconductor melts, ZAMM Z. Angew. Math. Mech., 86 (2006), 423-437.
doi: 10.1002/zamm.200410247. |
[6] |
P. E. Druet, O. Klein, J. Sprekels, F. Tröltzsch and I. Yousept, Optimal control of three-dimensional state-constrained induction heating problems with nonlocal radiation effects, SIAM J. Control Optim., 49 (2011), 1707-1736.
doi: 10.1137/090760544. |
[7] |
R. Griesse and K. Kunisch, Optimal control for a stationary MHD system in velocity-current formulation, SIAM J. Control Optim., 45 (2006), 1822-1845.
doi: 10.1137/050624236. |
[8] |
M. Gunzburger and C. Trenchea, Analysis and discretization of an optimal control problem for the time-periodic MHD equations, J. Math. Anal. Appl., 308 (2005), 440-466.
doi: 10.1016/j.jmaa.2004.11.022. |
[9] |
M. Hinze, Control of weakly conductive fluids by near wall Lorentz forces, GAMM-Mitt., 30 (2007), 149-158.
doi: 10.1002/gamm.200790004. |
[10] |
M. Hinze and S. Volkwein, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, in Dimension reduction of large-scale systems, Lect. Notes Comput. Sci. Eng.Berlin, Springer, 45 (2005), 261-306.
doi: 10.1007/3-540-27909-1_10. |
[11] |
D. Hömberg and J. Sokołowski, Optimal shape design of inductor coils for surface hardening, Numer. Funct. Anal. Optim., 42 (2003), 1087-1117.
doi: 10.1137/S0363012900375822. |
[12] |
L. S. Hou and A. J. Meir, Boundary optimal control of MHD flows, Appl. Math. Optim., 32 (1995), 143-162.
doi: 10.1007/BF01185228. |
[13] |
L. S. Hou and S. S. Ravindran, Computations of boundary optimal control problems for an electrically conducting fluid, J. Comput. Phys., 128 (1996), 319-330.
doi: 10.1006/jcph.1996.0213. |
[14] |
D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. |
[15] |
M. Kolmbauer, The Multiharmonic Finite Element and Boundary Element Method for Simulation and Control of Eddy Current Problems, Phd thesis, 2012. |
[16] |
M. Kolmbauer and U. Langer, A Robust Preconditioned MinRes Solver for Distributed Time-Periodic Eddy Current Optimal Control Problems, SIAM J. Sci. Comput., 34 (2012), B785-B809.
doi: 10.1137/110842533. |
[17] |
K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems, Numer. Math., 90 (2001), 117-148.
doi: 10.1007/s002110100282. |
[18] |
K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, SIAM J. Numerical Analysis, 40 (2002), 492-515.
doi: 10.1137/S0036142900382612. |
[19] |
C. Meyer, P. Philip and F. Tröltzsch, Optimal control of a semilinear {PDE} with nonlocal radiation interface conditions, SIAM J. Control Optimization, 45 (2006), 699-721.
doi: 10.1137/040617753. |
[20] |
S. Nicaise, S. Stingelin and F. Tröltzsch, On two optimal control problems for magnetic fields, To appear in Computational Methods in Applied Mathematics, (2014).
doi: 10.1515/cmam-2014-0022. |
[21] |
S. Nicaise and F. Tröltzsch, A coupled Maxwell integrodifferential model for magnetization processes. Mathematische Nachrichten, 287 (2014), 432-452.
doi: 10.1002/mana.201200206. |
[22] |
S. S. Ravindran, Real-time computational algorithm for optimal control of an MHD flow system, SIAM J. Sci. Comput., 26 (2005), 1369-1388 (electronic).
doi: 10.1137/S1064827502400534. |
[23] |
F. Tröltzsch, Optimal Control of Partial Differential Equations. Theory, Methods and Applications, 112, American Math. Society, Providence, 2010. |
[24] |
S. Volkwein, Model Reduction Using Proper Orthogonal Decomposition, Lecture notes, Institute of Mathematics and Scientific Computing, University of Graz, 2007. |
[25] |
I. Yousept, Optimal control of Maxwell's equations with regularized state constraints, Comput. Optim. Appl., 52 (2012), 559-581.
doi: 10.1007/s10589-011-9422-2. |
[26] |
I. Yousept and F. Tröltzsch., PDE-constrained optimization of time-dependent 3d electromagnetic induction heating by alternating voltages. ESAIM M2AN, 46 (2012), 709-729.
doi: 10.1051/m2an/2011052. |
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