检索结果-内蒙古大学图书馆

Fast a posteriori state error estimation for reliable frequency sweeping in microwave circuits via the reduced-basis method

学校读者我要写书评

暂无评论

arXiv 2021年

作者： de la Rubia, Valentín Chellappa, Sridhar Feng, Lihong Benner, Peter Departamento de Matemática Aplicada a las TIC ETSI de Telecomunicación Universidad Politécnica de Madrid Madrid28040 Spain Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany

We develop a compact, reliable model order reduction approach for fast frequency sweeps in microwave circuits by means of the reduced-basis method. Contrary to what has been previously done, special emphasis is placed on certifying the accuracy of the reduced-order model with respect to the original full-order model in an effective and efficient way. Previous works on model order reduction accuracy certification rely on costly a posteriori error estimators, which typically require expensive inf-sup constant evaluations of the underlying full-order model. This scenario is often too time-consuming and unaffordable in electromagnetic applications. As a result, less expensive and heuristic error estimators are commonly used instead. Very often, one is interested in knowing about the full state vector, instead of just some output quantities derived from the full state. Therefore, error estimators for the full state vector become relevant. In this work, we detail the frequency behavior of both the electric field and the state error when an approximation to the electric field solution is carried out. Both field quantities share the same frequency behavior. Based on this observation, we focus on the efficient estimation of the electric field state error and propose a fast evaluation of the reduced-order model state error in the frequency band of analysis, minimizing the number of full-order model evaluations. This methodology is of paramount importance to carry out a reliable fast frequency sweep in microwave circuits. Finally, real-life applications will illustrate the capabilities and efficiency of the proposed approach. © 2021, CC BY.

关键词： Computer aided design

Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric systems in Electromagnetics

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Chellappa, Sridhar Feng, Lihong de la Rubia, Valentín Benner, Peter Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg39106 Germany Departamento de Matemática Aplicada a las TIC ETSI de Telecomunicación Universidad Politécnica de Madrid Madrid28040 Spain

A reliable model order reduction process for parametric analysis in electromagnetics is detailed. Special emphasis is placed on certifying the accuracy of the reduced-order model. For this purpose, a sharp state error estimator is proposed. Standard a posteriori state error estimation for model order reduction relies on the inf-sup constant. For parametric systems, the inf-sup constant is parameter-dependent. The a posteriori error estimation for systems with very small or vanishing inf-sup constant poses a challenge, since it is inversely proportional to the inf-sup constant, resulting in overly pessimistic error estimation especially at and around resonance frequencies. Such systems appear in electromagnetics since the inf-sup constant values are close to zero at points close to resonant frequencies, where they eventually vanish. We propose a novel a posteriori state error estimator which avoids the calculation of the inf-sup constant. The proposed state error estimator is compared with the standard error estimator and a recently proposed one in the literature. It is shown that our proposed error estimator outperforms both existing estimators. Numerical experiments are performed on real-life microwave devices such as narrowband and wideband antennas, two types of dielectric resonator filters as well as a dual-mode waveguide filter. These examples show the capabilities and efficiency of the proposed methodology. © 2021, CC BY.

关键词： Galerkin methods

Model order reduction for gas and energy networks

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Himpe, Christian Grundel, Sara Benner, Peter Computational Methods in Systems and Control Theory Group The Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstraße 1 MagdeburgD-39106 Germany

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network *** Codes 93-04, 76N15, 93B20 Copyright © 2020, The Authors. All rights reserved.

关键词： Nonlinear equations

Non-intrusive Time-POD for Optimal control of a Fixed-Bed Reactor for CO 2 Methanation

学校读者我要写书评

暂无评论

IFAC-PapersOnLine 2021年第3期54卷 122-127页

作者： Jens Bremer Jan Heiland Peter Benner Kai Sundmacher Max Planck Institute Magdeburg Dpt. Process Systems Engineering Sandtorstraße 2 39106 Magdeburg Germany and Otto von Guericke University Magdeburg Chair for Process Systems Engineering Universitätsplatz 2 39106 Magdeburg (Sundmacher) Max Planck Institute Magdeburg Dpt. Computational Methods in Systems and Control Theory and Otto von Guericke University Magdeburg Fakultät für Mathematik

The optimization of a controlled process in a simulation without access to the model itself is a common scenario and very relevant to many chemical engineering applications. A general approach is to apply a black-box optimization algorithm to a parameterized control scheme. The success then depends on the quality of the parametrization that should be low-dimensional though rich enough to express the salient features. This work proposes using solution snapshots to extract dominant modes of the temporal dynamics of a process and use them for low-dimensional parametrizations of control functions. The approach is called proper orthogonal decomposition in time (time-POD). We provide theoretical reasoning and illustrate the performance for the optimal control of a methanation reactor.

关键词： Optimal control Model order reduction Proper orthogonal decomposition Fixed-bed reactor Carbon dioxide methanation Nonlinear programming Black-box model

Topical Issue Scientific Machine Learning (1/2)

学校读者我要写书评

暂无评论

GAMM Mitteilungen 2021年第1期44卷 e202100010-e202100010页

作者： Benner, Peter Klawonn, Axel Stoll, Martin Computational Methods in Systems and Control Theory Max Planck institute for Dynamics of Complex Technical Systems Magdeburg Germany Fakultät für Mathematik Otto-von-Guericke Universität Magdeburg Germany Department of Mathematics and Computer Science University of Cologne Germany Center for Data and Simulation Science University of Cologne Germany Chair of Scientific Computing Department of Mathematics TU Chemnitz Germany

Model order reduction via substructuring for a nonlinear, differential-algebraic machine tool model with moving loads

学校读者我要写书评

暂无评论

PAMM 2023年第1期23卷

作者： Quirin Aumann Peter Benner Jens Saak Julia Vettermann Mathematics in Industry and Technology Faculty of Mathematics Technische Universität Chemnitz Reichenhainer Str. 41 09126 Chemnitz Germany Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg Germany

Machine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired displacement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process-parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low-dimensional models are required for various applications, e.g., in digital twins, the correction of thermally induced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo-mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring techniques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo-mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced-order model and the original one.

关键词：

Adjacency-based, non-intrusive reduced-order modeling for fluid-structure interactions

学校读者我要写书评

暂无评论

PAMM 2023年第4期23卷

作者： Leonidas Gkimisis Thomas Richter Peter Benner Computational Methods in Systems and Control Theory (CSC) Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Faculty of Mathematics Institute for Analysis and Numerics Otto-von-Guericke Otto-von-Guericke-Universität Magdeburg Universitätsplatz 2 Magdeburg Germany

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for non-intrusive model reduction applied to Fluid-Structure Interaction (FSI) problems. The approach is based on the a priori known sparsity of the full-order system operators, which is dictated by grid adjacency information. In order to enforce this type of sparsity, we solve a “local”, regularized least-squares problem for each degree of freedom on a grid, considering only the training data from adjacent degrees of freedom (DoFs), thus making computation and storage of the inferred full-order operators feasible. After constructing the non-intrusive, sparse full-order model (FOM), Proper Orthogonal Decomposition (POD) is used for its projection to a reduced dimension subspace and thus the construction of a reduced-order model (ROM). The methodology is applied to the challenging Hron-Turek benchmark FSI3, for Re = 200. A physics-informed, non-intrusive ROM is constructed to predict the two-way coupled dynamics of a solid with a deformable, slender tail, subject to an incompressible, laminar flow. Results considering the accuracy and predictive capabilities of the inferred reduced models are discussed.

关键词：

Parallel algorithms for tensor train arithmetic

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Al Daas, Hussam Ballard, Grey Benner, Peter Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Computer Science Department Wake Forest University Winston SalemNC United States

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms and inner products, orthonormalization, and rounding (rank truncation). These are the kernel operations for applications such as iterative Krylov solvers that exploit the TT structure. The parallel algorithms are designed for distributed- memory computation, and we propose a data distribution and strategy that parallelizes computations for individual cores within the TT format. We analyze the computation and communication costs of the proposed algorithms to show their scalability, and we present numerical experiments that demonstrate their efficiency on both shared-memory and distributed-memory parallel systems. For example, we observe better single-core performance than the existing MATLAB TT-Toolbox in rounding a 2GB TT tensor, and our implementation achieves a 34× speedup using all 40 cores of a single node. We also show nearly linear parallel scaling on larger TT tensors up to over 10,000 cores for all mathematical operations. Copyright © 2020, The Authors. All rights reserved.

关键词： Tensors

GR decompositions and their relations to Cholesky-like factorizations

学校读者我要写书评

暂无评论

PAMM 2021年第1期20卷

作者： Peter Benner Carolin Penke Max Planck Institute for Dynamics of Complex Technical Systems: Computational Methods in Systems and Control Theory Sandtorstr. 1 39106 Magdeburg

For a given matrix, we are interested in computing GR decompositions A = GR , where G is an isometry with respect to given scalar products. The orthogonal QR decomposition is the representative for the Euclidian scalar product. For a signature matrix, a respective factorization is given as the hyperbolic QR decomposition. Considering a skew-symmetric matrix leads to the symplectic QR decomposition. The standard approach for computing GR decompositions is based on the successive elimination of subdiagonal matrix entries. For the hyperbolic and symplectic case, this approach does in general not lead to a satisfying numerical accuracy. An alternative approach computes the QR decomposition via a Cholesky factorization, but also has bad stability. It is improved by repeating the procedure a second time. In the same way, the hyperbolic and the symplectic QR decomposition are related to the LDL T and a skew-symmetric Cholesky-like factorization. We show that methods exploiting this connection can provide better numerical stability than elimination-based approaches.

关键词：