Adaptive POD–DEIM basis construction and its application to a nonlinear population balance system

Feng, Lihong; Mangold, Michael; Benner, Peter

doi:10.1002/aic.15749

Cited by 12 publications

(26 citation statements)

References 41 publications

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“…An optimal choice of operation and design parameters will require a systematic mathematical optimization. This will be done in our future work using the model reduction approaches presented in (Mangold et al, 2015;Feng et al, 2016).…”

Section: Discussionmentioning

confidence: 99%

Modelling geometrical and fluid-dynamic aspects of a continuous fluidized bed crystallizer for separation of enantiomers

Mangold

Khlopov

Temmel

et al. 2017

Chemical Engineering Science

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Continuous selective crystallization using mixed suspension mixed product removal (MSMPR) crystallizers is an attractive method for separating enantiomers. Recent experimental results confirm the feasibility of the approach, but also indicate that the operation conditions for nominal operation lie in a rather small window. A systematic analysis and an optimal design are needed to exploit the full potential of the method. In this contribution, a mathematical process model based on population balance equations is presented. In contrast to other studies in literature, the considered crystallizer is not a stirred tank, but has a conical shape that requires a spatially distributed model formulation. Parameter studies identify the key operation and design parameters for maximizing the mass of the product crystals and for shaping their size distribution. The proposed model focuses on geometrical and fluid-dynamic aspects, but at the current stage does not include purity aspects.

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Section: Discussionmentioning

confidence: 99%

Modelling geometrical and fluid-dynamic aspects of a continuous fluidized bed crystallizer for separation of enantiomers

Mangold

Khlopov

Temmel

et al. 2017

Chemical Engineering Science

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“…• Discretization: Finite volume/Finite difference method in space and Semi-implicit Euler method in time. • Primal-dual formulation for improved convergence and effectivity [2,3,4].…”

Section: A Posteriori Error Estimationmentioning

confidence: 99%

Adaptive POD-DEIM model reduction based on an improved error estimator

Chellappa

Feng

Benner

2018

Preprint

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For reliable, efficient, rapid simulations of dynamical systems, a reduced order model (ROM) with certified accuracy is highly desirable. The ROM is derived from a full order model (FOM) through model reduction. In this work, we propose an adaptive approach for nonlinear model reduction by making use of a suitable output error estimator, thus enable the generation of a compact ROM, with appropriate balance between the state and nonlinear approximations.

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“…In the worst case, the ROM might be unstable. To avoid these issues, the authors in Reference 13 introduced a method of adaptively constructing the RB and the DEIM bases. The adaptivity is guided by an a posteriori output error indicator for the ROM.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, a compact and reliable ROM is obtained. The algorithm in Reference 13 has several drawbacks. First, it is only applicable to nonparametric systems.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive basis construction and improved error estimation for parametric nonlinear dynamical systems

Chellappa

Feng

Benner

2020

Numerical Meth Engineering

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Summary An adaptive scheme to generate reduced‐order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the proper orthogonal decomposition (POD)‐Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively determine the number of the reduced basis vectors and the number of the interpolation basis vectors for basis construction. The proposed technique is able to derive a suitable match between the RB and the interpolation basis vectors, making the generation of a stable, compact and reliable ROM possible. This is achieved by adaptively adding new basis vectors or removing unnecessary ones, at each iteration of the greedy algorithm. An efficient output error indicator plays a key role in the adaptive scheme. We also propose an improved output error indicator based on previous work. Upon convergence of the POD‐Greedy algorithm, the new error indicator is shown to be sharper than the existing ones, implicating that a more reliable ROM can be constructed. The proposed method is tested on several nonlinear dynamical systems, namely, the viscous Burgers' equation and two other models from chemical engineering.

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Adaptive POD–DEIM basis construction and its application to a nonlinear population balance system

Cited by 12 publications

References 41 publications

Modelling geometrical and fluid-dynamic aspects of a continuous fluidized bed crystallizer for separation of enantiomers

Modelling geometrical and fluid-dynamic aspects of a continuous fluidized bed crystallizer for separation of enantiomers

Adaptive POD-DEIM model reduction based on an improved error estimator

Adaptive basis construction and improved error estimation for parametric nonlinear dynamical systems

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