Literatur

Books
2011
[BennHM11] Model Reduction for Circuit Simulation, (Peter Benner, Michael Hinze, E. Jan W. ter Maten, eds.), Springer-Verlag: Berlin, Heidelberg, volume 74, 2011.
2009
[HinzePinnauUlbrichUlbrich] Optimization with PDE constraints (M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich), Springer, volume 23, 2009.
2008
[SchiVR08] Model Order Reduction: Theory, Research Aspects and Applications, (W. Schilders, H. van der Vorst, J. Rommes, eds.), Springer, Berlin, Heidelberg, volume 13, 2008.
2007
[PatR07] Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Partial Differential Equations (A. T. Patera, G. Rozza), MIT, 2007. [pdf]
2005
[BenMS05] Dimension Reduction of Large-Scale Systems, (P. Benner, V. Mehrmann, D. Sorensen, eds.), Springer-Verlag, Berlin/Heidelberg, volume 45, 2005.
1996
[HolLB96] Turbulence, Coherent Structures, Dynamical Systems and Symmetry (P. Holmes, J. Lumley, G. Berkooz), Cambridge University Press, 1996.
Book Chapters
2012
[Drewes] Subgradient Based Outer Approximation for Mixed Integer Second Order Cone Programming (S. Drewes, S. Ulbrich), Chapter in Mixed Integer Nonlinear Programming, Springer, volume 154, 2012.
[Clever] Generalized Multilevel SQP-Methods for PDAE-constrained Optimization Based on Space-Time Adaptive PDA Solvers (D. Clever, J. Lang, S. Ulbrich, J. C. Ziems), Chapter in Constrained optimization and optimal control for partial differential equations, Birkhäuser Verlag, volume 160, 2012.
2011
[StrR11] Model order reduction of nonlinear systems in circuit simulation: status and applications (M. Striebel, J. Rommes), Chapter in (Peter Benner, Michael Hinze, E. Jan W. ter Maten, eds.), Springer-Verlag: Berlin, Heidelberg, volume 74, 2011.
[HKV11] POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks (M. Hinze, M. Kunkel, M. Vierling), Chapter in , Springer, volume 74, 2011.
2009
[VerMSM10] Model order reduction for nonlinear IC models (A. Verhoeven, E. Jan W. ter Maten, M. Striebel, R. Mattheij), Chapter in (A. Korytowski, K. Malanowski, W. Mitkowski, M. Szymkat, eds.), Springer-Verlag, volume 312, 2009.
2008
[IoaC08] Reduced order models of on-chip passive components and interconnects, workbench and test structures, in Model Order Reduction: Theory, Research Aspects and Applications (D. Ioan, G. Ciuprina), Chapter in (W. Schilders, H. van der Vorst, J. Rommes, eds.), Springer, Berlin, Heidelberg, volume 13, 2008.
[HiVo05] Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition (M. Hinze, S Volkwein), Chapter in 10 (P. Benner, V. Mehrmann, D. Sorensen, eds.), Springer-Verlag, Berlin/Heidelberg, volume 39, 2008.
2005
[HinzeVolkwein] Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: error estimates and suboptimal control (Michael Hinze, Stefan Volkwein), Chapter in Dimension reduction of large-scale systems, Springer, volume 45, 2005. [doi]
2001
[AfHi01] Adaptive Control of A Wake Flow Using Proper Orthogonal Decomposition (Konstantin Afanasiev, Michael Hinze), Chapter in 13 (Michael P. Polis, John Cagnol, Jean-Paul Zolésio, eds.), CRC Press, 2001. [doi]
Refereed Articles
2013
[Roth] A Discrete Adjoint Approach for the Optimization of Unsteady Turbulent Flows (R. Roth, S. Ulbrich), In Flow, Turbulence and Combustion, 2013. (To appear) [doi]
[Herkt_2013aa] Convergence analysis of Galerkin POD for linear second order evolution equations (S. Herkt, M. Hinze, R. Pinnau), In to appear in ETNA, 2013.
2012
[SichauUlbrich] A Second Order Approximation Technique for Robust Shape Optimization (A. Sichau, S. Ulbrich), In Journal of Applied Mechanics and Materials, volume 104, 2012.
[HessUlbrich] An Inexact l1 Penalty SQP Algorithm for PDE Constrained Optimization with an Application to Shape Optimization in Linear Elasticity (W. Hess, S. Ulbrich), In Optimization Methods and Software, 2012. (in press) [doi]
[HKSS12] Model order reduction of coupled circuit-device systems (M. Hinze, M. Kunkel, A. Steinbrecher, T. Stykel), In Int. J. Numer. Model., volume 25, 2012. [doi]
2011
[ZiemsUlbrich] Adaptive multilevel inexact SQP methods for PDE-constrained optimization (J. Carsten Ziems, Stefan Ulbrich), In SIAM J. Optim., volume 21, 2011. [doi]
2010
[TUV10] Comparison of the Reduced-Basis and POD a-Posteriori Error Estimators for an Elliptic Linear-Quadratic Optimal Control Problem (T. Tomm, K. Urban, S. Volkwein), In Mathematical and Computer Modelling of Dynamical Systems, 2010.
[Giles1] Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 1: Linearized approximations and linearized output functionals (M. Giles, S. Ulbrich), In SIAM J. Numer. Anal., volume 48, 2010.
[Giles] Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 2: Adjoint approximations and extensions (M. Giles, S. Ulbrich), In SIAM J. Numer. Anal., volume 48, 2010.
[CS10] Nonlinear model reduction via discrete empirical interpolation (S. Charturantabut, D. Sorensen), In SIAM J. Sci. Comput., volume 32, 2010.
[Bertsimas] Nonconvex robust optimization for problems with constraints (Dimitris Bertsimas, Omid Nohadani, Kwong Meng Teo), In INFORMS J. Comput., volume 22, 2010. [doi]
2009
[NSMT09] System reduction for Galerkin models of fluid flow (B.R. Noack, M. Schlegel, M. Morzyński, G. Tadmor), In Int. J. Numer. Meth. Fluids, volume 63, 2009.
[HiKuVi09] POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks (M. Hinze, M. Kunkel, M. Vierling), In Hamburger Beiträge zur Angewandten Mathematik 2009-03, 2009.
[FenBK09] Parametric model order reduction accelerated by recycling algorithm (L Feng, P. Benner, J. Korvink), In Proc. 48th IEEE CDC and 28th Chinese Control Conf., 2009. (Los Alamitos, CA)
2008
[HiVo08] Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition (M. Hinze, S. Volkwein), In Comput. Optim. Appl., volume 39, 2008.
[HaasO08] Reduced basis method for finite volume approximations of parametrized linear evolution equations (B. Haasdonk, M. Ohlberger), In Math. Model. Numer. Anal., volume 42, 2008. (~)
[GrattonSartenaerToint] Recursive trust-region methods for multiscale nonlinear optimization (Serge Gratton, Annick Sartenaer, Philippe L. Toint), In SIAM J. Optim., volume 19, 2008. [doi]
[CleHSetal08] Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields (M. Clemens, M. Helias, T. Steinmetz, G. Wimmer), In J. Comput. Appl. Math., volume 215, 2008.
2006
[WitSchWei2006] Model order reduction for large systems in computational electromagnetics (T. Wittig, R. Schuhmann, T. Weiland), In Linear Algebra and Its Applications: Special Issue on Order Reduction of Large-Scale Systems, volume 415, 2006.
[BockDiehl] An approximation technique for robust nonlinear optimization (Moritz Diehl, Hans Georg Bock, Ekaterina Kostina), In Math. Program., volume 107, 2006. [doi]
2005
[Rowl05] Model reduction for fluids, using balanced proper orthogonal decomposition (C.W. Rowley), In Internat. J. Bifur. Chaos Appl. Sci. Engrg, volume 15, 2005.
[LewisNash] Model problems for the multigrid optimization of systems governed by differential equations (Robert Michael Lewis, Stephen G. Nash), In SIAM J. Sci. Comput., volume 26, 2005. [doi]
[BorziKunisch] A multigrid scheme for elliptic constrained optimal control problems (A. Borzì, K. Kunisch), In Comput. Optim. Appl., volume 31, 2005. [doi]
[BCB05] Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced order model (M. Bergmann, L. Cordier, J. Brancher), In Phys. Fluids, volume 17, 2005.
2004
[UlbrichUlbrichVicente] A globally convergent primal-dual interior-point filter method for nonlinear programming (Michael Ulbrich, Stefan Ulbrich, Luís N. Vicente), In Math. Program., volume 100, 2004. [doi]
[Ulbrich] On the superlinear local convergence of a filter-SQP method (Stefan Ulbrich), In Math. Program., volume 100, 2004. [doi]
2002
[WitMSetal02a] Model order reduction and equivalent circuit extraction for fit discretized electromagnetic systems (T. Wittig, I. Munteanu, Schuhmann R., T. Weiland), In International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, volume 15, 2002.
[WitMSetal02] Two-step Lanczos algorithm for model order reduction (T. Wittig, I. Munteanu, R. Schuhmann, T. Weiland), In IEEE Transactions on Magnetics, volume 38, 2002.
[WillP02] Balanced model reduction via the proper orthogonal decomposition (K. Willcox, J. Peraire), In AIAA Journal, volume 40, 2002.
2000
[HK2000] Three control methods for time – dependent Fluid Flow Flow (M. Hinze, K. Kunisch), In Turbulence and Combustion, volume 65, 2000.
[BeckerKappRannacher] Adaptive finite element methods for optimal control of partial differential equations: basic concept (Roland Becker, Hartmut Kapp, Rolf Rannacher), In SIAM J. Control Optim., volume 39, 2000. [doi]
1987
[Sir87] Turbulence and the dynamics of coherent structures. I: Coherent structures. II: Symmetries and transformations. III: Dynamics and scaling (L. Sirovich), In Q. Appl. Math., volume 45, 1987.
Refereed Conference Papers
2012
[HK10] Residual based sampling in POD model order reduction of drift-diffusion equations in parametrized electrical networks (M. Hinze, M. Kunkel), In ZAMM, volume 92, 2012.
2011
[Hinze_2011aa] Model order reduction for networks of ODE and PDE systems (M. Hinze, U. Matthes), In Proceedings of the IFIP 2011, 2011. (accepted for publication)
1998
[HK1998] On Suboptimal Control Strategies for the Navier-Stokes Equations (M. Hinze, K. Kunisch), In ESAIM: Proceedings, volume 4, 1998.
[HKM10] POD Model Order Reduction of electrical networks with semiconductors modeled by the transient Drift-Diffusion equations (M. Hinze, M. Kunkel, U. Matthes), In .
[HK2012] Discrete empirical interpolation in POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks (M. Hinze, M. Kunkel), In .
Other Publications
2011
[ZiemsUlbrich1] Adaptive Multilevel Generalized SQP-Methods for PDE-constrained Optimization (J. Carsten Ziems, Stefan Ulbrich), Technical report, Department of Mathematics, TU Darmstadt, Germany, 2011. (Submitted) [pdf]
2003
[Rewi03] A Trajectory Piecewise-Linear Approach to Model Order Reduction of Nonlinear Dynamical Systems (M. Rewieński), PhD thesis, , 2003.
2000
[Sachs] Trust-region Proper Orthogonal Decomposition for Flow Control (E. Arian, M. Fahl, E. W. Sachs), Technical report, NASA/CR-2000-210124, ICASE Report, 2000.
[AFS00] Trust-region proper orthogonal decomposition for flow control (E. Arian, M. Fahl, E. Sachs), 2000. (2000-25, NASA/CR-2000-210124, ICASE Report)