# Publications 2017

** Alla, A.; Schmidt, A. & Haasdonk, B.:**
*Benner, Peter and Ohlberger, Mario and Patera, Anthony and Rozza, Gianluigi and Urban, Karsten **(Eds.)*,
Model Order Reduction Approaches for Infinite Horizon Optimal Control Problems via the HJB Equation,
*Model Reduction of Parametrized Systems, *
*Springer International Publishing, *
**2017**, 333-347.

@inbook
{ASH2017,

author = {Alla, Alessandro and Schmidt, Andreas and Haasdonk, Bernard}
,

editor = {Benner, Peter and Ohlberger, Mario and Patera, Anthony and Rozza, Gianluigi and Urban, Karsten}
,

title = {Model Order Reduction Approaches for Infinite Horizon Optimal Control Problems via the HJB Equation}
,

booktitle = {Model Reduction of Parametrized Systems}
,

publisher = {Springer International Publishing}
,

year = {2017}
,

pages = {333--347}
,

url = {https://doi.org/10.1007/978-3-319-58786-8_21}
,

doi = {10.1007/978-3-319-58786-8_21}
}

**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.

** De Marchi, S.; Idda, A. & Santin, G.:**
*Fasshauer, Gregory E. and Schumaker, Larry L. **(Eds.)*,
A Rescaled Method for RBF Approximation,
*Approximation Theory XV: San Antonio 2016, *
*Springer International Publishing, *
**2017**, 39-59.

@inbook
{DeMarchi2017b,

author = {De Marchi, Stefano and Idda, Andrea and Santin, Gabriele}
,

editor = {Fasshauer, Gregory E. and Schumaker, Larry L.}
,

title = {A Rescaled Method for RBF Approximation}
,

booktitle = {Approximation Theory XV: San Antonio 2016}
,

publisher = {Springer International Publishing}
,

year = {2017}
,

pages = {39--59}
,

url = {https://doi.org/10.1007/978-3-319-59912-0_3}
,

doi = {10.1007/978-3-319-59912-0_3}
}

**Abstract: ** In the recent paper [1], a new method to compute stable kernel-based interpolants has been presented. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allows us to consider its error and stability properties.

** Dibak, C.; Schmidt, A.; Dürr, F.; Haasdonk, B. & Rothermel, K.:**
Server-Assisted Interactive Mobile Simulations for Pervasive Applications,
*Proceedings of the 15th IEEE International Conference on Pervasive Computing and Communications (PerCom), *
*University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Germany, *
*IEEE, *
**2017**, 1-10.

@inproceedings
{Dibak17,

author = {Christoph Dibak and Andreas Schmidt and Frank Dürr and Bernard Haasdonk and Kurt Rothermel}
,

title = {Server-Assisted Interactive Mobile Simulations for Pervasive Applications}
,

booktitle = {Proceedings of the 15th IEEE International Conference on Pervasive Computing and Communications (PerCom)}
,

publisher = {IEEE}
,

year = {2017}
,

pages = {1--10}
,

url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2017-02&engl=1}
}

**Abstract: ** Currently, various hardware and software companies are developing augmented reality devices, most prominently Microsoft with its Hololens. Besides gaming, such devices can be used for serious pervasive applications, like interactive mobile simulations to support engineers in the field. Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy. Therefore, we propose a framework to support mobile simulations by distributing the computation between mobile device and a remote server. For the computation of parameter-dependent solutions of the simulation, we use the reduced basis method, which allows to drastically reduce the computation time and energy consumption. We present three approaches for the distributed execution of the reduced basis method between mobile device and server. Evaluations show that we can speed-up the numerical computation to over 131 times while using 73 times less energy compared to offloading everything to a server.

** Fehr, J.; Grunert, D.; Bhatt, A. & Hassdonk, B.:**
A Sensitivity Study of Error Estimation in Reduced Elastic Multibody Systems,
*Proceedings of MATHMOD 2018, Vienna, Austria, *
**2017**.

@inproceedings
{Fehr2017,

author = {Fehr, J. and Grunert, D. and Bhatt, A. and Hassdonk, B.}
,

title = {A Sensitivity Study of Error Estimation in Reduced Elastic Multibody Systems}
,

booktitle = {Proceedings of MATHMOD 2018, Vienna, Austria}
,

year = {2017}
}

** Haasdonk, B.:**
*P. Benner and A. Cohen and M. Ohlberger and K. Willcox **(Eds.)*,
Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems,
*Model Reduction and Approximation: Theory and Algorithms, *
*SIAM, Philadelphia, *
**2017**, 65-136.

@incollection
{Haasdonk2017,

author = {B. Haasdonk}
,

editor = {P. Benner and A. Cohen and M. Ohlberger and K. Willcox}
,

title = {Reduced Basis Methods for Parametrized PDEs -- A Tutorial Introduction for Stationary and Instationary Problems}
,

booktitle = {Model Reduction and Approximation: Theory and Algorithms}
,

publisher = {SIAM, Philadelphia}
,

year = {2017}
,

pages = {65--136}
,

url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=938}
}

** Haasdonk, B. & Santin, G.:**
Greedy Kernel Approximation for Sparse Surrogate Modelling,
*Proceedings of the KoMSO Challenge Workshop on Reduced-Order Modeling for Simulation and Optimization, *
**2017**.

@inproceedings
{HS2017a,

author = {B. Haasdonk and G. Santin}
,

title = {Greedy Kernel Approximation for Sparse Surrogate Modelling}
,

booktitle = {Proceedings of the KoMSO Challenge Workshop on Reduced-Order Modeling for Simulation and Optimization}
,

year = {2017}
,

url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1613}
}

**Abstract: ** Modern simulation scenarios frequently require multi-query or real-time responses of simulation models for statistical analysis, optimization or process control. However, the underlying simulation models may be very time-consuming rendering the simulation task difficult or infeasible. This motivates the need for rapidly computable surrogate models. We address the case of surrogate modelling of functions from vectorial input to vectorial output spaces. These appear for instance in simulation of coupled models or in the case of approximating general input-output maps. We review some recent methods and theoretical results in the field of greedy kernel approximation schemes. In particular we recall the VKOGA procedure for approximating vector valued functions. We collect some recent con- vergence statements that provide sound foundation for these algorithms, in particular quasi-optimal convergence rates in case of kernels inducing Sobolev spaces. We provide some initial experiments that can be obtained with non-symmetric greedy kernel approximation schemes. The results indicate better stability and hence overall more accurate models.

** Martini, I.; Rozza, G. & Haasdonk, B.:**
Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models,
*Journal of Scientific Computing, *
**2017**.

@article
{Martini2015,

author = {Martini, I. and Rozza, G. and Haasdonk, B.}
,

title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models}
,

journal = {Journal of Scientific Computing}
,

year = {2017}
,

url = {http://link.springer.com/article/10.1007/s10915-017-0430-y}
,

doi = {10.1007/s10915-017-0430-y}
}

** Santin, G. & Haasdonk, B.:**
Convergence rate of the data-independent P-greedy algorithm in kernel-based approximation,
*Dolomites Research Notes on Approximation, *
**2017***, 10*, 68-78.

@article
{SH16b,

author = {G. Santin and B. Haasdonk}
,

title = {Convergence rate of the data-independent P-greedy algorithm in kernel-based approximation}
,

journal = {Dolomites Research Notes on Approximation}
,

year = {2017}
,

volume = {10}
,

pages = {68--78}
,

url = {http://www.emis.de/journals/DRNA/9-2.html}
}

**Abstract: ** Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples’ locations on the behavior of the approximation, and feasible optimal strategies are not known for general problems. Nevertheless, efficient and greedy point-selection strategies are known. This paper gives a proof of the convergence rate of the data-independent $P$-greedy algorithm, based on the application of the convergence theory for greedy algorithms in reduced basis methods. The resulting rate of convergence is shown to be quasi-optimal in the case of kernels generating Sobolev spaces. As a consequence, this convergence rate proves that, for kernels of Sobolev spaces, the points selected by the algorithm are asymptotically uniformly distributed, as conjectured in the paper where the algorithm has been introduced

** Schmidt, A. & Haasdonk, B.:**
Reduced basis approximation of large scale parametric algebraic Riccati equations,
*ESAIM: Control, Optimisation and Calculus of Variations, *
*EDP Sciences, *
**2017**.

@article
{SH17,

author = {Schmidt, Andreas and Haasdonk, Bernard}
,

title = {Reduced basis approximation of large scale parametric algebraic Riccati equations}
,

journal = {ESAIM: Control, Optimisation and Calculus of Variations}
,

publisher = {EDP Sciences}
,

year = {2017}
,

url = {http://dx.doi.org/10.1051/cocv/2017011}
,

doi = {10.1051/cocv/2017011}
}

** Tempel, P.; Schmidt, A.; Haasdonk, B. & Pott, A.:**
Application of the Rigid Finite Element Method to the Simulation of Cable-Driven Parallel Robots,
*Computational Kinematics, *
*Springer International Publishing, *
**2017**, 198-205.

@incollection
{Tempel2017,

author = {Philipp Tempel and Andreas Schmidt and Bernard Haasdonk and Andreas Pott}
,

title = {Application of the Rigid Finite Element Method to the Simulation of Cable-Driven Parallel Robots}
,

booktitle = {Computational Kinematics}
,

publisher = {Springer International Publishing}
,

year = {2017}
,

pages = {198--205}
,

url = {https://doi.org/10.1007%2F978-3-319-60867-9_23}
,

doi = {10.1007/978-3-319-60867-9_23}
}