Ehemalige Professoren: Prof. Dr. Karsten Eppler

Prof. Dr. Karsten Eppler war bis zum Wintersemester 2018/2019 Inhaber der
Professur für Numerik der Optimalen Steuerung

Kontakt
über das Sekretariat des Institutes

Forschung

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. Diplomarbeit, 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. Habilitationsschrift, TU Berlin (2007), 78 S.

Journals and refereed proceedings

On switching points of optimal controls for coercive parabolic boundary control problems. Optimization 17 (1986), 93-101 (with F. Tr öltzsch).
The Lagrange principle and quasidifferential calculus. WZ der 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 der TU Kmst. (Chemnitz) 31 (1989), 174-178.
Flexible Bahnkurven durch Getriebe mit gesteuerten Antrieben. VDI-Zeitschrift für integrierte Produktionstechnik 133 (1991) Nr. 12, 80-83 (mit M. Berger u. 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 (mit H. Harbrecht). Comput. Optim. App., vol. 39 (2008), 297–318.
Wavelet based boundary element methods in exterior electromagnetic shaping (mit H. Harbrecht). Eng. Anal. Bound. Elem., vol. 32 (2008), 645–657.
A new fictitious domain method in shape optimization (mit H. Harbrecht, M.Mommer). Comput. Optim. Appl., vol. 40 (2008), 281–298.
Preconditioning the pressure tracking in fluid dynamics by shape Hessian information (mit S. Schmidt, V. Schulz und 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 (mit H. Harbrecht). SIAM J. Control Optim., vol. 48 (2009/10), 29012916.
Tracking the Dirichlet data in L2 is ill-posed (mit H. Harbrecht). J. Optim. Theory Appl., vol. 145 (2010), 1735.
On a Kohn-Vogelius Like Formulation of Free Boundary Problems (mit H. Harbrecht). Comput. Optim. Appl., vol. 52 (2012), 6985.
Shape optimization for free boundary problemsanalysis and numerics (mit 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

Dokumentation zur Berechnungssoftware Abkühlprozesse von Profilwalzgut in Kühlstrecken“. Abschlussdokumentation für Mannesmann-Demag-Sack GmbH (1993).
Temperaturfeldberechnungen für das selektive Kühlen von Profilen in Walzstraßen. (mit R. Lezius et. al.) DFG-Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung“ Report Nr. 538 (1994).
Exterior electromagnetic shaping: AD-based computation of shape derivatives (mit H.Harbrecht, S. Schlenkrich und A. Walther). Preprint SPP1253 (DFG), Nr.: SPP1253-15-01, eingereicht.

Scientific talks

Talks at conferences

Eisenach 1984: Internationale Tagung "Mathematische Optimierung"
Breitenstein 1987: Frühjahrstagung der Pädagogischen Hochschule Halle
Trassenheide 1988: Internationale Tagung "Variationsrechnung und optimale Prozesse"
Bayreuth 1991: Workshop "Numerische Behandlung nichtlinearer parametrischer Optimierungs- und Steuerprobleme“ (2 Vorträge)
Lodz (Bronislawow) 1991: International Conference on Optimization and Control
Paris, Januar 1995: Workshop zur Beantragung eines EU-Projektes
Chemnitz, März 1995: 1. Sächs. Kolloquium "Inverse Probleme" Trier, Juli 1996: 6. deutsch-französische Konferenz Optimierung
Burg, April 1997: 1. DFG-Workshop Sensitivitätsanalyse“
Oybin, September 1997: 2. Sächs. Kolloquium "Inverse Probleme“
Chemnitz, April 1998: Conference on Control (Ifip-WG 7.2)
Trier, März 1999: International Conference on Optimization
Burg, April 1999: 2. DFG-Workshop "Sensitiviätsanalyse“
Edinburgh, (GB) Juli 1999: International Congress on Industrial and Applied Mathematics (ICIAM) 1999
Zagan (PL), September 1999: 1. deutsch-polnische Konferenz Optimierung
Göttingen, April 2000: GAMM-Jahrestagung 2000
Daytona Beach (USA), Mai 2000: 3. International Conference on Nonlinear Problems in Aviation and Aerospace
Perpignan (Fr), Juni 2000: 14. International Conference on Mathematical Theory of Networks and Systems
Dresden, September 2000: DMV-Jahrestagung 2000 (2 Vorträge)
Burg, Mai 2001: 3. DFG-Workshop "Sensitivitätsanalyse“
San Diego (USA), Juli 2001: 5. SIAM Conference on Control and Applications
Berlin, September 2001: 1.SIAM-EMS Conference (Koautor von H. Harbrecht + Organisation von 2 Minisymposien [mit T. Slawig])
Decin (Tsch), September 2001: Workshop "Adjoints and AD“
Augsburg, März 2002: GAMM-Jahrestagung 2002
Cottbus, September 2002: French-German-Polish Conference on Optimization (FGPO)
Oberwolfach, Februar 2003: Numerical Techniques for Optimization Problems with PDE Constraints (invited)
Sydney (Au), Juli 2003: International Congress on Industrial and Applied Mathematics (ICIAM) 2003
Sophia Antipolis (Fr), Juli 2003: 21st IFIP TC 7 Conference on System Modeling and Optimization
Berlin, Dezember 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: Numerik-Kolloqium der TU Berlin
Luxembourg, March 2005: GAMM Jahrestagung 2005
Cambridge (USA), June 2005: 3rd MIT-conference (2 Vorträge)
Turin (It), July 2005: 22nd IFIP TC 7 Conference on System Modeling and Optimization
Chemnitz, September 2005: Minisymposium zu Inversen Problemen
Berlin, September 2005: Workshop "New Trends in Simulation and Optimization of PDE“
Zürich, Januar 2006, Institutsvortrag Prof. Schwab
Dresden, Januar 2006, Institutsvortrag IWR/Numath
Compiegne (Fra), Februar 2006, Institutsvortrag
Oberwolfach, Februar/März 2006: Numerical Techniques for Optimization Problems with PDE Constraints (invited)
Chemnitz, September 2006: Minisymposium zu Inversen Problemen
Cracow (PL), July 2007: 23rd IFIP TC 7 Conference on System Modeling and Optimization
Bremen, April 2008: GAMM Jahrestagung 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; Sektionskolloquium der Pädagogischen Hochschule
Leipzig, Juni 1999; Prof. Luckhaus/Prof. Klötzler
Linz, Januar 2004; RICAM-Seminar (Prof. Langer)
Kiel, November 2004; Prof. Schneider
Berlin, February 2005; Numerik-Kolloqium der TU Berlin
Utrecht (NL), March 2005; Prof. Stevenson
Zürich, Januar 2006; Prof. Schwab
Dresden, Januar 2006; Dr. Walther (IWR/Numath)
Compiegne (Fra), Februar 2006; Dr. Dambrine
Trier, June 2007: Prof. Tichatschke

Selected titles

Uber Umschaltpunkte optimaler Steuerungen für koerzitive parabolische Randsteuerprobleme. Optimierungs–Tagung 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 elektromagnetic 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. Zürich 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 numerische 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.