Prof. Dr. Karsten Eppler

Until the 2018/2019 winter semester, Prof. Dr. Karsten Eppler held the
Chair of Numerical Optimal Control

Contact
via the secretariat of the Institute

Research Interests

Research Interests

Numerical methods for PDEs (FEM, BEM), Optimization methods in finite and infinite dimensions, Optimal control for PDEs and discretization, Shape optimization, Inverse Shape problems (shape identification), Integral equation methods

Publications

Diploma thesis, Ph.D.-thesis, habilitation thesis

  • Zur numerischen Lösung eines parabolischen Randsteuerproblems. Diploma thesis, TH Kmst. (Chemnitz) (1984), 46 S (On the numerical solution of a parabolic boundary control problem).

  • Untersuchungen zu einer Klasse zeitoptimaler Steuerprobleme bei semilinearen parabolischen Anfangsrandwertaufgaben. Dissertation TU Kmst. (Chemnitz) (1988), 107 S (On a class of time optimal control problems for semilinear parabolic boundary value problems).

  • Efficient Shape Optimization Algorithms for Elliptic Boundary Value Problems by Boundary Element Methods. Habilitation thesis, TU Berlin (2007), 78 pp.

Journals and refereed proceedings

  • On switching points of optimal controls for coercive parabolic boundary control problems. Optimization 17 (1986), 93-101 (with F. Tröltzsch).

  • The Lagrange principle and quasidifferential calculus. WZ of the TU Kmst. (Chemnitz) 29 (1987), 187-192 (with B. Luderer).

  • On the existence of generalized solutions of semilinear parabolic differential equations with noncontinuous boundary data. WZ of the TU Kmst. (Chemnitz) 31 (1989), 174-178.

  • Flexible trajectories by gears with controlled drives. VDI-Zeitschrift für integrierte Produktionstechnik 133 (1991) No. 12, 80-83 (with M. Berger and A. Fricke)

  • On the existence of optimal solutions for time-optimal semilinear parabolic boundary control problems. ZAA 12 (1993), 153-169.

  • Boundary control of semilinear elliptic equations - existence of optimal solutions. (with A. Unger) Control and Cybernetics vol. 26 (1997) No. 2, 249-259.

  • Fréchet-differentiability and sufficient optimality conditions for shape functionals. In: K.-H. Hoffmann, G. Leugering, F. Tr ̈ltzsch (eds.): Optimal control of Partial Differential Equations. ISNM vol. 133, 133-143, Birkhäuser, Basel 1999.

  • Second derivatives and sufficient optimality conditions for shape functionals. Control and Cybernetics vol. 29 (2000) No. 2, 485-512.

  • Boundary integral representations of second derivatives in shape optimization. Discuss. Math. Differential Incl. Contr. Opt. vol. 20 (2000) No. 1, 63-78.

  • Optimal shape design for elliptic equations via BIE-methods. J. of Applied Mathematics and Computer Science vol. 10 (2000) No. 3, 487-516.

  • Some remarks on sufficient conditions for nonsmooth functions. (with B. Luderer) Optimization vol. 49 (2001), 293-301.

  • Discrete and continuous optimal control strategies in the selective cooling of steel. (with F. Tröltzsch) ZAMM vol. 81 (2001), Suppl. 2, 247-248.

  • Optimal Control Problems for the Nonlinear Heat Equation. (with F. Tröltzsch) In: Grötschel, Martin et al. (eds.): Online optimization of large scale systems. 173-183, Springer, Berlin 2001.

  • Fast Optimization Methods in the Selective Cooling of Steel. (with F. Tr öltzsch) In: Gr ötschel, Martin et al. (ed.): Online optimization of large scale systems. 185-204, Springer, Berlin 2001.

  • On extension of boundary integral representations for second shape derivatives. Proceedings ICNPAA 2000, (Daytona Beach, USA), vol. 1, 227-234 (2001).

  • Numerical Solution of Elliptic Shape Optimization Problems using wavelet-based BEM. (with H. Harbrecht), Optimization, Methods and Software vol. 18 (2003), 105-123.

  • Second order Lagrange multiplier approximation for constrained shape optimization problems. (with H. Harbrecht), in Control and Boundary Analysis", (Lecture Notes in Pure and Applied Mathematics), edited by J. Cagnol et. al., Marcel Dekker, Boca Raton, 240:107-118, (2005).

  • Exterior electromagnetic shaping using wavelet BEM. (with H. Harbrecht), Math. Methods Appl. Sci, vol. 28 (2005), 387-405.

  • Fast wavelet BEM for 3d electromagnetic shaping. (with H. Harbrecht) Appl. Numer. Math., 54:537-554 (2005)

  • A regularized Newton method in electrical impedance tomography using shape Hessian information. (with H. Harbrecht) Control & Cybernetics, 34:203-225, (2005).

  • 2nd Order Shape Optimization using wavelet BEM. (with H. Harbrecht), Optimization, Methods and Software, vol. 21 (2006), 135-153.

  • Efficient treatment of stationary free boundary problems. (with H. Harbrecht), Appl. Numer. Math., vol. 56 (2006), 1326-1339.

  • Coupling of FEM and BEM in shape optimization. (with H. Harbrecht), Numer. Math., vol. 104 (2006), 47-68.

  • Shape optimization for 3D electrical impedance tomography. (with H. Harbrecht) In: Free and Moving Boundaries: Analysis, Simulation", (Lecture Notes in Pure and Applied Mathematics vol. 252), edited by R. Glowinski and J.-P. Zolesio, Chapman & Hall, Boca Raton (2007), 165-183.

  • On Convergence in Elliptic Shape Optimization. (with H. Harbrecht and R. Schneider) SIAM J. Control Optimization, vol. 45 (2007), 61-83.

  • Detecting perfectly insulated obstacles by shape optimization techniques of order two. (with L. Afraites, M. Dambrine and D. Kateb) Discrete Contin. Dyn. Syst., Ser. B, vol. 8 (2007), 389416.

  • Compact gradient tracking in shape optimization (with H. Harbrecht). Comput. Optim. App., vol. 39 (2008), 297-318.

  • Wavelet based boundary element methods in exterior electromagnetic shaping (with H. Harbrecht). Eng. Anal. Bound. Elem. vol. 32 (2008), 645-657.

  • A new fictitious domain method in shape optimization (with H. Harbrecht, M.Mommer). Comput. Optim. Appl., vol. 40 (2008), 281-298.

  • Preconditioning the pressure tracking in fluid dynamics by shape Hessian information (with S. Schmidt, V. Schulz and C. Ilic). J. Optim. Theory Appl., vol. 141 (2009), 513-531.

  • A shape calculus analysis for tracking type formulations in electrical impedance tomography. J. Inverse Ill-Posed Probl. vol. 17 (2009), 733751.

  • Tracking Neumann data for stationary free boundary problems (with H. Harbrecht). SIAM J. Control Optim., vol. 48 (2009/10), 29012916.

  • Tracking the Dirichlet data in L2 is ill-posed (with H. Harbrecht). J. Optim. Theory Appl., vol. 145 (2010), 1735.

  • On a Kohn-Vogelius Like Formulation of Free Boundary Problems (with H. Harbrecht). Comput. Optim. Appl., vol. 52 (2012), 6985.

  • Shape optimization for free boundary problemsanalysis and numerics (with H. Harbrecht). In: Constrained optimization and optimal control for partial differential equations", (International Series of Numerical Mathematics vol. 160), Birkhuser/Springer, Basel (2012), 277-288.

Recent preprints

  • On Hadamard representations of shape gradients - a computational guide; 2016, accepted, revised 2018.
  • On a proposal for the Fréchet-part of second derivatives in Shape Optimization; 2016, error correction in progress.
  • On starshaped calculus for shape functionals in arbitrary spatial dimension; 2017, submitted, corrected.

Unpublished manuscripts

  • On the local stability of the n-sphere for the n-dimensional Dido problem; 2016.
  • Comments on using parametric approaches in shape optimization; 2018
  • On Hadamard shape gradient representations in linear elasticity; 2016, second revision 2018.

Preprints, software manuals

  • Documentation for the calculation software "Abkühlprozesse von Profilwalzgut in Kühlstrecken". Final documentation for Mannesmann-Demag-Sack GmbH (1993).
  • Temperature field calculations for the selective cooling of profiles in rolling mills. (with R. Lezius et. al.) DFG priority program "Anwendungsbezogene Optimierung und Steuerung" Report No. 538 (1994).
  • Exterior electromagnetic shaping: AD-based computation of shape derivatives (with H. Harbrecht, S. Schlenkrich and A. Walther). Preprint SPP1253 (DFG), No.: SPP1253-15-01, submitted.

Scientific talks

Talks at conferences

  • Eisenach 1984: International Conference "Mathematical Optimization"
  • Breitenstein 1987: Spring conference of the University of Education Halle
  • Trassenheide 1988: International Conference "Calculus of Variations and Optimal Processes"
  • Bayreuth 1991: Workshop "Numerical treatment of non-linear parametric optimization and control problems" (2 lectures)
  • Lodz (Bronislawow) 1991: International Conference on Optimization and Control
  • Paris, January 1995: Workshop on the application for an EU project
  • Chemnitz, March 1995: 1st Sächs. Colloquium "Inverse Problems" Trier, July 1996: 6th German-French Conference on Optimization
  • Burg, April 1997: 1st DFG Workshop "Sensitivity Analysis"
  • Oybin, September 1997: 2nd Saxon. Colloquium "Inverse Problems"
  • Chemnitz, April 1998: Conference on Control (Ifip-WG 7.2)
  • Trier, March 1999: International Conference on Optimization
  • Burg, April 1999: 2nd DFG-Workshop "Sensitivity Analysis"
  • Edinburgh, (GB) July 1999: International Congress on Industrial and Applied Mathematics (ICIAM) 1999
  • Zagan (PL), September 1999: 1st German-Polish Optimization Conference
  • Göttingen, April 2000: GAMM Annual Conference 2000
  • Daytona Beach (USA), May 2000: 3rd International Conference on Nonlinear Problems in Aviation and Aerospace
  • Perpignan (Fr), June 2000: 14th International Conference on Mathematical Theory of Networks and Systems
  • Dresden, September 2000: DMV-Jahrestagung 2000 (2 lectures)
  • Burg, May 2001: 3rd DFG-Workshop "Sensitivity Analysis"
  • San Diego (USA), July 2001: 5th SIAM Conference on Control and Applications
  • Berlin, September 2001: 1st SIAM-EMS Conference (co-author of H. Harbrecht + organization of 2 minisymposia [with T. Slawig])
  • Decin (Tsch), September 2001: Workshop "Adjoints and AD"
  • Augsburg, March 2002: GAMM Annual Meeting 2002
  • Cottbus, September 2002: French-German-Polish Conference on Optimization (FGPO)
  • Oberwolfach, February 2003: Numerical Techniques for Optimization Problems with PDE Constraints (invited)
  • Sydney (Au), July 2003: International Congress on Industrial and Applied Mathematics (ICIAM) 2003
  • Sophia Antipolis (Fr), July 2003: 21st IFIP TC 7 Conference on System Modeling and Optimization
  • Berlin, December 2003: Workshop Optimal control of PDEs
  • Pisa (It), February 2004: IFIP TC 7.2 Workshop (invited)
  • Jyväskylä (Fin), July 2004: ECCOMAS Congress
  • Houston (USA), December 2004: IFIP TC 7.2 Workshop (invited)
  • Berlin, February 2005: Numerics Colloquium of the TU Berlin
  • Luxembourg, March 2005: GAMM Annual Conference 2005
  • Cambridge (USA), June 2005: 3rd MIT-conference (2 talks)
  • Turin (It), July 2005: 22nd IFIP TC 7 Conference on System Modeling and Optimization
  • Chemnitz, September 2005: Minisymposium on Inverse Problems
  • Berlin, September 2005: Workshop "New Trends in Simulation and Optimization of PDE"
  • Zurich, January 2006, Lecture by Prof. Schwab
  • Dresden, January 2006, Lecture IWR/Numath
  • Compiegne (Fra), February 2006, Lecture at the Institute
  • Oberwolfach, February/March 2006: Numerical Techniques for Optimization Problems with PDE Constraints (invited)
  • Chemnitz, September 2006: Minisymposium on Inverse Problems
  • Cracow (PL), July 2007: 23rd IFIP TC 7 Conference on System Modeling and Optimization
  • Bremen, April 2008: GAMM Annual Conference 2008
  • Venice, July 2008: WCCM/ECCOMAS08
  • Graz, September 2008: START-Workshop
  • Regensburg, March 2009: Optimization with interfaces and free boundaries
  • Oberwiesental, September 2009: FEM Symposium
  • Hauss i. Ennstal, March 2010: Ski-Seminar
  • Lamprecht, July 2010: Summer School (invited) and ANPDECO

Talks at institutes

  • Halle, April 1986; Section Colloquium of the University of Education
  • Leipzig, June 1999; Prof. Luckhaus/Prof. Klötzler
  • Linz, January 2004; RICAM seminar (Prof. Langer)
  • Kiel, November 2004; Prof. Schneider
  • Berlin, February 2005; Numerics Colloquium of the TU Berlin
  • Utrecht (NL), March 2005; Prof. Stevenson
  • Zurich, January 2006; Prof. Schwab
  • Dresden, January 2006; Dr. Walther (IWR/Numath)
  • Compiegne (Fra), February 2006; Dr. Dambrine
  • Trier, June 2007: Prof. Tichatschke

Selected titles

  • Über Umschaltpunkte optimaler Steuerungen für koerzitive parabolische Randsteuerprobleme. Optimization Conference Eisenach 1984.
  • Allgemeine Konvergenzaussagen bei der Approximation semilinearer parabolischer Randsteuerprobleme. Workshop Bayreuth 1991.
  • On the existence of optimal solutions of semilinear parabolic boundary control problems. Lodz (Bronislawow) 1991.
  • Optimal shape design for elliptic equations via BIE-methods - Computation of directional derivatives for integral functionals. Paris 1995.
  • On the symmetry of second derivatives in shape optimization. Trier 1996.
  • Second derivatives and sufficient optimality conditions in shape optimization. Oybin 1997.
  • Fréchet-differentiability and sufficient second-order optimality conditions for some shape optimization problems. Chemnitz 1998.
  • Sufficient optimality conditions and application to some shape problems. Edinburgh 1999.
  • Discrete and continuous optimal control strategies in the selective cooling of steel. Daytona Beach 2000.
  • Potential Methods for Elliptic Shape Optimization Problems. San Diego 2001.
  • First and second order shape optimization algorithms using wavelet-based BEM. Augsburg 2002.
  • About two- and tridimensional exterior electromagnetic shaping of liquid metals. Berlin 2003.
  • Sufficient second order conditions: Stability of stationary solutions and stability of numerical methods in shape optimization, Kiel 2004.
  • Free boundary computations by second order shape optimization methods. Houston 2004.
  • Shape optimization for elliptic pde: The shape Hessian provides a proper preconditioning. Berlin 2005.
  • Exterior electromagnetic shaping: AD-based computation of shape derivatives. Luxembourg 2005.
  • Fast BEM methods for the efficient treatment of elliptic shape optimization problems. MIT 2005.
  • Treating the EIT-problem by higher order shape calculus - the (n+1)st explanation for exponential ill-posedness. Chemnitz 2005.
  • Second Order Shape Optimization Methods for Elliptic PDE: Coercivity of the Shape Hessian, Convergence and Stability of Numerical Computations. Berlin 2005.
  • Shape Optimization Methods for Elliptic PDE: Coercivity, Convergence and Stability of Numerical Methods. Zurich 2006.
  • Investigating shape identification problems by higher order shape calculus - a new concept for proving ill-posedness? Compiegne 2006
  • On convergence for elliptic shape optimization problems. Cracow 2007.
  • Shape Optimization Methods for Shape dentification Problems. Bremen 2008.
  • On the well-posedness of free boundary problems. Graz 2008.
  • Fast BEM methods for the efficient treatment of elliptic shape optimization problems, Oberwiesental 2009.
  • Shape optimization for elliptic BVP - Analytical and numerical methods, Hauss i. Ennstal 2010.
  • Shape optimization for elliptic BVP's: Calculus, Sufficient conditions and Well-posedness, Lamprecht 2010.
  • On the computation of Hadamard shape gradient representations, Lamprecht 2010.

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Markus Herrich
Last modified: Mar 17, 2026