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Relevant bibliographies by topics / Augmented Krylov Model Order Reduction

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Academic literature on the topic 'Augmented Krylov Model Order Reduction'

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Published: 6 September 2023

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

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Augmented Krylov Model Order Reduction"

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Olsson, K. Henrik A. "Model Order Reduction with Rational Krylov Methods." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-401.

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Maciver, Mark Alasdair. "Electromagnetic characterisation of structures using Krylov subspace model order reduction methods." Thesis, University of Glasgow, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.433619.

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Agbaje, Oluwaleke Abimbola. "Krylov subspace model order reduction for nonlinear and bilinear control systems." Thesis, Coventry University, 2016. http://curve.coventry.ac.uk/open/items/62c3a18c-4d39-4397-9684-06d77b9cd187/1.

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The use of Krylov subspace model order reduction for nonlinear/bilinear systems, over the past few years, has become an increasingly researched area of study. The need for model order reduction has never been higher, as faster computations for control, diagnosis and prognosis have never been higher to achieve better system performance. Krylov subspace model order reduction techniques enable this to be done more quickly and efficiently than what can be achieved at present. The most recent advances in the use of Krylov subspaces for reducing bilinear models match moments and multimoments at some expansion points which have to be obtained through an optimisation scheme. This therefore removes the computational advantage of the Krylov subspace techniques implemented at an expansion point zero. This thesis demonstrates two improved approaches for the use of one-sided Krylov subspace projection for reducing bilinear models at the expansion point zero. This work proposes that an alternate linear approximation can be used for model order reduction. The advantages of using this approach are improved input-output preservation at a simulation cost similar to some earlier works and reduction of bilinear systems models which have singular state transition matrices. The comparison of the proposed methods and other original works done in this area of research is illustrated using various examples of single input single output (SISO) and multi input multi output (MIMO) models.

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Yan, Boyuan. "Advanced non-Krylov subspace model order reduction techniques for interconnect circuits." Diss., [Riverside, Calif.] : University of California, Riverside, 2009. http://proquest.umi.com/pqdweb?index=0&did=1957340951&SrchMode=2&sid=4&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1268670715&clientId=48051.

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Thesis (Ph. D.)--University of California, Riverside, 2009.
Includes abstract. Available via ProQuest Digital Dissertations. Title from first page of PDF file (viewed March 12, 2010). Includes bibliographical references (p. 122-126). Also issued in print.

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Barkouki, Houda. "Rational Lanczos-type methods for model order reduction." Thesis, Littoral, 2016. http://www.theses.fr/2016DUNK0440/document.

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La solution numérique des systèmes dynamiques est un moyen efficace pour étudier des phénomènes physiques complexes. Cependant, dans un cadre à grande échelle, la dimension du système rend les calculs infaisables en raison des limites de mémoire et de temps, ainsi que le mauvais conditionnement. La solution de ce problème est la réduction de modèles. Cette thèse porte sur les méthodes de projection pour construire efficacement des modèles d'ordre inférieur à partir des systèmes linéaires dynamiques de grande taille. En particulier, nous nous intéressons à la projection sur la réunion de plusieurs sous-espaces de Krylov standard qui conduit à une classe de modèles d'ordre réduit. Cette méthode est connue par l'interpolation rationnelle. En se basant sur ce cadre théorique qui relie la projection de Krylov à l'interpolation rationnelle, quatre algorithmes de type Lanczos rationnel pour la réduction de modèles sont proposés. Dans un premier temps, nous avons introduit une méthode adaptative de type Lanczos rationnel par block pour réduire l'ordre des systèmes linéaires dynamiques de grande taille, cette méthode est basée sur l'algorithme de Lanczos rationnel par block et une méthode adaptative pour choisir les points d'interpolation. Une généralisation de ce premier algorithme est également donnée, où différentes multiplicités sont considérées pour chaque point d'interpolation. Ensuite, nous avons proposé une autre extension de la méthode du sous-espace de Krylov standard pour les systèmes à plusieurs-entrées plusieurs-sorties, qui est le sous-espace de Krylov global. Nous avons obtenu des équations qui décrivent cette procédure. Finalement, nous avons proposé une méthode de Lanczos étendu par block et nous avons établi de nouvelles propriétés algébriques pour cet algorithme. L'efficacité et la précision de tous les algorithmes proposés, appliqués sur des problèmes de réduction de modèles, sont testées dans plusieurs exemples numériques
Numerical solution of dynamical systems have been a successful means for studying complex physical phenomena. However, in large-scale setting, the system dimension makes the computations infeasible due to memory and time limitations, and ill-conditioning. The remedy of this problem is model reductions. This dissertations focuses on projection methods to efficiently construct reduced order models for large linear dynamical systems. Especially, we are interesting by projection onto unions of Krylov subspaces which lead to a class of reduced order models known as rational interpolation. Based on this theoretical framework that relate Krylov projection to rational interpolation, four rational Lanczos-type algorithms for model reduction are proposed. At first, an adaptative rational block Lanczos-type method for reducing the order of large scale dynamical systems is introduced, based on a rational block Lanczos algorithm and an adaptive approach for choosing the interpolation points. A generalization of the first algorithm is also given where different multiplicities are consider for each interpolation point. Next, we proposed another extension of the standard Krylov subspace method for Multiple-Input Multiple-Output (MIMO) systems, which is the global Krylov subspace, and we obtained also some equations that describe this process. Finally, an extended block Lanczos method is introduced and new algebraic properties for this algorithm are also given. The accuracy and the efficiency of all proposed algorithms when applied to model order reduction problem are tested by means of different numerical experiments that use a collection of well known benchmark examples

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Wyatt, Sarah Alice. "Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27668.

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Dynamical systems are mathematical models characterized by a set of differential or difference equations. Model reduction aims to replace the original system with a reduced system of significantly smaller dimension that still describes the important dynamics of the large-scale model. Interpolatory model reduction methods define a reduced model that interpolates the full model at selected interpolation points. The reduced model may be obtained through a Krylov reduction process or by using the Iterative Rational Krylov Algorithm (IRKA), which iterates this Krylov reduction process to obtain an optimal $\mathcal{H}_2$ reduced model. This dissertation studies interpolatory model reduction for first-order descriptor systems, second-order systems, and DAEs. The main computational cost of interpolatory model reduction is the associated linear systems. Especially in the large-scale setting, inexact solves become desirable if not necessary. With the introduction of inexact solutions, however, exact interpolation no longer holds. While the effect of this loss of interpolation has previously been studied, we extend the discussion to the preconditioned case. Then we utilize IRKA's convergence behavior to develop preconditioner updates. We also consider the interpolatory framework for DAEs and second-order systems. While interpolation results still hold, the singularity associated with the DAE often results in unbounded model reduction errors. Therefore, we present a theorem that guarantees interpolation and a bounded model reduction error. Since this theorem relies on expensive projectors, we demonstrate how interpolation can be achieved without explicitly computing the projectors for index-1 and Hessenberg index-2 DAEs. Finally, we study reduction techniques for second-order systems. Many of the existing methods for second-order systems rely on the model's associated first-order system, which results in computations of a $2n$ system. As a result, we present an IRKA framework for the reduction of second-order systems that does not involve the associated $2n$ system. The resulting algorithm is shown to be effective for several dynamical systems.
Ph. D.

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Hijazi, Abdallah. "Implementation of harmonic balance reduce model order equation." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0139/document.

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MOR (Model Order Reduction) est devenu un domaine très répondu dans la recherche grâce à l'intérêt qu'il peut apporter dans la réduction des systèmes, ce qui permet d'économiser du temps, de la mémoire et le coût de CPU pour les outils de CAO. Ce domaine contient principalement deux branches: linéaires et non linéaires. MOR linéaire est un domaine mature avec des techniques numériques bien établie et bien connus dans la domaine de la recherche, par contre le domaine non linéaire reste vague, et jusqu'à présent il n'a pas montré des bons résultats dans la simulation des circuits électriques. La recherche est toujours en cours dans ce domaine, en raison de l’intérêt qu'il peut fournir aux simulateurs contemporains, surtout avec la croissance des puces électroniques en termes de taille et de complexité, et les exigences industrielles vers l'intégration des systèmes sur la même puce.Une contribution significative, pour résoudre le problème de Harmonic Balance (Equilibrage Harmonique) en utilisant la technique MOR, a été proposé en 2002 par E. Gad et M. Nakhla. La technique a montré une réduction substantielle de la dimension du système, tout en préservant, en sortie, la précision de l'analyse en régime permanent. Cette méthode de MOR utilise la technique de projection par l'intermédiaire de Krylov, et il préserve la passivité du système. Cependant, il souffre de quelques limitations importantes dans la construction de la matrice “pre-conditioner“ qui permettrait de réduire le système. La limitation principale est la nécessité d'une factorisation explicite comme une suite numérique de l'équation des dispositifs non linéaires . cette limitation rend la technique difficile à appliquer dans les conditions générales d'un simulateur. Cette thèse examinera les aspects non linéaires du modèle de réduction pour les équations de bilan harmoniques, et il étudiera les solutions pour surmonter les limitations mentionnées ci-dessus, en particulier en utilisant des approches de dérivateur numériques
MOR recently became a well-known research field, due to the interest that it shows in reducing the system, which saves time, memory, and CPU cost for CAD tools. This field contains two branches, linear and nonlinear MOR, the linear MOR is a mature domain with well-established theory and numerical techniques. Meanwhile, nonlinear MOR domain is still stammering, and so far it didn’t show good and successful results in electrical circuit simulation. Some improvements however started to pop-up recently, and research is still going on this field because of the help that it can give to the contemporary simulators, especially with the growth of the electronic chips in terms of size and complexity due to industrial demands towards integrating systems on the same chip. A significant contribution in the MOR technique of HB solution has been proposed a decade ago by E. Gad and M. Nakhla. The technique has shown to provide a substantial system dimension reduction while preserving the precision of the output in steady state analysis. This MOR method uses the technique of projection via Krylov, and it preserves the passivity of the system. However, it suffers a number of important limitations in the construction of the pre-conditioner matrix which is ought to reduce the system. The main limitation is the necessity for explicit factorization as a power series of the equation of the nonlinear devices. This makes the technique difficult to apply in general purpose simulator conditions. This thesis will review the aspects of the nonlinear model order reduction technique for harmonic balance equations, and it will study solutions to overcome the above mentioned limitations, in particular using numerical differentiation approaches

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Panzer, Heiko [Verfasser]. "Model Order Reduction by Krylov Subspace Methods with Global Error Bounds and Automatic Choice of Parameters / Heiko Panzer." München : Verlag Dr. Hut, 2014. http://d-nb.info/1063222176/34.

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Panzer, Heiko K. F. [Verfasser], Boris [Akademischer Betreuer] Lohmann, and Athanasios C. [Akademischer Betreuer] Antoulas. "Model Order Reduction by Krylov Subspace Methods with Global Error Bounds and Automatic Choice of Parameters / Heiko K. F. Panzer. Gutachter: Athanasios C. Antoulas ; Boris Lohmann. Betreuer: Boris Lohmann." München : Universitätsbibliothek der TU München, 2014. http://d-nb.info/1064976263/34.

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Panzer, Heiko [Verfasser], Boris [Akademischer Betreuer] Lohmann, and Athanasios C. [Akademischer Betreuer] Antoulas. "Model Order Reduction by Krylov Subspace Methods with Global Error Bounds and Automatic Choice of Parameters / Heiko K. F. Panzer. Gutachter: Athanasios C. Antoulas ; Boris Lohmann. Betreuer: Boris Lohmann." München : Universitätsbibliothek der TU München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:91-diss-20140916-1207822-0-0.

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Book chapters on the topic "Augmented Krylov Model Order Reduction"

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Heres, P. J., and W. H. A. Schilders. "Orthogonalisation in Krylov Subspace Methodsfor Model Order Reduction." In Scientific Computing in Electrical Engineering, 39–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-32862-9_6.

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Sreekumar, Harikrishnan K., Rupert Ullmann, Stefan Sicklinger, and Sabine C. Langer. "Efficient Krylov Subspace Techniques for Model Order Reduction of Automotive Structures in Vibroacoustic Applications." In Model Reduction of Complex Dynamical Systems, 259–82. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72983-7_12.

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Jehle, Jonas Siegfried, Luca Mechelli, and Stefan Volkwein. "POD-Based Augmented Lagrangian Method for State Constrained Heat-Convection Phenomena." In IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018, 127–39. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21013-7_9.

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Conference papers on the topic "Augmented Krylov Model Order Reduction"

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Kumar, Neeraj, K. J. Vinoy, and S. Gopalakrishnan. "Augmented Krylov model order reduction for finite element approximation of plane wave scattering problems." In 2013 IEEE MTT-S International Microwave and RF Conference. IEEE, 2013. http://dx.doi.org/10.1109/imarc.2013.6777714.

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Amin, N. Mohd, and R. R. Krisnamoorthy. "Krylov Subspace model order reduction for FE seismic analysis." In 2012 IEEE Symposium on Business, Engineering and Industrial Applications (ISBEIA). IEEE, 2012. http://dx.doi.org/10.1109/isbeia.2012.6422877.

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Garrido, S. Sebastian E., and Roy A. McCann. "Krylov subspace based model order reduction of distribution networks." In 2017 North American Power Symposium (NAPS). IEEE, 2017. http://dx.doi.org/10.1109/naps.2017.8107214.

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Cong Teng and Xia Li. "New algorithms for second order model reduction based on Krylov projections." In 2011 International Conference on Electric Information and Control Engineering (ICEICE). IEEE, 2011. http://dx.doi.org/10.1109/iceice.2011.5778209.

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Nabi, M., M. A. Bazaz, and P. Guha. "Krylov-subspace based model order reduction for field-circuit coupled systems." In 2009 European Conference on Circuit Theory and Design (ECCTD 2009). IEEE, 2009. http://dx.doi.org/10.1109/ecctd.2009.5275034.

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Yetkin, E. Fatih, and Hasan Dag. "Parallel implementation of iterative rational Krylov methods for model order reduction." In 2009 Fifth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control. IEEE, 2009. http://dx.doi.org/10.1109/icsccw.2009.5379421.

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Wolf, Thomas, Heiko K. F. Panzer, and Boris Lohmann. "ℌ2 pseudo-optimality in model order reduction by Krylov subspace methods." In 2013 European Control Conference (ECC). IEEE, 2013. http://dx.doi.org/10.23919/ecc.2013.6669585.

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Cao, Xingang, Joseph Maubach, Siep Weiland, and Wil Schilders. "A Novel Krylov Method for Model Order Reduction of Quadratic Bilinear Systems." In 2018 IEEE Conference on Decision and Control (CDC). IEEE, 2018. http://dx.doi.org/10.1109/cdc.2018.8619575.

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Salimbahrami, Behnam, Rudy Eid, and Boris Lohmann. "Model reduction by second order Krylov subspaces: Extensions, stability and proportional damping." In 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control. IEEE, 2006. http://dx.doi.org/10.1109/cacsd-cca-isic.2006.4777115.

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Salimbahrami, Behnam, Rudy Eid, and Boris Lohmann. "Model Reduction by Second Order Krylov Subspaces: Extensions, Stability and Proportional Damping." In 2006 IEEE Conference on Computer-Aided Control Systems Design. IEEE, 2006. http://dx.doi.org/10.1109/cacsd.2006.285535.

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