Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1—Philosophy, Features, and Application for (Parametric) Model Order Reduction

Benner, Peter; Köhler, Martin; Saak, Jens

doi:10.1007/978-3-030-72983-7_18

Cited by 13 publications

(16 citation statements)

References 57 publications

(49 reference statements)

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“…The solutions to the large-scale projected Riccati equations ( 23) have been computed in MATLAB 9.7.0.1190202 (R2019b) using the routines from the M-M.E.S.S. library version 2.0.1 [16,41]. Also, the errors in coprime factorizations have been computed in MATLAB.…”

Section: Numerical Resultsmentioning

confidence: 99%

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

2022

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Output-based controllers are known to be fragile with respect to model uncertainties. The standard $$\mathcal {H}_{\infty }$$ H ∞ -control theory provides a general approach to robust controller design based on the solution of the $$\mathcal {H}_{\infty }$$ H ∞ -Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with guaranteed robustness margins for the stabilization of incompressible flow problems. The performance and the robustness of the reduced-order controller with respect to linearization and model reduction errors are investigated and illustrated in numerical examples.

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Section: Numerical Resultsmentioning

confidence: 99%

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

2022

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“…With the same arguments, projection methods based on ( 15) are guaranteed to preserve the internal system structure. To give a concise overview, the following proposition states the most important result from [8] to solve (12) for systems of the form (14).…”

Section: Structure-preserving Interpolationmentioning

confidence: 99%

“…The MATLAB toolboxes M-M.E.S.S. version 2.0.1 [12,50] and SOLBT version 3.0 [14] have been used in some of the experiments. The models and data have been created with Kratos Mutliphysics 8.1 [23,28].…”

Section: Numerical Experimentsmentioning

confidence: 99%

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods

Aumann,

Werner

2022

Preprint

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Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems. Such models typically exhibit a second-order structure and their material properties as well as their excitation may be depending on the driving frequency. We show and compare the effectiveness of all considered methods by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic problems.

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“…Algorithm 2 has been implemented for dense coefficients in the MORLAB toolbox [25,26] and for the large-scale sparse case in the M-M.E.S.S. toolbox [17,53].…”

Section: Algorithm 2: Low-rank Riccati Iteration (Lr-ri)mentioning

confidence: 99%

A low-rank solution method for Riccati equations with indefinite quadratic terms

Benner,

Heiland,

Werner

2021

Preprint

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Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients, there is no approach available to compute solutions in the large-scale sparse setting. In this paper, we develop an iterative method to compute low-rank approximations of stabilizing solutions of large-scale sparse continuous-time algebraic Riccati equations with indefinite quadratic terms. We test the developed approach for dense examples in comparison to other established matrix equation solvers, and investigate the applicability and performance in large-scale sparse examples.

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Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1—Philosophy, Features, and Application for (Parametric) Model Order Reduction

Cited by 13 publications

References 57 publications

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

Robust output-feedback stabilization for incompressible flows using low-dimensional $$\mathcal {H}_{\infty }$$-controllers

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods

A low-rank solution method for Riccati equations with indefinite quadratic terms

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