Relevant bibliographies by topics / Fast diagonalization method

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Academic literature on the topic 'Fast diagonalization method'

Author: Grafiati
Published: 28 September 2024

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Journal articles on the topic "Fast diagonalization method"

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Si, Wei, and Qiang Xu. "Virtual Boundary Element Collocation Method with RBF Interpolation on Virtual Boundary and Diagonalization Feature in Fast Multipole Method." Advanced Materials Research 378-379 (October 2011): 166–70. http://dx.doi.org/10.4028/www.scientific.net/amr.378-379.166.

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The algorithm idea of virtual boundary element collocation method with RBF interpolation on virtual boundary and diagonalization feature in fast multipole method is presented to study 2-D elasticity problems in this paper. In other words, the new fast multipole method (FMM) adopting diagonalization and the generalized minimal residual (GMRES) algorithm are jointly employed to solve the equations related to virtual boundary element collocation method (VBEM) with RBF interpolation on virtual boundary. In this paper, the numerical scheme suitable for original FMM with respect to two-dimensional problem of elasticity is optimized, through the introduction of concept of diagonalization, in terms of the radial basis function to express the unknown virtual load functions, in order to further improve the efficiency of the problem to be solved. Then large-scale numerical simulations of elastostatics might be achieved by the method. Numerical examples in the paper have proved the feasibility, efficiency and calculating precision of the method.
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Zhang Na, 张娜, 冯金超 Feng Jinchao, 李哲 Li Zhe, and 贾克斌 Jia Kebin. "Fast Photoacoustic Imaging Reconstruction Method Based on Lanczos Double Diagonalization." Chinese Journal of Lasers 45, no. 3 (2018): 0307018. http://dx.doi.org/10.3788/cjl201845.0307018.

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Nyka, Krzysztof. "Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components." Electronics 8, no. 3 (February 27, 2019): 260. http://dx.doi.org/10.3390/electronics8030260.

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A new technique of local model-order reduction (MOR) in 3-D finite element method (FEM) for frequency-domain electromagnetic analysis of waveguide components is proposed in this paper. It resolves the problem of increasing solution time of the reduced-order system assembled from macromodels created in the subdomains, into which an analyzed structure is partitioned. This problem becomes particularly relevant for growing size and count of the macromodels, and when they are cloned in multiple locations of the structures or are used repeatedly in a tuning and optimization process. To significantly reduce the solution time, the diagonalized macromodels are created by means of the simultaneous diagonalization and subsequently assembled in the global system. For the resulting partially diagonal matrix, an efficient dedicated solver based on the Schur complement technique is proposed. The employed MOR method preserves frequency independence of the macromodels, which is essential for efficient diagonalization, as it can be performed once for the whole analysis bandwidth. The numerical validation of the proposed procedures with respect to accuracy and speed was carried out for varying size and count of macromodels. An exemplary finite periodical waveguide structure was chosen to investigate the influence of macromodel cloning on the resultant efficiency. The results show that the use of the diagonalized macromodels provided a significant solution speedup without any loss of accuracy.
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Montardini, M., G. Sangalli, and M. Tani. "Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method." Computer Methods in Applied Mechanics and Engineering 338 (August 2018): 162–85. http://dx.doi.org/10.1016/j.cma.2018.04.017.

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Liu, Fang, Yongbin Liu, Fenglin Chen, and Bing He. "Residual life prediction for ball bearings based on joint approximate diagonalization of eigen matrices and extreme learning machine." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 9 (December 10, 2015): 1699–711. http://dx.doi.org/10.1177/0954406215621585.

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Data-driven approaches have been proved effective for remaining useful life estimation of key components (bearings for example) in rotating machinery. In such approaches, it is important to determine an appropriate degradation indicator from the collected run-to-failure life cycle data. In this paper, a new degradation indicator is introduced based on the joint approximate diagonalization of eigen matrices algorithm. First, a matrix consisting of time domain, frequency domain, and time–frequency domain features extracted from the collected data instances is created. Then a two-layer joint approximate diagonalization of eigen matrices is introduced to transform the matrix to the advanced features (a vector) that represents the behavior of the bearing’s degradation. As an independent component analysis method, the designed two-layer joint approximate diagonalization of eigen matrices is able to eliminate the redundancy of the directly extracted features. Further, the obtained vector is input into an extreme learning machine to train a remaining useful life prediction model. Finally, a set of experimental cases are utilized to verify the presented method. Results show that the two-layer joint approximate diagonalization of eigen matrices is capable of exploring features that reflects the trend of bearing’s degradation state much better. And due to the easy parameter configuration and fast learning speed, the extreme learning machine is capable of training a model that can effectively predict the remaining useful life of the bearings.
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Eibert, T. F. "A multilevel fast spectral domain algorithm for electromagnetic analysis of infinite periodic arrays with large unit cells." Advances in Radio Science 4 (September 4, 2006): 41–47. http://dx.doi.org/10.5194/ars-4-41-2006.

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Abstract. A multilevel fast spectral domain algorithm (MLFSDA) is introduced for the efficient evaluation of the matrix vector products due to the boundary integral (BI) operator within a hybrid finite element - BI (FEBI) method for the analysis of infinite periodic arrays. The MLFSDA utilizes the diagonalization property of the spectral domain (SD) BI representation and handles the large numbers of Floquet modes required for large (with respect to wavelength) periodic unit cells by similar hierarchical techniques as applied in the multilevel fast multipole method/algorithm (MLFMM/MLFMA). With the capability of the MLFSDA to handle very large periodic unit cells, it becomes possible to model finite antennas and scatterers with the infinite periodic array model. For a cavity-backed antenna element and for a semi-finite array of 4 cavity-backed antenna elements in the finite direction, the dependence of the input impedances on the unit cell sizes is investigated and it is found that array resonances disappear for reasonably large unit cell dimensions. Finally, a semi-finite array of antipodal Vivaldi antenna elements is considered and simulation results for infinite periodic, finite, and semi-finite array configurations are compared to measured data.
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Lay-Ekuakille, A., G. Griffo, D. Pellicanò, P. Maris, and M. Cacciola. "A Hardware for Processing Magnetic Pressure Sensor Signals from Leak Detection in Waterworks." International Journal of Measurement Technologies and Instrumentation Engineering 3, no. 3 (July 2013): 35–45. http://dx.doi.org/10.4018/ijmtie.2013070103.

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Leaks in pipelines and waterworks are detected using different methods and among them spectral analysis is one of the most interesting ones. Sources of signals to be processed are different, for example: reflected signals from ground penetrating radar and acoustic sources, signals from dedicated sensors mounted on pipelines, etc… In the latter case, magnetic pressure sensors located on the pipeline acquire vibrations and oscillations of liquids (e.g. water) in the pipeline, following a leak in the pipeline. These vibrations and oscillations are transformed in electrical signal and processed using different methods and techniques like FFT (Fast Fourier Transform), ANN (Artificial Neural Network), STFT (Short-Term Fourier Transform), and Impedance Method (IM). But there are other advanced methodical approaches that can improve the quality of the signal related to the leak; one of them is FDM (Filter Diagonalization Method). Even in presence of an advanced method, recovered signal displays undesired attenuation and noisy behavior due to different reasons, namely, hardware, background noise, materials used for pipeline construction, sensors, etc.. This paper presents a complementary hardware for processing the above signals. The hardware is based on innovating approach that minimizes additional noisy components.
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Cornejo Fuentes, Joaquín, Thomas Elguedj, David Dureisseix, and Arnaud Duval. "A cheap preconditioner based on fast diagonalization method for matrix-free weighted-quadrature isogeometric analysis applied to nonlinear transient heat transfer problems." Computer Methods in Applied Mechanics and Engineering 414 (September 2023): 116157. http://dx.doi.org/10.1016/j.cma.2023.116157.

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Cervellino, Antonio, Cinzia Giannini, Antonietta Guagliardi, and Massimo Ladisa. "Unfolding a two-dimensional powder diffraction image: conformal mapping." Journal of Applied Crystallography 41, no. 4 (July 1, 2008): 701–4. http://dx.doi.org/10.1107/s0021889808019092.

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A new procedure aimed at unfolding a two-dimensional powder diffraction image into both a one-dimensional azimuthal and a radial scan is presented. In this approach, the sample-to-detector distance is the only parameter that must be adjusted in a separate step by using a standard sample. The technique consists of three steps: tracking the beam centre as the local maximum of the self-convolution of the original two-dimensional map, detector tilt and rotation determination by an intensity-tensor diagonalization, and azimuthal/radial intensity integration by a conformal mapping of the original two-dimensional powder diffraction image. The X-ray powder diffraction (XRPD) intensity profile of the NIST Si 640c standard sample is used to test the performance. The results show the robustness of the method and its capability of efficiently tagging the pixels in a two-dimensional readout system by matching the ideal geometry of the detector to the real beam–sample–detector frame. The technique is a fast, versatile and user-friendly tool for the simultaneous analysis of both azimuthal and radial spectra of two-dimensional XRPD images.
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Liu, Wang, Huang, and Yang. "An Improved Second-Order Blind Identification (SOBI) Signal De-Noising Method for Dynamic Deflection Measurements of Bridges Using Ground-Based Synthetic Aperture Radar (GBSAR)." Applied Sciences 9, no. 17 (August 30, 2019): 3561. http://dx.doi.org/10.3390/app9173561.

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Ground-based synthetic aperture radar (GBSAR) technology has been widely used for bridge dynamic deflection measurements due to its advantages of non-contact measurements, high frequency, and high accuracy. To reduce the influence of noise in dynamic deflection measurements of bridges using GBSAR—especially for noise of the instantaneous vibrations of the instrument itself caused by passing vehicles—an improved second-order blind identification (SOBI) signal de-noising method is proposed to obtain the de-noised time-series displacement of bridges. First, the obtained time-series displacements of three adjacent monitoring points in the same time domain are selected as observation signals, and the second-order correlations among the three time-series displacements are removed using a whitening process. Second, a mixing matrix is calculated using the joint approximation diagonalization technique for covariance matrices and to further obtain three separate signal components. Finally, the three separate signal components are converted in the frequency domain using the fast Fourier transform (FFT) algorithm, and the noise signal components are identified using a spectrum analysis. A new, independent, separated signal component matrix is generated using a zeroing process for the noise signal components. This process is inversely reconstructed using a mixing matrix to recover the original amplitude of the de-noised time-series displacement of the middle monitoring point among three adjacent monitoring points. The results of both simulated and on-site experiments show that the improved SOBI method has a powerful signal de-noising ability.
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Dissertations / Theses on the topic "Fast diagonalization method"

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Bahari, Mustapha. "Transport optimal pour la génération de maillage et le r-raffinement." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5032.

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Dans cette thèse, nous développons des solveurs rapides et des procédures de génération de maillage adaptatif basés sur le transport optimal dans le contexte de l'Analyse Isogéométrique, en utilisant les B-Splines comme base des éléments finis. Notre approche garantit la construction d'une bijection, abordant ainsi un défi majeur de l'Analyse Isogéométrique. Nous utilisons des éléments finis standard pour résoudre l'équation de Monge-Ampère. Cependant, une analyse de cette approche montre des limitations significatives, notamment lorsqu'elle est confrontée à des variations importantes au voisinage de la frontière. Pour surmonter ce défi, nous dérivons une nouvelle formulation utilisant une discrétisation B-Splines compatible basée sur la suite de DeRham. De plus, nous introduisons de nouveaux solveurs rapides utilisant la méthode de diagonalisation rapide pour aborder efficacement cette question.Nous proposons une variété de tests et d'applications pour illustrer la performance et l'efficacité de notre approche. Celles-ci incluent des tests utilisant des solutions construites de l'équation de Monge-Ampère ainsi que des fonctions de densité analytiques. De plus, nous appliquons notre solveur à des problèmes elliptiques et à des problèmes dépendant du temps, en relevant des défis tels que l'obtention d'une précision élevée, la capture précise des interfaces, et la réduction efficace des oscillations.Finalement, la paramétrisation B-spline de presque toutes les géométries présentées repose sur les informations donnnées par le bord, utilisant une nouvelle approche basée sur le transport optimal
In this thesis, we develop fast solvers and adaptive mesh generation procedures based on the Optimal Transport using B-Splines Finite Elements within the Isogeometric Analysis framework. Our approach ensures the construction of a bijection mapping, addressing a major challenge in Isogeometric Analysis.Initially, we employ standard B-Splines Finite Elements to solve the Monge-Ampère Equation. However, an analysis of this approach reveals significant limitations, particularly when confronted with high variations near the boundary. To overcome this challenge, we derive a new formulation utilizing compatible B-Splines discretization based on a discrete DeRham sequence. Furthermore, we introduce new fast solvers using the Fast Diagonalization method to address this issue effectively.We provide various tests and applications to demonstrate the performance and efficiency of our novel approach. These include testing our approach using manufactured solutions of the Monge-Ampère equation and employing analytical density functions. Additionally, we apply our solver to elliptic problems and time-dependent problems, addressing challenges such as achieving higher accuracy, accurately capturing sharp interfaces, and effectively reducing oscillations.Finally, the parameterization of nearly all presented geometries relies on CAD-boundary information, employing a novel approach based on optimal transport
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Book chapters on the topic "Fast diagonalization method"

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Wilhelm, Dirk, and Leonhard Kleiser. "Domain Decomposition Method and Fast Diagonalization Solver for Spectral Element Simulations." In Computational Fluid Dynamics 2000, 429–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56535-9_64.

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Journal articles
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