Preprints
Alla, A.; Schmidt, A. & Haasdonk, B.:
Model order reduction approaches for infinite horizon optimal control problems via the HJB equation,
University of Stuttgart,
2016.
@techreport
{ASH16,
author = {Alessandro Alla and Andreas Schmidt and Bernard Haasdonk}
,
title = {Model order reduction approaches for infinite horizon optimal control problems via the HJB equation}
,
year = {2016}
,
note = {Accepted for publication in MoRePaS 2015 Special Issue}
,
url = {https://arxiv.org/abs/1607.02337}
}
Abstract: We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati equation based approach. Finally, we present numerical examples and discuss several features of the different methods analyzing advantages and disadvantages of the reduction methods.
Carlberg, K.; Brencher, L.; Haasdonk, B. & Barth, A.:
Data-driven time parallelism via forecasting,
2016.
@unpublished
{CBHB16,
author = {Carlberg, Kevin and Brencher, Lukas and Haasdonk, Bernard and Barth, Andrea}
,
title = {Data-driven time parallelism via forecasting}
,
year = {2016}
,
note = {submitted to SIAM J. of Sci. Comp.}
}
De Marchi, S.; Iske, A. & Santin, G.:
Image Reconstruction from Scattered Radon Data by Weighted Positive Definite Kernel Functions,
2017.
@techreport
{DeMarchi2017,
author = {De Marchi,Stefano and Iske, Armin and Santin, Gabriele}
,
title = {Image Reconstruction from Scattered Radon Data by Weighted Positive Definite Kernel Functions}
,
year = {2017}
}
Fritzen, F.; Haasdonk, B.; Ryckelynck, D. & Schöps, S.:
An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem,
University of Stuttgart,
2016.
@techreport
{FHRS16,
author = {Felix Fritzen and Bernard Haasdonk and David Ryckelynck and Sebastian Schöps}
,
title = {An algorithmic comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a nonlinear thermal problem}
,
year = {2016}
,
url = {https://arxiv.org/abs/1610.05029}
}
Geßner, T.; Haasdonk, B.; Lenz, M.; Metscher, M.; Neubauer, R.; Ohlberger, M.; Rosenbaum, W.; Rumpf, M.; Schwörer, R.; Spielberg, M. & Weikard, U.:
A Procedural Interface for Multiresolutional Visualization of General Numerical Data,
University of Bonn,
1999.
@techreport
{Gessner1999,
author = {T. Geßner and B. Haasdonk and M. Lenz and M. Metscher and R. Neubauer and M. Ohlberger and W. Rosenbaum and M. Rumpf and R. Schwörer and M. Spielberg and U. Weikard}
,
title = {A Procedural Interface for Multiresolutional Visualization of General Numerical Data}
,
year = {1999}
,
number = {28}
}
Haasdonk, B.:
Reduzierte-Basis-Methoden, Vorlesungsskript SS 2011,
University of Stuttgart,
2011.
@techreport
{Haasdonk2011c,
author = {B. Haasdonk}
,
title = {Reduzierte-Basis-Methoden, Vorlesungsskript SS 2011}
,
year = {2011}
,
number = {2011-004}
}
Haasdonk, B.:
Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems,
IANS, University of Stuttgart, Germany,
2014.
@techreport
{Haasdonk2014a,
author = {B. Haasdonk}
,
title = {Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems}
,
year = {2014}
,
note = {Chapter in P. Benner, A. Cohen, M. Ohlberger and K. Willcox (eds.): "Model Reduction and Approximation: Theory and Algorithms", SIAM, Philadelphia, 2017}
,
url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938}
}
Haasdonk, B. & Ohlberger, M.:
Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations,
University of Freiburg, Institute of Applied Mathematics,
2006.
@techreport
{Haasdonk2006b,
author = {B. Haasdonk and M. Ohlberger}
,
title = {Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations}
,
year = {2006}
,
number = {12/2006}
,
note = {Extended version of M2AN article.}
}
Haasdonk, B.; Ohlberger, M. & Rozza, G.:
A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators,
University of Münster,
2007.
@techreport
{HOR07,
author = {B. Haasdonk and M. Ohlberger and G. Rozza}
,
title = {A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators}
,
year = {2007}
,
number = {09/07 - N, FB 10}
,
note = {Accepted by ETNA.}
}
Abstract: During the last decades, reduced basis (RB) methods have been developed to a wide methodology for model reduction of problems that are governed by parametrized partial differential equations ($P^2DE$s ). In particular equations of elliptic and parabolic type for linear, low polynomial or monotonic nonlinearities have been treated successfully by RB methods using finite element schemes. Due to the characteristic offline-online decomposition, the reduced models often become suitable for a multi-query or real-time setting, where simulation results, such as field-variables or output estimates, can be approximated reliably and rapidly for varying parameters. In the current study, we address a certain class of time-dependent evolution schemes with explicit discretization operators that are arbitrarily parameter dependent. We extend the RB-methodology to these cases by applying the empirical interpolation method to localized discretization operators. The main technical ingredients are: (i) generation of a collateral reduced basis modelling the effects of the discretization operator under parameter variations in the offline-phase and (ii) an online simulation scheme based on a numerical subgrid and localized evaluations of the evolution operator. We formulate an a-posteriori error estimator for quantification of the resulting reduced simulation error. Numerical experiments on a parametrized convection problem, discretized with a finite volume scheme, demonstrate the applicability of the model reduction technique. We obtain a parametrized reduced model, which enables parameter variation with fast simulation response. We quantify the computational gain with respect to the non-reduced model and investigate the error convergence.
Haasdonk, B.; Ohlberger, M.; Rumpf, M.; Schmidt, A. & Siebert, K.-G.:
h-p-Multiresolution Visualization of Adaptive Finite Element Simulations,
Mathematics Department, University of Freiburg,
2001.
@techreport
{Haasdonk2001c,
author = {B. Haasdonk and M. Ohlberger and M. Rumpf and A. Schmidt and K.-G. Siebert}
,
title = {h-p-Multiresolution Visualization of Adaptive Finite Element Simulations}
,
year = {2001}
,
number = {Preprint 01-26}
}
Haasdonk, B.; Poluru, B. & Teynor, A.:
Presto-Box 1.1 Library Documentation,
IIF-LMB, Universität Freiburg,
2003.
@techreport
{Haasdonk2003,
author = {Haasdonk, B. and Poluru, B.R. and Teynor, A.}
,
title = {Presto-Box 1.1 Library Documentation}
,
year = {2003}
,
number = {2/03}
}
Haasdonk, B.; Salomon, J. & Wohlmuth, B.:
A Reduced Basis Method for Parametrized Variational Inequalities,
University of Stuttgart,
2012.
@techreport
{HSW12preprint,
author = {B. Haasdonk and J. Salomon and B. Wohlmuth}
,
title = {A Reduced Basis Method for Parametrized Variational Inequalities}
,
year = {2012}
}
Haasdonk, B. & Santin, G.:
Greedy Kernel Approximation for Sparse Surrogate Modelling,
2017.
@techreport
{HS2017a,
author = {B. Haasdonk and G. Santin}
,
title = {Greedy Kernel Approximation for Sparse Surrogate Modelling}
,
year = {2017}
}
Pekalska, E. & Haasdonk, B.:
Kernel Quadratic Discriminant Analysis with Positive and Indefinite Kernels,
University of Münster,
2008.
@techreport
{Pekalska2008a,
author = {E. Pekalska and B. Haasdonk}
,
title = {Kernel Quadratic Discriminant Analysis with Positive and Indefinite Kernels}
,
year = {2008}
,
number = {06/08}
}
Tempel, P.; Schmidt, A.; Haasdonk, B. & Pott, A.:
Application of the Rigid Finite Element Method to the Simulation of Cable-Driven Parallel Robots,
University of Stuttgart,
2017.
@techreport
{TSHP17,
author = {Tempel, P. and Schmidt, A. and Haasdonk, B. and Pott, A.}
,
title = {Application of the Rigid Finite Element Method to the Simulation of Cable-Driven Parallel Robots}
,
year = {2017}
}
Wirtz, D. & Haasdonk, B.:
An Improved Vectorial Kernel Orthogonal Greedy Algorithm,
University of Stuttgart,
2012.
@techreport
{WH12c_pre,
author = {D. Wirtz and B. Haasdonk}
,
title = {An Improved Vectorial Kernel Orthogonal Greedy Algorithm}
,
year = {2012}
,
note = {In preparation}
,
url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=742}
}
Abstract: This work is concerned with derivation and analysis of a modifed vectorial kernel orthogonal greedy algorithm (VKOGA) for approximation of nonlinear vectorial functions. The algorithm pursues simultaneous approximation of all vector components over a shared linear subspace of the underlying function Hilbert space in a greedy fashion [14, 33] and inherits the selection principle of the f=P-Greedy algorithm [18]. For the considered algorithm we perform a limit analysis of the selection criteria for already included subspace basis functions. We show that the approximation gain is bounded globally and for the multivariate case the limit functions correspond to a directional Hermite interpolation. We further prove algebraic convergence similar to [13], improved by a dimension-dependent factor, and introduce a new a-posteriori error bound. Comparison to related variants of our algorithm are presented. Targeted applications of this algorithm are model reduction of multiscale models [40].
Wirtz, D.; Karajan, N. & Haasdonk, B.:
Model order reduction of multiscale models using kernel methods,
SRC SimTech, University of Stuttgart, Germany,
2012.
@techreport
{WHK13_pre,
author = {D. Wirtz and N. Karajan and B. Haasdonk}
,
title = {Model order reduction of multiscale models using kernel methods}
,
year = {2012}
,
note = {Submitted}
}
Wirtz, D.; Sorensen, D. & Haasdonk, B.:
A-posteriori error estimation for DEIM reduced nonlinear dynamical systems,
University of Stuttgart,
2012.
@techreport
{WSH12_pre,
author = {D. Wirtz and D.C. Sorensen and B. Haasdonk}
,
title = {A-posteriori error estimation for DEIM reduced nonlinear dynamical systems}
,
year = {2012}
,
note = {Submitted to SISC}
,
url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733}
}
Abstract: In this work an effcient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affne linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method [Chaturantabut & Sorensen (2010)]. The proposed a-posteriori error estimator can be effciently decomposed in an offine/online fashion and is obtained by a one dimensional auxiliary ODE during reduced simulations. Key elements for effcient online computation are partial similarity transformations and matrix DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model.
Wittwar, D.; Schmidt, A. & Haasdonk, B.:
Reduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation,
University of Stuttgart,
2017.
@techreport
{WSH17,
author = {Wittwar, D. and Schmidt, A. and Haasdonk, B.}
,
title = {Reduced Basis Approximation for the Discrete-time Parametric Algebraic Riccati Equation}
,
year = {2017}
}
