arXiv subjects

Boris Lohmann

Publications and source records attributed to Boris Lohmann.

24 records · Page 2Linked to original sources

arXiv2019

Practicable Simulation-Free Model Order Reduction by Nonlinear Moment Matching

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this reduction concept to nonlinear systems presented in [1], provide some new insights and propose some simplifications to achieve a feasible and numerically efficient nonlinear model reduction algorithm. This algorithm relies on the solution of nonlinear systems of equations rather than on the expensive simulation of the original model or the difficult solution of a nonlinear partial differential equation.

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arXiv2018

$\mathcal{H}_2$ Pseudo-Optimal Reduction of Structured DAEs by Rational Interpolation

In this contribution, we extend the concept of $\mathcal{H}_2$ inner product and $\mathcal{H}_2$ pseudo-optimality to dynamical systems modeled by differential-algebraic equations (DAEs). To this end, we derive projected Sylvester equations that characterize the $\mathcal{H}_2$ inner product in terms of the matrices of the DAE realization. Using this result, we extend the $\mathcal{H}_2$ pseudo-optimal rational Krylov algorithm for ordinary differential equations to the DAE case. This algorithm computes the globally optimal reduced-order model for a given subspace of $\mathcal{H}_2$ defined by poles and input residual directions. Necessary and sufficient conditions for $\mathcal{H}_2$ pseudo-optimality are derived using the new formulation of the $\mathcal{H}_2$ inner product in terms of tangential interpolation conditions. Based on these conditions, the cumulative reduction procedure combined with the adaptive rational Krylov algorithm, known as CUREd SPARK, is extended to DAEs. Important properties of this procedure are that it guarantees stability preservation and adaptively selects interpolation frequencies and reduced order. Numerical examples are used to illustrate the theoretical discussion. Even though the results apply in theory to general DAEs, special structures will be exploited for numerically efficient implementations.

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arXiv2017

A New Framework for $\mathcal{H}_2$-Optimal Model Reduction

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential interpolation and H2-optimal approxi- mations. The main advantage is given by a decoupling of the cost of optimization from the cost of reduction, resulting in a significant speedup in H2-optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing H2-optimal reduced models at a far lower cost than conventional algorithms. The paper ends with a brief discussion on how the idea behind the framework can be extended to approximate further system classes, thus showing that this truly is a general framework for interpolatory H2 reduction rather than just an additional reduction algorithm.

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arXiv2016

Model reduction of linear time-varying systems with applications for moving loads

In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new degrees of freedom, which also come along with some challenges. This paper deals with both simple methods for the reduction of particular linear time-varying systems, as well as with a more advanced technique considering the emerging time derivatives.

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arXiv2015

Stability-Preserving, Adaptive Model Order Reduction of DAEs by Krylov-Subspace Methods

Systems of differential-algebraic equations (DAEs) represent a widespread formalism in the modeling of constrained mechanical systems and electrical networks. Due to the automatic, object-oriented generation of the equations of motion and the resulting redundancies in the descriptor variables, DAE systems often reach a very high order. This motivates the use of model order reduction (MOR) techniques that capture the relevant input-output dynamics in a reduced model of much smaller order, while satisfying the constraints and preserving fundamental properties. Due to their particular structure, new MOR techniques designed to work directly on the DAE are required that reduce the dynamical part while preserving the algebraic. In this contribution, we exploit the specific structure of index-1 systems in semi-explicit form and present two different methods for stability-preserving MOR of DAEs. The first technique preserves strictly dissipativity of the underlying dynamics, the second takes advantage of H2-pseudo-optimal reduction and further allows for an adaptive selection of reduction parameters such as reduced order and Krylov shifts.

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arXiv2013

ADI iteration for Lyapunov equations: a tangential approach and adaptive shift selection

A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are presented. Numerical examples emphasize the potential of the new results.

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