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Journal articles on the topic 'Augmented Krylov Model Order Reduction'

Author: Grafiati

Published: 6 September 2023

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1

Kerfriden, P., P. Gosselet, S. Adhikari, and S. P. A. Bordas. "Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems." Computer Methods in Applied Mechanics and Engineering 200, no. 5-8 (January 2011): 850–66. http://dx.doi.org/10.1016/j.cma.2010.10.009.

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2

Zimmerling, Jörn, Vladimir Druskin, Mikhail Zaslavsky, and Rob F. Remis. "Model-order reduction of electromagnetic fields in open domains." GEOPHYSICS 83, no. 2 (March 1, 2018): WB61—WB70. http://dx.doi.org/10.1190/geo2017-0507.1.

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We have developed several Krylov projection-based model-order reduction techniques to simulate electromagnetic wave propagation and diffusion in unbounded domains. Such techniques can be used to efficiently approximate transfer function field responses between a given set of sources and receivers and allow for fast and memory-efficient computation of Jacobians, thereby lowering the computational burden associated with inverse scattering problems. We found how general wavefield principles such as reciprocity, passivity, and the Schwarz reflection principle translate from the analytical to the numerical domain and developed polynomial, extended, and rational Krylov model-order reduction techniques that preserve these structures. Furthermore, we found that the symmetry of the Maxwell equations allows for projection onto polynomial and extended Krylov subspaces without saving a complete basis. In particular, short-term recurrence relations can be used to construct reduced-order models that are as memory efficient as time-stepping algorithms. In addition, we evaluated the differences between Krylov reduced-order methods for the full wave and diffusive Maxwell equations and we developed numerical examples to highlight the advantages and disadvantages of the discussed methods.

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3

Freund, Roland W. "Model reduction methods based on Krylov subspaces." Acta Numerica 12 (May 2003): 267–319. http://dx.doi.org/10.1017/s0962492902000120.

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In recent years, reduced-order modelling techniques based on Krylov-subspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools for tackling the large-scale time-invariant linear dynamical systems that arise in the simulation of electronic circuits. This paper reviews the main ideas of reduced-order modelling techniques based on Krylov subspaces and describes some applications of reduced-order modelling in circuit simulation.

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4

Michiels, Wim, Elias Jarlebring, and Karl Meerbergen. "Krylov-Based Model Order Reduction of Time-delay Systems." SIAM Journal on Matrix Analysis and Applications 32, no. 4 (October 2011): 1399–421. http://dx.doi.org/10.1137/100797436.

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5

Olsson, K. Henrik A., and Axel Ruhe. "Rational Krylov for eigenvalue computation and model order reduction." BIT Numerical Mathematics 46, S1 (September 9, 2006): 99–111. http://dx.doi.org/10.1007/s10543-006-0085-9.

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6

Bazaz, Mohammad Abid, Mashuq un Nabi, and S. Janardhanan. "Automated and efficient order selection in Krylov-based model order reduction." International Journal of Modelling, Identification and Control 18, no. 4 (2013): 332. http://dx.doi.org/10.1504/ijmic.2013.053538.

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7

Radić-Weissenfeld, Lj, S. Ludwig, W. Mathis, and W. John. "Model order reduction of linear time invariant systems." Advances in Radio Science 6 (May 26, 2008): 129–32. http://dx.doi.org/10.5194/ars-6-129-2008.

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Abstract. This paper addresses issues related to the order reduction of systems with multiple input/output ports. The order reduction is divided up into two steps. The first step is the standard order reduction method based on the multipoint approximation of system matrices by applying Krylov subspace. The second step is based on the rejection of the weak part of a system. To recognise the weak system part, Lyapunov equations are used. Thus, this paper introduces efficient solutions of the Lyapunov equations for port to port subsystems.

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8

Li, Bin, Liang Bao, Yiqin Lin, and Yimin Wei. "Model-order reduction ofkth order MIMO dynamical systems using blockkth order Krylov subspaces." International Journal of Computer Mathematics 88, no. 1 (January 2011): 150–62. http://dx.doi.org/10.1080/00207160903353319.

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9

MOHAMED, K., A. MEHDI, and M. ABDELKADER. "AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS." ANZIAM Journal 59, no. 1 (April 5, 2017): 115–33. http://dx.doi.org/10.1017/s1446181117000049.

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We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

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10

Guan, Le, Jia Li Gao, Zhi Wen Wang, Guo Qing Zhang, and Jin Kui Chu. "A Refined Arnoldi Algorithm Based Krylov Subspace Technique for MEMS Model Order Reduction." Key Engineering Materials 503 (February 2012): 260–65. http://dx.doi.org/10.4028/www.scientific.net/kem.503.260.

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A refined approach producing MEMS numerical macromodels is proposed in this paper by generating the iterative Krylov subspace using a refined Arnoldi algorithm, which can reduce the degrees of freedom of the original system equations described by the state space method. Projection of the original system matrix onto the Krylov subspace which is spanned by a refined Arnoldi algorithm is still based on the transfer function moment matching principle. The idea of the iterative version is to expect that a new initial vector will contain more and more information on the required eigenvectors that is called refined vector. The refined approach improves approximation accuracy of the system matrix eigenvalues equivalent to a more accurate approximation to the poles of the system transfer function, obtaining a more accurate reduced-order model. The clamped beam model and the FOM model are reduced order by classical Arnoldi and refined Arnoldi algorithm in numerical experiments. From the computing result it is concluded that the refined Arnoldi algorithm based Krylov subspace technique for MEMS model order reduction has more accuracy and reaches lower order number of reduced order model than the classical Arnoldi process.

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11

Binion, David, and Xiaolin Chen. "A Krylov enhanced proper orthogonal decomposition method for frequency domain model reduction." Engineering Computations 34, no. 2 (April 18, 2017): 285–306. http://dx.doi.org/10.1108/ec-11-2015-0344.

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Purpose This paper aims to describe a method for efficient frequency domain model order reduction. The method attempts to combine the desirable attributes of Krylov reduction and proper orthogonal decomposition (POD) and is entitled Krylov enhanced POD (KPOD). Design/methodology/approach The KPOD method couples Krylov’s moment-matching property with POD’s data generalization ability to construct reduced models capable of maintaining accuracy over wide frequency ranges. The method is based on generating a sequence of state- and frequency-dependent Krylov subspaces and then applying POD to extract a single basis that generalizes the sequence of Krylov bases. Findings The frequency response of a pre-stressed microelectromechanical system resonator is used as an example to demonstrate KPOD’s ability in frequency domain model reduction, with KPOD exhibiting a 44 per cent efficiency improvement over POD. Originality/value The results indicate that KPOD greatly outperforms POD in accuracy and efficiency, making the proposed method a potential asset in the design of frequency-selective applications.

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12

Motlubar Rahman, Md, Mahtab Uddin, M. Monir Uddin, and L. S. Andallah. "SVD-Krylov based techniques for structure-preserving reduced order modelling of second-order systems." Mathematical Modelling and Control 1, no. 2 (2021): 79–89. http://dx.doi.org/10.3934/mmc.2021006.

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<abstract><p>We introduce an efficient structure-preserving model-order reduction technique for the large-scale second-order linear dynamical systems by imposing two-sided projection matrices. The projectors are formed based on the features of the singular value decomposition (SVD) and Krylov-based model-order reduction methods. The left projector is constructed by utilizing the concept of the observability Gramian of the systems and the right one is made by following the notion of the interpolation-based technique iterative rational Krylov algorithm (IRKA). It is well-known that the proficient model-order reduction technique IRKA cannot ensure system stability, and the Gramian based methods are computationally expensive. Another issue is preserving the second-order structure in the reduced-order model. The structure-preserving model-order reduction provides a more exact approximation to the original model with maintaining some significant physical properties. In terms of these perspectives, the proposed method can perform better by preserving the second-order structure and stability of the system with minimized $ \mathcal{H}_2 $-norm. Several model examples are presented that illustrated the capability and accuracy of the introducing technique.</p></abstract>

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13

Wang, Xinsheng, Chenxu Wang, and Mingyan Yu. "The Minimum Norm Least-Squares Solution in Reduction by Krylov Subspace Methods." Journal of Circuits, Systems and Computers 26, no. 01 (October 4, 2016): 1750006. http://dx.doi.org/10.1142/s0218126617500062.

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In recent years, model order reduction (MOR) of interconnect system has become an important technique to reduce the computation complexity and improve the verification efficiency in the nanometer VLSI design. The Krylov subspaces techniques in existing MOR methods are efficient, and have become the methods of choice for generating small-scale macro-models of the large-scale multi-port RCL networks that arise in VLSI interconnect analysis. Although the Krylov subspace projection-based MOR methods have been widely studied over the past decade in the electrical computer-aided design community, all of them do not provide a best optimal solution in a given order. In this paper, a minimum norm least-squares solution for MOR by Krylov subspace methods is proposed. The method is based on generalized inverse (or pseudo-inverse) theory. This enables a new criterion for MOR-based Krylov subspace projection methods. Two numerical examples are used to test the PRIMA method based on the method proposed in this paper as a standard model.

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14

Sun, Daoheng. "MODEL ORDER REDUCTION AND SIMULATION OF MEMS BASED ON KRYLOV SUBSPACE." Chinese Journal of Mechanical Engineering 40, no. 05 (2004): 58. http://dx.doi.org/10.3901/jme.2004.05.058.

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15

NIKKU, SHAHI, and KUMAR AWADHESH. "MODEL ORDER REDUCTION USING KRYLOV-SUBSPACE BASED TWO-SIDED ARNOLDI ALGORITHM." i-manager’s Journal on Instrumentation and Control Engineering 4, no. 2 (2016): 29. http://dx.doi.org/10.26634/jic.4.2.4880.

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16

Breiten, Tobias, and Tobias Damm. "Krylov subspace methods for model order reduction of bilinear control systems." Systems & Control Letters 59, no. 8 (August 2010): 443–50. http://dx.doi.org/10.1016/j.sysconle.2010.06.003.

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17

Walker, Nadine, Benjamin Fröhlich, and Peter Eberhard. "Model Order Reduction for Parameter Dependent Substructured Systems using Krylov Subspaces." IFAC-PapersOnLine 51, no. 2 (2018): 553–58. http://dx.doi.org/10.1016/j.ifacol.2018.03.093.

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18

Lu, Kailiang, Ya'nan Fan, Jianmei Zhou, Xiu Li, He Li, and Kerui Fan. "3D anisotropic TEM modeling with loop source using model reduction method." Journal of Geophysics and Engineering 19, no. 3 (June 1, 2022): 403–17. http://dx.doi.org/10.1093/jge/gxac029.

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Abstract For model reduction techniques, there have been relatively few studies performed regarding the forward modeling of anisotropic media in comparison to transient electromagnetic (TEM) forward modeling of isotropic media. The transient electromagnetic method (TEM) responses after the current has been turned off can be represented as a homogeneous ordinary differential equation (ODE) with an initial value, and the ODE can be solved using a matrix exponential function. However, the order of the matrix exponential function is large and solving it directly is challenging, thus this study employs the Shift-and-Invert (SAI-Krylov) subspace algorithm. The SAI-Krylov subspace technique is classified as a single-pole approach compared to the multi-pole rational Krylov subspace approach. It only takes one LU factorization of the coefficient matrix, along with hundreds of backward substitutions. The research in this paper shows that the anisotropic medium has little effect on the optimal shift ${\gamma _{opt}}$ and subspace order m. Furthermore, as compared to the mimetic finite volume method (SAI-MFV) of the SAI-Krylov subspace technique, the method proposed in this paper (SAI-FEM) can further improve the computing efficiency by roughly 13%. In contrast to the standard implicit time step iterative technique, the SAI-FEM method does not require discretization in time, and the TEM response at any moment within the off-time period can be easily computed. Next, the accuracy of the SAI-FEM algorithm was verified by 1D solutions for an anisotropic layer model and a 3D anisotropic model. Finally, the electromagnetic characteristics of the anisotropic anomalous body of the center loop device and separated device of the airborne transient electromagnetic method were analyzed, and it was found that horizontal conductivity has a considerable influence on the TEM response of the anisotropic medium.

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19

Sindler, Jaroslav, and Matej Sulitka. "KRYLOV SUBSPACE MODEL ORDER REDUCTION OF LARGE SCALE FINITE ELEMENT DYNAMICAL SYSTEMS." MM Science Journal 2013, no. 03 (October 1, 2013): 428–33. http://dx.doi.org/10.17973/mmsj.2013_10_201313.

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20

Kumar, Neeraj, Kalarickaparambil J. Vinoy, and Srinivasan Gopalakrishnan. "Improved Well-Conditioned Model Order Reduction Method Based on Multilevel Krylov Subspaces." IEEE Microwave and Wireless Components Letters 28, no. 12 (December 2018): 1065–67. http://dx.doi.org/10.1109/lmwc.2018.2878957.

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21

Tan, Sheldon X. D., Boyuan Yan, and Hai Wang. "Recent advance in non-Krylov subspace model order reduction of interconnect circuits." Tsinghua Science and Technology 15, no. 2 (April 2010): 151–68. http://dx.doi.org/10.1016/s1007-0214(10)70045-6.

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22

Yan, Zhe, and Fangming Lu. "A Large Scale System Model-Order Reduction Method Based on SVD-Krylov." International Journal of Grid and Distributed Computing 9, no. 10 (October 31, 2016): 119–28. http://dx.doi.org/10.14257/ijgdc.2016.9.10.11.

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23

Xu, Kang-Li, Ping Yang, and Yao-Lin Jiang. "Structure-preserving model reduction of second-order systems by Krylov subspace methods." Journal of Applied Mathematics and Computing 58, no. 1-2 (October 30, 2017): 305–22. http://dx.doi.org/10.1007/s12190-017-1146-8.

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24

Heres, P. J., D. Deschrijver, W. H. A. Schilders, and T. Dhaene. "Combining Krylov subspace methods and identification-based methods for model order reduction." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 20, no. 6 (2007): 271–82. http://dx.doi.org/10.1002/jnm.644.

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25

Wang, Xinsheng, and Mingyan Yu. "The Error Bound of Timing Domain in Model Order Reduction by Krylov Subspace Methods." Journal of Circuits, Systems and Computers 27, no. 06 (February 22, 2018): 1850093. http://dx.doi.org/10.1142/s0218126618500937.

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In this paper, we present four different error bound estimates of timing domain in model order reduction by Krylov subspace methods. Firstly, we give integral method based on the impulse response in time domain. The second method is to use small sample statistical method to estimate the error bound based on an error system. The error induced by model order reduction process is constructed by an independent system output. We next present the error bound based on frequency domain error bound transformed into time domain method. The final method is reconstructing an error system, which is factorized to the sum of two parts, resulting from model order reduction by Krylov subspace. It is shown that the first factor is of the reduced order system except for subtracting an auxiliary variable, while the second factor is of the original system except for adding an auxiliary variable. In addition, we also give the analysis of the four methods. A few numerical examples are used to show the efficiency of the four different error bound estimate methods.

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26

Sulitka, M., J. Šindler, J. Sušeň, and J. Smolík. "Application of Krylov Reduction Technique for a Machine Tool Multibody Modelling." Advances in Mechanical Engineering 6 (January 1, 2014): 592628. http://dx.doi.org/10.1155/2014/592628.

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Quick calculation of machine tool dynamic response represents one of the major requirements for machine tool virtual modelling and virtual machining, aiming at simulating the machining process performance, quality, and precision of a workpiece. Enhanced time effectiveness in machine tool dynamic simulations may be achieved by employing model order reduction (MOR) techniques of the full finite element (FE) models. The paper provides a case study aimed at comparison of Krylov subspace base and mode truncation technique. Application of both of the reduction techniques for creating a machine tool multibody model is evaluated. The Krylov subspace reduction technique shows high quality in terms of both dynamic properties of the reduced multibody model and very low time demands at the same time.

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27

Perev, K. "The Unifying Feature of Projection in Model Order Reduction." Information Technologies and Control 12, no. 3-4 (December 1, 2014): 17–27. http://dx.doi.org/10.1515/itc-2016-0003.

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Abstract This paper considers the problem of model order reduction of linear systems with the emphasis on the common features of the main approaches. One of these features is the unifying role of operator projection in model reduction. It is shown how projections are implemented for different methods of model reduction and what their properties are. The other common feature is the subspaces where projections are defined. The main approaches for model reduction which are considered in the paper are balanced truncation, proper orthogonal decomposition and the Lanczos procedure from the Krylov subspace methods. It is shown that the range spaces of system gramians for balanced truncation and the range space of the reachability and observability matrices for the Lanczos procedure coincide. The connection between balanced truncation and the proper orthogonal decomposition method is also established. Therefore, the methods for model reduction are similar in terms of general operational principles, and differ mostly in their technical implementation. Several numerical examples are considered showing the validity of the proposed conjectures.

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28

Vakilzadeh, Mohsen, Ramin Vatankhah, and Mohammad Eghtesad. "Tracking control of suspended microchannel resonators based on Krylov model order reduction method." Journal of Vibration and Control 25, no. 5 (November 7, 2018): 1019–30. http://dx.doi.org/10.1177/1077546318809609.

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In this paper, trajectory tracking control of suspended microchannel resonators (SMRs) is studied. A finite element procedure based on modified strain gradient theory will be used to model the SMR. Finite element methods usually lead to a model with a relatively high number of degrees of freedom. Thus, first, we will utilize the second order Krylov subspace method based on multi-moment matching to obtain a second order bilinear reduced system. Then, an output feedback controller and an optimal controller which take much less computation time and effort will be designed for the reduced system. The SMR is a micro-resonator which oscillates in a special frequency in practical cases, and thus tracking the desired paths is considered here as the control objective. Simulation results show the excellent performance of the proposed controllers.

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29

Jiang, Yao-Lin, Chun-Yue Chen, and Hai-Bao Chen. "Model-order reduction of coupled DAE systems via technique and Krylov subspace method." Journal of the Franklin Institute 349, no. 10 (December 2012): 3027–45. http://dx.doi.org/10.1016/j.jfranklin.2012.09.004.

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30

Saiduzzaman, Md, Md Shafiqul Islam, Mohammad Monir Uddin, and Mohammad Osman Gani. "Comparative study on techniques of model order reduction using rational Krylov subspace method." Journal of Interdisciplinary Mathematics 25, no. 7 (October 3, 2022): 1971–78. http://dx.doi.org/10.1080/09720502.2022.2133224.

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31

Benner, Peter, Tobias Breiten, and Tobias Damm. "Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems." PAMM 10, no. 1 (November 16, 2010): 601–2. http://dx.doi.org/10.1002/pamm.201010293.

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32

Hasan, Shazzad, and M. Monir Uddin. "Model Reduction of Structured Dynamical Systems by Projecting onto the Dominant Eigenspace of the Gramians." Journal of Modeling and Optimization 10, no. 2 (December 31, 2018): 94. http://dx.doi.org/10.32732/jmo.2018.10.2.94.

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This paper studies the structure preserving (second-order to second-order) model order reduction of second-order systems applying the projection onto the dominant eigenspace of the Gramians of the systems. The projectors which create the reduced order model are generated cheaply from the low-rank Gramian factors. The low-rank Gramian factors are computed efficiently by solving the corresponding Lyapunov equations of the system using the rational Krylov subspace method. The efficiency of the theoretical results are then illustrated by numerical experiments.

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33

Shi, Jian, and Ben Lian Xu. "Model Order Reduction for Pre-Stressed Harmonic Analysis of Micromechanical Beam Resonators." Applied Mechanics and Materials 40-41 (November 2010): 739–43. http://dx.doi.org/10.4028/www.scientific.net/amm.40-41.739.

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A second-order system model order reduction method for pre-stressed harmonic analysis of electrostatically actuated microbeams is demonstrated, which produces a low dimensional approximation of the original system and enables a substantial reduction of simulation time. The moment matching property for second-order dynamic systems is studied and the block Arnoldi algorithm is adopted for the generation of the Krylov subspace, which extracts the low order model from the discretized system assembled through finite element analysis. The difference between two successive reduced models suggests the choice of the order for the reduce model. A detailed comparison research among the full model and the reduced models is performed. The research results confirm the effectiveness of the presented method.

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34

Rösner, M., and R. Lammering. "Basic principles and aims of model order reduction in compliant mechanisms." Mechanical Sciences 2, no. 2 (October 17, 2011): 197–204. http://dx.doi.org/10.5194/ms-2-197-2011.

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Abstract. Model order reduction appears to be beneficial for the synthesis and simulation of compliant mechanisms due to computational costs. Model order reduction is an established method in many technical fields for the approximation of large-scale linear time-invariant dynamical systems described by ordinary differential equations. Based on system theory, underlying representations of the dynamical system are introduced from which the general reduced order model is derived by projection. During the last years, numerous new procedures were published and investigated appropriate to simulation, optimization and control. Singular value decomposition, condensation-based and Krylov subspace methods representing three order reduction methods are reviewed and their advantages and disadvantages are outlined in this paper. The convenience of applying model order reduction in compliant mechanisms is quoted. Moreover, the requested attributes for order reduction as a future research direction meeting the characteristics of compliant mechanisms are commented.

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35

Wang, Ning, Huifang Wang, and Shiyou Yang. "A Broadband Enhanced Structure-Preserving Reduced-Order Interconnect Macromodeling Method for Large-Scale Equation Sets of Transient Interconnect Circuit Problems." Energies 13, no. 21 (November 2, 2020): 5746. http://dx.doi.org/10.3390/en13215746.

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In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature. Compared to other MOR methods, the structure-preserving reduced-order interconnect macromodeling (SPRIM) based on Krylov subspaces will achieve a higher reduction radio and precision for large multi-port Resistor-Capacitor-Inductor (RCL) circuits. However, for very wide band frequency transients, the performance of a Krylov subspace-based MOR method is not satisfactory. Moreover, the selection of the expansion point in this method has not been comprehensively studied in the literature. From this point of view, a broadband enhanced structure-preserving reduced-order interconnect macromodeling (SPRIM) method is proposed to reduce the order of equation sets of a transient interconnect circuit model. In addition, a method is introduced to determine the optimal expansion point at each frequency in the proposed method. The proposed method is validated by the numerical results on a transient problem of an insulated-gate bipolar transistor (IGBT)-based inverter busbar under different exciting conditions.

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36

Han, Jeong Sam, and Seung Hyun Kim. "Automation of Krylov Subspace Model Order Reduction for Transient Response Analysis with Multiple Loading." Journal of the Computational Structural Engineering Institute of Korea 34, no. 2 (April 1, 2021): 101–11. http://dx.doi.org/10.7734/coseik.2021.34.2.101.

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37

Weile, D. S., and E. Michielssen. "Analysis of frequency selective surfaces using two-parameter generalized rational Krylov model-order reduction." IEEE Transactions on Antennas and Propagation 49, no. 11 (2001): 1539–49. http://dx.doi.org/10.1109/8.964089.

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38

Lin, Yiqin, Liang Bao, and Yimin Wei. "A model-order reduction method based on Krylov subspaces for mimo bilinear dynamical systems." Journal of Applied Mathematics and Computing 25, no. 1-2 (September 2007): 293–304. http://dx.doi.org/10.1007/bf02832354.

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39

Bruns, Angelika, and Peter Benner. "Parametric model order reduction of thermal models using the bilinear interpolatory rational Krylov algorithm." Mathematical and Computer Modelling of Dynamical Systems 21, no. 2 (June 12, 2014): 103–29. http://dx.doi.org/10.1080/13873954.2014.924534.

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40

Volzer, Thomas, and Peter Eberhard. "Model Order Reduction of Large-Scale Finite Element Systems in an MPI Parallelized Environment for Usage in Multibody Simulation." Archive of Mechanical Engineering 63, no. 4 (December 1, 2016): 475–94. http://dx.doi.org/10.1515/meceng-2016-0027.

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Abstract 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 block size and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.

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41

Tengs, E., F. Charrassier, M. Holst, and Pål-Tore Storli. "Model Order Reduction Technique Applied on Harmonic Analysis of a Submerged Vibrating Blade." International Journal of Applied Mechanics and Engineering 24, no. 1 (February 1, 2019): 131–42. http://dx.doi.org/10.2478/ijame-2019-0009.

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Abstract 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.

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Ahmad, Shahbaz, Faisal Fairag, Adel M. Al-Mahdi, and Jamshaid ul Rahman. "Preconditioned augmented Lagrangian method for mean curvature image deblurring." AIMS Mathematics 7, no. 10 (2022): 17989–8009. http://dx.doi.org/10.3934/math.2022991.

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<abstract><p>Image deblurring models with a mean curvature functional has been widely used to preserve edges and remove the staircase effect in the resulting images. However, the Euler-Lagrange equations of a mean curvature model can be used to solve fourth-order non-linear integro-differential equations. Furthermore, the discretization of fourth-order non-linear integro-differential equations produces an ill-conditioned system so that the numerical schemes like Krylov subspace methods (conjugate gradient etc.) have slow convergence. In this paper, we propose an augmented Lagrangian method for a mean curvature-based primal form of the image deblurring problem. A new circulant preconditioned matrix is introduced to overcome the problem of slow convergence when employing a conjugate gradient method inside of the augmented Lagrangian method. By using the proposed new preconditioner fast convergence has been observed in the numerical results. Moreover, a comparison with the existing numerical methods further reveal the effectiveness of the preconditioned augmented Lagrangian method.</p></abstract>

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Pierquin, Antoine, Thomas Henneron, Stephane Clenet, and Stephane Brisset. "Model-Order Reduction of Magnetoquasi-Static Problems Based on POD and Arnoldi-Based Krylov Methods." IEEE Transactions on Magnetics 51, no. 3 (March 2015): 1–4. http://dx.doi.org/10.1109/tmag.2014.2358374.

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Bonotto, Matteo, Paolo Bettini, and Angelo Cenedese. "Model-Order Reduction of Large-Scale State-Space Models in Fusion Machines via Krylov Methods." IEEE Transactions on Magnetics 53, no. 6 (June 2017): 1–4. http://dx.doi.org/10.1109/tmag.2017.2660760.

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Panagiotopoulos, Dionysios, Elke Deckers, and Wim Desmet. "Krylov subspaces recycling based model order reduction for acoustic BEM systems and an error estimator." Computer Methods in Applied Mechanics and Engineering 359 (February 2020): 112755. http://dx.doi.org/10.1016/j.cma.2019.112755.

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Druskin, Vladimir, Rob Remis, and Mikhail Zaslavsky. "An extended Krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains." Journal of Computational Physics 272 (September 2014): 608–18. http://dx.doi.org/10.1016/j.jcp.2014.04.051.

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Han, Jeong Sam. "Krylov subspace-based model order reduction for Campbell diagram analysis of large-scale rotordynamic systems." Structural Engineering and Mechanics 50, no. 1 (April 10, 2014): 19–36. http://dx.doi.org/10.12989/sem.2014.50.1.019.

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Tamri, A., L. Mitiche, and A. B. H. Adamou-Mitiche. "A Second Order Arnoldi Method with Stopping Criterion and Reduced Order Selection for Reducing Second Order Systems." Engineering, Technology & Applied Science Research 12, no. 3 (June 6, 2022): 8712–17. http://dx.doi.org/10.48084/etasr.4974.

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This paper introduces a new algorithm for reducing large dimensional second-order dynamic systems through the Second Order Arnold Reduction (SOAR) procedure, with a stopping criterion to select an acceptable good order for the reduced model based on a new coefficient called the Numerical-Rank Performance Coefficient (NRPC), for efficient early termination and automatic optimal order selection of the reduced model. The key idea of this method is to calculate the NRPC coefficient for each iteration of the SOAR algorithm and measure the dynamic evolution information of the original system, which is added to each vector of the Krylov subspace generated by the SOAR algorithm. When the dynamical tolerance condition is verified, the iterative procedure of the algorithm stops. Three benchmark models were used as numerical examples to check the effectiveness and simplicity of the proposed algorithm.

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ASAI, Mitsuteru, Norliyati MOHD AMIN, and Yoshimi SONODA. "Practical Determination of an Effective Reduced Order in a Model Order Reduction of Dynamic FEM via Krylov Subspace." Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) 67, no. 2 (2011): I_85—I_93. http://dx.doi.org/10.2208/jscejam.67.i_85.

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Manatskov, Yuriy M., Torsten Bertram, Danil V. Shaykhutdinov, and Nikolay I. Gorbatenko. "Study of methods for dimension reduction of complex dynamic linear systems models." MATEC Web of Conferences 226 (2018): 04036. http://dx.doi.org/10.1051/matecconf/201822604036.

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Complex dynamic linear systems of equations are solved by numerical iterative methods, which need much computation and are timeconsuming ones, and the optimization stage requires repeated solution of these equation systems that increases the time on development. To shorten the computation time, various methods can be applied, among them preliminary (estimated) calculation or oversimple models calculation, however, while testing and optimizing the full model is used. Reduced order models are very popular in solving this problem. The main idea of a reduced order model is to find a simplified model that may reflect the required properties of the original model as accurately as possible. There are many methods for the model order reduction, which have their advantages and disadvantages. In this article, a method based on Krylov subspaces and SVD methods is considered. A numerical experiments is given.

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