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16 papers · 1 filter
Hankel-Norm Approximation of Large-Scale Descriptor Systems
Peter Benner, Steffen W. R. Werner
The Hankel-norm approximation is a model reduction method which provides the best approximation in the Hankel semi-norm. In this paper the computation of the optimal Hankel-norm ap…
Preconditioning PDE-constrained optimization with -sparsity and control constraints
Margherita Porcelli, Valeria Simoncini, Martin Stoll
PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the…
Space-time Galerkin POD with application in optimal control of semi-linear parabolic partial differential equations
Manuel Baumann, Peter Benner, Jan Heiland
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted a…
emgr - The Empirical Gramian Framework
Christian Himpe
System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were…
Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system
Jessica Bosch, Christian Kahle, Martin Stoll
Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow, Applied Numerical…
-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems
Peter Benner, Pawan Goyal, Serkan Gugercin
We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analy…