.
. . .
.
. mathematik ebuilding
.
. . .
.
. . .
. .
. . .
. . .
. .
. . .

Selected Publications of Volker Schulz (since 1999)

Articles in journals and refereed proceedings volumes:
Author / Title
G. Heidel, V. Khoromskaia, B. Khoromskij and V. Schulz: Tensor approach to optimal control problems with fractional d-dimensional elliptic operator in constraints., arXiv:1809.01971, submitted to SICON, 2019
D. Luft, V. Schulz and K. Welker: Efficient Techniques for Shape Optimization with Variational Inequalities using Adjoints., arXiv:1904.08650 (submitted to SIAM J. Optimization), 2019
Ch. Vollmann and V. Schulz: Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion., Computing and Visualization in Science, Vol 20, pp. 29-46, 2019, arXiv:1708.02526
V. Schulz and K. Welker: On Optimization Transfer Operators in Shape Space, International Series of Numerical Mathematics, Vol. 169, pp. 259-275, 2018
B. Führ, V. Schulz and K. Welker: Shape optimization for interface identification with obstacle problems, Vietnam Journal of Mathematics, Vol. 46, Issue 4, pp. 967-985, 2018
G. Heidel and V. Schulz: A Riemannian trust-region method for low-rank tensor completion., Numerical Linear Algebra with Applications, Vol. 25, Issue 6, 2018, DOI:10.1002/nla.2175, arXiv:1703.10019
Ch. Schenk, V. Schulz, A. Rosch and Ch. von Wallbrunn: Less cooling energy in wine fermentation - A case study in mathematical modeling, simulation and optimization, Food and Bioproducts Processing, Vol. 103, pp. 131-138, 2017
L. Grasedyck, Ch. Löbbert, G. Wittum, A. Nägel, V. Schulz, M. Siebenborn, R. Krause, P. Benedusi, Uwe Küster, and B. Dick: Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations. In: H.-J. Bungartz, Ph. Neumann, W. E. Nagel, editors, Software for Exascale Computing - SPPEXA 2013-2015, Springer Lecture Notes in Computational Science, vol. 113, pp. 507-526, 2016
V. Schulz, M. Siebenborn and K. Welker: PDE constrained shape optimization as optimization on shape manifolds, In: F. Nielsen and F. Barbaresco, editors, Geometric Science of Information, Lecture Notes in Computer Science, Volume 9389, pp. 499-508, 2015, DOI: 10.1007/978-3-319-25040-3_54.
V. Schulz and M. Siebenborn: Computational comparison of surface metrics for PDE constrained shape optimization. Computational Methods in Applied Mathematics, vol. 16, issue 3, pp. 485-496, 2016
A. Nägel, V. Schulz, M. Siebenborn, and G. Wittum: Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes. Computing and Visualization in Science, vol. 17, pp. 79-88, 2015
Dishi Liu, Alexander Litvinenko, Claudia Schillings, and V. Schulz: Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches. arXiv:1505.05731, 2016 (accepted with SIAM JUQ)
V. Schulz, M. Siebenborn and K. Welker: Efficient PDE constrained shape optimization based on Steklov-Poincaré type metrics. arXiv:1506.02244, SIAM J. Optim., Vol. 26, No. 4, pp. 2800-2819, 2016
T. Bosse, N. Gauger, A. Griewank, S. Guenther, and V. Schulz: One-shot approaches to design optimization. In G. Leuering et a., editors, Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol 165, pp. 43-66, 2014
V. Schulz, M. Siebenborn and K. Welker: Structured inverse modeling in parabolic diffusion problems, SIAM J. Control Optim., Vol. 53, No. 6, pp. 3319-3338, 2015.
V. Schulz, M. Siebenborn and K. Welker: Towards a Lagrange-Newton approach for PDE constrained shape optimization, in A. Pratelli and G. Leugering, editors, New trends in shape optimization, International Series of Numerical Mathematics, vol. 166, pages 229 - 249, 2015. (arXiv:1405.3266)
C. Schillings, and V. Schulz: On the influence of robustness measures on shape optimization with stochastic uncertainties. Optimization and Engineering, Vol. 16, No. 2, pp. 347-386, 2015, DOI 10.1007/s11081-014-9251-0
M. Siebenborn and V. Schulz: GPU accelerated discontinuous Galerkin for Euler Equation and its Adjoint, Simulation Series, Vol. 45, No. 6, pp. 15-21, 2013
M. Siebenborn, V. Schulz and S. Schmidt: A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations Computing and Visualization in Science, vol. 15, no. 2, pp. 61-73, 2012
S. Schmidt, C. Ilic, V. Schulz and N. Gauger: Three dimensional large scale aerodynamic shape optimization based on the shape calculus, AIAA Journal, Vol. 51, No. 11 (2013), pp. 2615-2627.
B. Rosenbaum and V. Schulz: Comparing sampling strategies for aerodynamic Kriging surrogate models ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 92(11-12):852-868,2012
B. Rosenbaum and V. Schulz: Efficient response surface methods based on generic surrogate models. SIAM Journal on Scientific Computing, vol. 35, No. 2, pp. B529-B550, 2013
A. Borzi and V. Schulz: Computational optimization of systems governed by partial differential equations. SIAM book series on Computational Science and Engineering 08, SIAM Philadelphia 2012. (ISBN 978-1-611972-04-7)
V. Schulz: A Riemannian view on shape optimization. Foundations of Computational Mathematics,14:483-501, 2014.
N. Gauger, C. Ilic, S. Schmidt and V. Schulz: Non-parametric aerodynamic shape optimization. in G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich and S. Ulbrich (eds.), Constrained Optimization and Optimal Control for Partial Differential Equations, International Series of Numerical Mathematics, vol, 160, pp. 289-300, Birkhäuser 2012.
S. Schmidt and V. Schulz: A 2589 Line Topology Optimization Code Written for the Graphics Card. Computing and Visualization in Science. Vol. 14, pages 249-256, 2011
S. Schmidt, C. Ilic, N. Gauger and V. Schulz: Airfoil design for compressible inviscid flow based on shape calculus. Optimization and Engineering, Vol. 12, No. 3, pp. 349-369, 2011.
S. Schmidt, V. Schulz, C. Ilic and N. Gaguer: Large scale aerodynamic shape optimization based on shape calculus. In I. H. Tuncer, editor, ECCOMAS-CFD & Optimization, 2011- 054, ISBN 978-605-61427-4-1, 2011
S. Schmidt, V. Schulz, C. Ilic and N. Gaguer: Three dimensional large scale aerodynamic shape optimization based on shape calculus. In 41st AIAA Fluid Dynamics Conference and Exhibit, number AIAA 2011-3718, Honolulu, Hawaii, 27. - 30. June 2011.
C. Schillings, S. Schmidt, and V. Schulz: Efficient shape optimization for certain and uncertain aerodyamic design. Computers and Fluids, Vol. 46, No. 1, pp. 78-87, 2011
S. Schmidt and V. Schulz: Shape derivatives for general objective functions and the incompressible Navier-Stokes equations. Control and Cybernetics, Vol. 39, No. 3, pp. 677-713, 2010
A. Borzi, V. Schulz, C. Schillings and G. von Winckel On the treatment of distributed uncertainties in PDE-constrained optimization. GAMM-Mitteilungen, Vol. 33, No. 2, pp. 230-246, 2010.
K. Ito, K. Kunisch, V. Schulz, and I. Gherman: Approximate nullspace iterations for KKT systems. SIAM J. Matrix Anal. Appl., Vol. 31, No. 4, pp. 1835-1847, 2010
V. Schulz and C. Schillings On the nature and treatment of uncertainties in aerodynamic design. AIAA Journal, vol. 47, No. 3, pp. 646-654, 2009.
K. Eppler, S. Schmidt, V. Schulz, and C. Ilic: Preconditioning the Pressure Tracking in Fluid Dynamics by Shape Hessian Information. Journal of Optimization Theory and Applications, Vol. 141, Issue 3, pages 513-531, 2009.
S. Schmidt and V. Schulz Impulse Response Approximations of Discrete Shape Hessians with Application in CFD. SIAM Journal on Control and Optimization, vol. 48, no. 4, pp. 2562-2580, 2009.
S. Schmidt and V. Schulz: Pareto-curve continuation in multi-objective optimization. Pacific Journal of Optimization, Volume 4, Number 2, pp. 243-257, 2008.
V. Schulz and G. Wittum Transforming smoothers for PDE constrained optimization problems Computing and Visualization in Science, Vol. 11., No. 4-6, pp. 207-219, 2008.
A. Borzi and V. Schulz Multigrid methods for PDE optimization. SIAM Review, Vol. 51, Issue 2, pp. 361-395, 2009
S.B. Hazra, V. Schulz, and J. Brezillon: Simultaneous Pseudo-Time Stepping for 3D Aerodynamic Shape Optimization. Journal of Numerical Mathematics, Vol. 16, No. 2, pp. 139-161, 2008.
N. Kroll, N.R. Gauger, J. Brezillon, R. Dwight, A. Fazzolari, D. Vollmer, K. Becker, H. Barnewitz, V. Schulz and S.B. Hazra Flow simulation and shape optimization for aircraft design. Journal of Computational and Applied Mathematics, Vol. 203, No. 2, pp. 397-411, 2007
B. Kaltenbacher, T. Lahmer, and V. Schulz: Optimal measurement selection for piezoelectric material tensor identification. Inverse Problems in Science and Engineering, Vol 16, No. 3, pp. 369-387, 2008.
S. B. Hazra and V. Schulz Simultaneous pseudo-timestepping for state constrained optimization problems in aerodynamics. In 'Real-Time PDE-Constrained Optimization' (Eds.: L. Biegler, O. Ghattas, M. Heinkenschloss, D. Keyes and B. van Bloemen Waanders), pp. 169-182, SIAM 2007.
I. Gherman, V. Schulz and J.T. Betts: Optimal flight trajectories for the validation of aerodynamic models. Optimization Methods and Software, Vol. 21, No. 6, pp. 889-900, 2006
S.B. Hazra and V. Schulz: Simultaneous pseudo-timestepping for aerodynamic shape optimization problems with state constraints. SIAM J. Sci. Comput., vol 28, No. 3, pp. 1078 - 1099, 2006.
I. Gherman, V. Schulz: Preconditioning of One-Shot Pseudo-Timestepping Methods for Shape Optimization. PAMM Vol. 5(1), 741 - 742, 2005
N. Kroll, N. Gauger, J. Brezillon, K. Becker, and V. Schulz: Ongoing acitivities in shape optimization within the German project MEGADESIGN. In Nettaanmaki, Rossi, Korotov, Onate, Knoerzer (eds.), ECCOMAS 2004.
S. B. Hazra, V. Schulz: On efficient computation of the optimization problem arising in inverse modeling of non-stationary multiphase multicomponent flow through porous media. Computational optimization and applications, Vol. 31, No. 1, pp.69-85, 2005
S. B. Hazra, V. Schulz, J. Brezillon, N. Gauger: Aerodynamic shape optimization using simultaneous pseudo-timestepping. Journal of Computational Physics, Vol. 204, No.1, pp. 46-64, 2005.
S. B. Hazra, H. Class, R. Helmig, V. Schulz: Forward and inverse problems in modeling of multiphase flow and transport through porous media. Computational Geosciences Vol. 8, No. 1, pp. 21-47, 2004
V. Schulz: Simultaneous solution approaches for large optimization problems, Journal for Computational and Applied Mathematics, Vol. 164-165, pp. 629-641, 2004.
S. B. Hazra, V. Schulz: Simultaneous Pseudo-timestepping for PDE-model based optimization problems. Bit Numerical Mathematics, Vol. 44, No. 3, pp. 457-472, 2004.
G. Wittum, V. Schulz, B. Maar, D. Logashenko: Numerical methods for parameter estimation in Bingham-fluids. In W. Jäger, H.-J. Krebs (eds.): Mathematics - Key Technology for the Future, pp. 204-215, Springer Berlin, Heidelberg 2003.
S. B. Hazra, V. Schulz: Numerical Parameter Identification in Multiphase Flow through Porous Media. Computing and Visualization in Science, Vol. 5, pp. 107-113, 2002.
R.H.W. Hoppe, S.I. Petrova and V.H. Schulz: A primal-dual Newton-type interior-point method for topology optimization. J.Optim.Theory Appl., Vol.114, No.3, pp. 545-571, 2002.
R. H.W. Hoppe, S. Petrova, and V. Schulz: 3D Structural Optimization in Electromagnetics. In: Proc. 13th Int. Conf. ''Domain Decomposition Methods and Applications'', Lyon, October 9-12, 2000 (N. Debit et al.; eds.), pp. 479-486, CIMNE, Barcelona, 2002.
R.H.W. Hoppe, S.I. Petrova and V.H. Schulz: Topology Optimization of High Power Electronic Devices.International Series of Numerical Mathematics (ISNM), Vol. 139, pp.119-131, 2001
D. Logashenko, B. Maar, V. Schulz, G. Wittum: Optimal geometrical design of Bingham parameter measurement devices. International Series of Numerical Mathematics (ISNM), Vol. 138, pp. 167-183, 2001.
H.G. Bock, W. Egartner, W. Kappis, V. Schulz: Practical shape optimization for turbine and compressor blades. Optimization and Engineering, Vol. 3, pp. 395-414, 2002.
Th. Dreyer, B. Maar, V. Schulz: Multigrid Optimization in Applications. Journal of Computational and Applied Mathematics, vol. 120, No. 1-2, pp. 67-84, 2000.
V. Schulz and O. Deutschmann: Process Optimization of Reactive Systems Modeled by Elementary Reactions. In F. Keil, W. Mackens, H. Voss, J. Werther (eds.), Scientific Computing in Chemical Engineering II, pp. 354-361, Springer, 1999.
B. Maar and V. Schulz: Interior Point Multigrid Methods for Topology Optimization. Structural Optimization, vol. 19, No. 3, pp. 214-224, 2000.
V. Schulz, A. Bardossy, and R. Helmig: Conditional Statistical Inverse Modeling in Groundwater Flow by Multigrid Methods. Computational Geosciences 3, pp. 49-68, 1999.
M. von Schwerin, O. Deutschmann, and V. Schulz: Process Optimization of Reactive Systems by Partially Reduced SQP Methods. Computers & Chemical Engineering, Vol. 24, pp. 89-97, 2000.



Edited publications:
Author / Title
V. Schulz and D. Seck: Shape Optimization, Homogenization and Optimal Control, DFG-AIMS workshop held at the AIM Center Senegal, March 13-16, 2017. International Series of Numerical Mathematics, vol. 169, Birkhäuser 2018
P. Benner, R. Herzog, M. Hinze, A. Rösch, A. Schiela, and V.Schulz (guest editors): Comput. Optim. Appl. (2015) 62:1-3, Special Issue for EUCCO 2013
M. Heinkenschloss, V. Schulz: Numerical Methods for PDE Constrained Optimization with Uncertain Data. Oberwolfach Reports Vol. 10. No. 1, European Mathematical Society Publishing House, 2013, pp. 239-294.
G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich and S. Ulbrich (eds.): Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, Vol, 160, Birkhäuser 2012.
M. Hinze, V. Schulz (guest editors): Special issue (Themenheft) 2 on PDE-constrained optimization, GAMM Mitteilungen, Vol. 33, No. 2, 2010.
M. Heinkenschloss, R.H.W. Hoppe, V. Schulz: Numerical Techniques for Optimization Problems with PDE Constraints. Oberwolfach Report No. 4/2009, OWR Vol. 6. No. 1, European Mathematical Society Publishing House, ISSN 1660-8933, 2009, pp.
A. Adimurti, S.B. Hazra, V. Schulz (guest editors): The first Indo-German Conference on PDE, Scientific Computing and Optimization in Applications. Special Issue of the Journal of Computational and Applied Mathematics, vol. 203, issue 2, 2007
M. Heinkenschloss, R.H.W. Hoppe, V. Schulz: Numerical Techniques for Optimization Problems with PDE Constraints. Oberwolfach Report No. 11/2006, OWR Vol. 3. No. 1, European Mathematical Society Publishing House, ISSN 1660-8933, 2006, pp. 585 - 651.
K.-H. Hoffmann, R.H.W. Hoppe, V. Schulz: Fast solution of discretized optimization problems. International Series on Numerical Mathematics (ISNM), vol. 138, Birkhäuser 2001.
V. Schulz (guest editor): SQP-based direct discretization methods for practical optimal control problems. Special issue of the Journal of Computational and Applied Mathematics, Vol 120, No. 1-2, 2000.



Other publications:
Author / Title
Alfio Borzi, Juri Merger, Jonas Müller, Achim Rosch, Christina Schenk, Dominik Schmidt, Stephan Schmidt, Volker Schulz, Kai Velten, Christian von Wallbrunn, Michael Zänglein: Novel model for wine fermentation including the yeast dying phase. arXiv:1412.6068, 2014
B. Rosenbaum and V. Schulz: Response Surface Methods for Efficient Aerodynamic Surrogate Models In N. Kroll, R. Radespiel, J. W. van der Burg and K Sorensen (eds.) Computational Flight Testing, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 123, pp. 113-130, Springer, 2013
V. Schulz and C. Schillings: Optimal Aerodynamic Design under Uncertainty In B. Eisfeld, H. Barnewitz, W. Fritz and F. Thiele (eds.) Management and Minimisation of Uncertainties and Errors in Numerical Aerdynamics, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 122, pp. 297-339, Springer, 2013
V. Schulz: Wer rechnen kann, ist klar im Vorteil - Modellgestützte Optimierung als Wirtschaftsfaktor. In Chr. Botzenhart, A. Burtscheidt und G. Hackenberg-Treutlein (Hrsg.) Gesellschaftliche Relevanz von Wissenschaft und Forschung - Ein interdisziplinärer Diskurs, Festschrift zum 20-jährigen Bestehen des Clubs der Altstipendiaten der Hanns-Seidel-Stiftung e.V., S. 220-235, Verlag Ferdinand Schöningh 2012.
V. Schulz and I. Gherman: One-Shot Methods for Aerodynamic Shape Optimization In N. Kroll, D. Schwamborn, K. Becker, H. Rieger and F. Thiele (eds.) MEGADESIGN and MegaOpt - German Initiatives for Aerodynamic Simulation and Optimization in Aircraft Design, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 107, pp. 207-220, Springer, 2009
H.G. Bock and V. Schulz: Mathematical aspects of CFD-model based optimization. In D. Thevenin and G. Janiga (eds.) Optimization and computational fluid dynamics, pp.61-78, Springer, 2007.
H. G. Bock, E. Kostina, A. Schäfer, J. P. Schlöder, and V. Schulz: Multiple set point partially reduced SQP method for optimal control of PDE In W. Jäger, R. Rannacher, and J.Warnatz (eds.) Reactive Flows, Diffusion and Transport, pp. 147-176, Springer, 2007
S.B. Hazra and V. Schulz: How to profit from adjoints in one-shot pseudotime-stepping optimization. Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems, EUROGEN 2005 (Eds.: R. Schilling et. al.), 2005.
D. Logashenko, B. Maar, V. Schulz, G. Wittum: Parameter estimation and geometrical optimal design for Bingham measurement devices. WIAS-Preprint No. 642, WIAS Berlin 2001.
R. H.W. Hoppe, S. Petrova, and V. Schulz: Topology Optimization of Conductive Media Described by Maxwell's Equations Proceedings of the Second International Conference on Numerical Analysis and Applications NAA/2000, June 11-15, 2000, Rousse, Bulgaria, in: Lecture Notes in Computer Science (L.~Vulkov et al.; eds.), Springer, 1988, pp.414-422, 2001.
V.H. Schulz: Alles optimal? - Mathematische Optimierung an den Lehrbuchgrenzen. Forschungsverbund Berlin e.V. Journal, No. 46, 10. Jahrgang, S. 6, 2001.
V.H. Schulz: Direct Discretization Methods for Optimization Boundary Value Problems in DAE. In A. Beghi, L. Finesso, G. Picci (eds.): Mathematical Theory of Networks and Systems, pp. 669 - 672, Il Poligrafo, Padua, 1999.


Last modified: April 23, 2019

. . .
.
Fachbereich IV - Mathematik
Universität Trier, 54286 Trier
.
. . .