46 citations · 165 across the 25 of their papers we have counts for
26 papers
Perspectives on Sustainable Computational Science and Engineering
Julia Kowalski, Ann S. Almgren, Achim Basermann +43
Computational Science and Engineering (CSE) combines expertise at the intersection of engineering, applied mathematics, and computer science to form powerful methods for model-base…
On the Solution of Large-scale Non-autonomous Differential Riccati Equations: a Numerical Study
Eugenio Mancinelli, Davide Palitta, Jens Saak
We explore the numerical solution of large-scale non-autonomous Differential Riccati Equations (DREs). While we assume to discretize the differential operator using a Backward Diff…
Reduced rank extrapolation for multi-term Sylvester equations
Peter Benner, Pascal den Boef, Patrick Kürschner +2
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and impleme…
Towards a mixed-precision ADI method for Lyapunov equations
Jonas Schulze, Jens Saak
We apply mixed-precision to the low-rank Lyapunov ADI (LR-ADI) by performing certain aspects of the algorithm in a lower working precision. Namely, we accumulate the overall soluti…
Towards an Efficient Shifted Cholesky QR for Applications in Model Order Reduction using pyMOR
Maximilian Bindhak, Art J. R. Pelling, Jens Saak
Many model order reduction (MOR) methods rely on the computation of an orthonormal basis of a subspace onto which the large full order model is projected. Numerically, this entails…
Application of operator inference to reduced-order modeling of constrained mechanical systems
Peter Benner, Yevgeniya Filanova, Igor Pontes Duff +1
Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-…
Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences
Pascal den Boef, Patrick Kürschner, Xiaobo Liu +5
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In thi…
A unifying framework for ADI-like methods for linear matrix equations and beneficial consequences
Jonas Schulze, Jens Saak
We derive the alternating-directions implicit (ADI) method based on a commuting operator split and apply the results in detail to the continuous time algebraic Lyapunov equation wi…
Numerical methods for closed-loop systems with non-autonomous data
B. Baran, P. Benner, J. Saak +1
By computing a feedback control via the linear quadratic regulator (LQR) approach and simulating a non-linear non-autonomous closed-loop system using this feedback, we combine two…
Using factorizations in Newton's method for solving general large-scale algebraic Riccati equations
Jens Saak, Steffen W. R. Werner
Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be…
Efficient solution of sequences of parametrized Lyapunov equations with applications
Davide Palitta, Zoran Tomljanović, Ivica Nakić +1
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall proce…
Diagonally-Addressed Matrix Nicknack: How to improve SpMV performance
Jens Saak, Jonas Schulze
We suggest a technique to reduce the storage size of sparse matrices at no loss of information. We call this technique Diagonally-Adressed (DA) storage. It exploits the typically l…
Towards a Benchmark Framework for Model Order Reduction in the Mathematical Research Data Initiative (MaRDI)
Peter Benner, Kathryn Lund, Jens Saak
The race for the most efficient, accurate, and universal algorithm in scientific computing drives innovation. At the same time, this healthy competition is only beneficial if the r…
Research-Data Management Planning in the German Mathematical Community
Tobias Boege, René Fritze, Christiane Görgen +13
In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized a…
Riccati-feedback Control of a Two-dimensional Two-phase Stefan Problem
Björn Baran, Peter Benner, Jens Saak
We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement t…
On an integrated Krylov-ADI solver for large-scale Lyapunov equations
Peter Benner, Davide Palitta, Jens Saak
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propo…
Optimization-based parametric model order reduction via first-order necessary conditions
Manuela Hund, Tim Mitchell, Petar Mlinarić +1
In this paper, we generalize existing frameworks for -optimal model order reduction to a broad class of parametric linear time-invariant systems.…
A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction
Stephan Rave, Jens Saak
In this contribution we aim to satisfy the demand for a publicly available benchmark for parametric model order reduction that is scalable both in degrees of freedom as well as par…
Parametric model order reduction using pyMOR
Petar Mlinarić, Stephan Rave, Jens Saak
pyMOR is a free software library for model order reduction that includes both reduced basis and system-theoretic methods. All methods are implemented in terms of abstract vector an…
Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1 -- Philosophy, Features and Application for (Parametric) Model
Peter Benner, Martin Köhler, Jens Saak
Matrix equations are omnipresent in (numerical) linear algebra and systems theory. Especially in model order reduction (MOR) they play a key role in many balancing based reduction…
Sustainable Research Software Hand-Over
Jörg Fehr, Christian Himpe, Stephan Rave +1
Scientific software projects evolve rapidly in their initial development phase, yet at the end of a funding period, the completion of a research project, thesis, or publication, fu…
A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems
Peter Benner, Zvonimir Bujanović, Patrick Kürschner +1
In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent y…
Efficient Solution of Large-Scale Algebraic Riccati Equations Associated with Index-2 DAEs via the Inexact Low-Rank Newton-ADI Method
Peter Benner, Matthias Heinkenschloss, Jens Saak +1
This paper extends the algorithm of Benner, Heinkenschloss, Saak, and Weichelt: An inexact low-rank Newton-ADI method for large-scale algebraic Riccati equations, Applied Numerical…
A Connection Between Time Domain Model Order Reduction and Moment Matching for LTI Systems
Manuela Hund, Jens Saak
We investigate the time domain model order reduction (MOR) framework using general orthogonal polynomials by Jiang and Chen 2012 and extend their idea by exploiting the structure o…