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1
Content available FFT-based simulation using a reduced set of frequencies adapted to the underlying microstructure
Gierden Christian, Waimann Johanna, Svendsen Bob, Reese Stefanie
Computer Methods in Materials Science
|
2021
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Vol. 21, No. 1
51--58
EN
Instead of the classical finite element (FE) based microstructure simulation, a Fast Fourier transform (FFT) based microstructure simulation, introduced by Moulinec and Suquet (1994, 1998), also enables the computation of highly resolved microstructural fields. In this context, the microscopic boundary value problem is captured by the Lippmann-Schwinger equation and solved by using Fast Fourier transforms (FFT) and fixed-point iterations. To decrease the computational effort of the fixed-point solver, Kochmann et al. (2019) introduced a model order reduction (MOR) technique based on solving the Lippmann-Schwinger equation in Fourier space with a reduced set of frequencies. Thereby, the accuracy of this MOR technique depends on the number of used frequencies and the choice of frequencies that are considered within the simulation. Instead of the earlier proposed fixed (Kochmann et al., 2019) or geometrically adapted (Gierden et al., 2021b) sampling patterns, we propose a sampling pattern which is updated after each load step based on the current strain. To show the precision of such a strain-based sampling pattern, an elasto-plastic two-phase composite microstructure is investigated.
2
Content available Model reduction using Harris hawk algorithm and moment matching
Sharma Aswant Kumar, Sambariya Dhanesh Kumar
Archives of Electrical Engineering
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2021
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Vol. 70, nr 4
959--978
EN
Physical machine systems are represented in the form of differential equations. These differential equations may be of the higher order and difficult to analyses. Therefore, it is necessary to convert the higher-order to lower order which replicates approximately similar properties of the higher-order system (HOS). This article presents a novel approach to reducing the higher-order model. The approach is based on the hunting demeanor of the hawk and escaping of the prey. The proposed method unifies the Harris hawk algorithm and the moment matching technique. The method is applied on single input single output (SISO), multi-input multi-output (MIMO) linear time–invariant (LTI) systems. The proposed method is justified by examining the result. The results are compared using the step response characteristics and response error indices. The response indices are integral square error, integral absolute error, integral time absolute error. The step response characteristics such as rise time, peak, peak time, settling time of the proposed reduced order follows 97%–100% of the original system characteristics.
3
Content available A new nondeterministic method for optimal selection of master degrees of freedom for dynamic condensation based on evolutionary optimization
Mucha Waldemar
Journal of Theoretical and Applied Mechanics
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2020
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Vol. 58 nr 2
445--458
EN
The following paper presents a new method for choosing a set of master degrees of freedom for the process of dynamic condensation in order to reduce a finite element model. The general rule is that the more degrees of freedom are eliminated, the more accurate the reduced model is. However, eliminating different subsets (of equal sizes) of degrees of freedom may influence the accuracy differently. Therefore, choosing an optimal subset is crucial. The presented method is based on multicriterial evolutionary optimization which makes it the first nondeterministic approach based on computational optimization technique for this application.
4
Content available Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
Chaturantabut Saifon
International Journal of Applied Mathematics and Computer Science
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2020
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Vol. 30, no. 4
615--628
EN
This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.
5
Content available Model order reduction technique applied on harmonic analysis of a submerged vibrating blade
Tengs E., Charrassier F., Holst M., Storli P.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 1
131--142
EN
As part of an ongoing study into hydropower runner failure, a submerged, vibrating blade is investigated both experimentally and numerically. The numerical simulations performed are fully coupled acoustic-structural simulations in ANSYS Mechanical. In order to speed up the simulations, a model order reduction technique based on Krylov subspaces is implemented. This paper presents a comparison between the full ANSYS harmonic response and the reduced order model, and shows excellent agreement. The speedup factor obtained by using the reduced order model is shown to be between one and two orders of magnitude. The number of dimensions in the reduced subspace needed for accurate results is investigated, and confirms what is found in other studies on similar model order reduction applications. In addition, experimental results are available for validation, and show good match when not too far from the resonance peak.
6
Content available Model reduction problem of linear discrete systems: Admissibles initial states
Abdelhak A., Rachik M.
Archives of Control Sciences
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2019
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Vol. 29, No. 1
41--55
EN
Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear system that produces, with a tolerance index ϵ, the same output function when the initial state belongs to a specified set, called ϵ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ϵ-admissible set.
7
Metody redukcji rzędu modelu w analizie elektromagnetycznej metodą elementów skończonych
Fotyga G.
Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne
|
2017
|
nr 6
581--584, CD
PL
Niniejszy artykuł opisuje nową technikę lokalnej redukcji rzędu modelu, która pozwala na poprawę efektywności Metody Elementów Skończonych (MES) w obliczeniach elektromagnetycznych. Zaproponowana technika została zaimplementowana w trójwymiarowym, wektorowym sformułowania MES. Jej efektywność została zweryfikowana poprzez symulację działania złożonych struktur mikrofalowych. Dzięki zaprezentowanemu algorytmowi uzyskano kilkudziesięciokrotne przyśpieszania analizy utrzymując żądaną dokładność obliczeń.
EN
The aim of this work is to improve the efficiency of the Finite Element Method (FEM) applied to electromagnetic problems by means of the novel technique of local model order reduction (MOR). The proposed technique has been implemented in the three-dimensional vector formulation of FEM. Its effectiveness has been verified by numerous simulations of microwave complex structures. The numerical tests prove that the proposed method provides significant reduction of the simulation time, without considerable loss of accuracy.
8
Content available Model Order Reduction of Large-Scale Finite Element Systems in an MPI Parallelized Environment for Usage in Multibody Simulation
Volzer T., Eberhard P.
Archive of Mechanical Engineering
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2016
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Vol. LXIII, nr 4
475--494
EN
The use of elastic bodies within a multibody simulation became more and more important within the last years. To include the elastic bodies, described as a finite element model in multibody simulations, the dimension of the system of ordinary differential equations must be reduced by projection. For this purpose, in this work, the modal reduction method, a component mode synthesis based method and a moment-matching method are used. Due to the always increasing size of the non-reduced systems, the calculation of the projection matrix leads to a large demand of computational resources and cannot be done on usual serial computers with available memory. In this paper, the model reduction software Morembs++ is presented using a parallelization concept based on the message passing interface to satisfy the need of memory and reduce the runtime of the model reduction process. Additionally, the behaviour of the Block-Krylov-Schur eigensolver, implemented in the Anasazi package of the Trilinos project, is analysed with regard to the choice of the size of the Krylov base, the blocksize and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.
PL
W ostatnich latach w symulacji układów wieloczłonowych coraz ważniejsze staje się uwzględnianie odkształcalności członów. By w symulacji układu wieloczłonowego można było wykorzystać człony odkształcalne, modelowane metodą elementów skończonych, rozmiar układu równań różniczkowych zwyczajnych musi być zredukowany drogą projekcji.W tym celu w prezentowanej pracy zastosowano metodę redukcji modalnej, metodę opartą na syntezie składowych postaciowych (CMS) oraz metodę dopasowania momentów. Wobec wciąż rosnącego rozmiaru układów niezredukowanych, obliczanie macierzy projekcji prowadzi do wielkiego zapotrzebowania na moce obliczeniowe i nie może być wykonane na zwykłych, szeregowych komputerach. W pracy zaprezentowano oprogramowanie do redukcji modelu Morembs++, w którym wykorzystuje się obliczenia równoległe z interfejsem transmisji wiadomości (MPI), co zaspokaja zapotrzebowanie na pamięć i zmniejsza czas wykonania niezbędnych obliczeń. Ponadto działanie blokowego solvera wartości własnych Kryłowa-Schura, zaimplementowanego w pakiecie oprogramowania Anasazi z projektu Trilinos, zostało przeanalizowane pod kątem wyboru rozmiaru bazy Kryłowa, rozmiaru bloku i liczby bloków. Rozważono także użycie solvera iteracyjnego w ramach metody opartej na syntezie składowych postaciowych (CMS).
9
A Comparison of Methods for Calculation of Transformation Matrices for Model Order Reduction Using GPU Parallel Computing
Raczyński D.
Zeszyty Naukowe. Elektryka / Politechnika Opolska
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2013
|
z. 69
91--92
EN
The purpose of this paper is to compare execution times for developed programs for determining transformation matrices in model order reduction using the balanced realization method. Six popular methods are implemented, named the: RPR, SR, BFSR, EIG-SR, EIGBFSR and Obinata-Anderson method. Each algorithm is prepared in two versions, one for execution on the main processor (CPU), and the other one for execution on graphics processor (GPU).
10
Analiza metod redukcji modeli nieliniowych wysokiego rzędu
Andrzejewski Ł.
Zeszyty Naukowe. Elektryka / Politechnika Opolska
|
2007
|
Vol. 322, z. 59
7-8
EN
The latest approach to the model order reduction and its previous achievements are considered in this paper. There is a comparison of most commonly used methods as well as a brief description of nonlinear model reduction via trajectory piecewise linearization.
11
Content available Problemy doboru dynamiki modelu w układzie regulacji typu MFC
Brzózka J.
Zeszyty Naukowe / Akademia Morska w Szczecinie
|
2006
|
nr 10 (82)
107-116
PL
W strukturze nadążnego, odpornego układu regulacji (MFC) wykorzystywany jest model procesu regulowanego. Tematem artykułu są metody wyznaczania dynamiki tego modelu.
EN
A plant model is used in the structure of the robust, model following control system. The article deals with the determination of dynamics of this model.
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