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Recent Publications

Recently Published Scientific Articles

Here, we present selected recent publications of the MPI Magdeburg.

2017

 Model Reduction and Approximation: Theory and Algorithms

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Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems.

Model Reduction and Approximation: Theory and Algorithms

  • contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework;
  • is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods; and
  • covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).

Original publication:

Peter Benner, Albert Cohen, Mario Ohlberger, and Karen Willcox (Eds.)
Model Reduction and Approximation: Theory and Algorithms
SIAM Publications, Philadelphia, PA, 2017.
ISBN: 978-1-611974-81-2


System Reduction for Nanoscale IC Design

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This book describes the computational challenges posed by the progression toward nanoscale electronic devices and increasingly short design cycles in the microelectronics industry, and proposes methods of model reduction which facilitate circuit and device simulation for specific tasks in the design cycle.

The goal is to develop and compare methods for system reduction in the design of high dimensional nanoelectronic ICs, and to test these methods in the practice of semiconductor development. Six chapters describe the challenges for numerical simulation of nanoelectronic circuits and suggest model reduction methods for constituting equations. These include linear and nonlinear differential equations tailored to circuit equations and drift diffusion equations for semiconductor devices. The performance of these methods is illustrated with numerical experiments using real-world data. Readers will benefit from an up-to-date overview of the latest model reduction methods in computational nanoelectronics.

Original publication:

Peter Benner
System Reduction for Nanoscale IC Design
Springer International Publishing AG. 2017.

DOI: 10.1007/978-3-319-07236-4


2016

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CO2 Methanation: Optimal Start-Up Control of a Fixed-Bed Reactor for Power-to-Gas Applications

Utilizing volatile renewable energy sources (e.g., solar, wind) for chemical production systems requires a deeper understanding of their dynamic operation modes. Taking the example of a methanation reactor in the context of power-to-gas applications, a dynamic optimization approach is used to identify control trajectories for a time optimal reactor start-up avoiding distinct hot spot formation. For the optimization, we develop a dynamic, two-dimensional model of a fixed-bed tube reactor for carbon dioxide methanation which is based on the reaction scheme of the underlying exothermic Sabatier reaction mechanism. While controlling dynamic hot spot formation inside the catalyst bed, we prove the applicability of our methodology and investigate the feasibility of dynamic carbon dioxide methanation. © 2016 American Institute of Chemical Engineers AIChE J, 2016

Original publication:

AIChE Journal /

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Extending the potential of moment analysis in chromatography

Essential goal of modeling chromatographic processes is to describe the dynamics of concentration fronts traveling through chromatographic columns. Most of the models developed originate from differential mass balances for the fluid and solid phases. Model reduction based on evaluating just a limited number of moments of the profiles is known to be a powerful tool to simplify the description of band profiles. This review article first describes the well-established method of moments for different standard models. Then the method is extended to evaluate more complex and realistic column models. The cases of applying columns packed with core-shell particles and the quantitative description of radial concentration profiles are analyzed.

Original publication:

Shamsul Quamar, Andreas Seidel-Morgenstern
Extending the potential of moment analysis in chromatography
Trends in Analytical Chemistry, Volume 81, Pages 87–101, July–August 2016.
DOI: 10.1016/j.trac.2016.01.007


 
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