Relevant bibliographies by topics / Numerical analysis – Numerical methods in Fourier analysis – Wavelets

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Numerical analysis – Numerical methods in Fourier analysis – Wavelets'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Numerical analysis – Numerical methods in Fourier analysis – Wavelets"

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Любимова, Mariya Lyubimova, Князева, and Tatyana Knyazeva. "Processing of tomographic images by means of wavelet analysis." Journal of New Medical Technologies. eJournal 8, no. 1 (November 5, 2014): 1–4. http://dx.doi.org/10.12737/4110.

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The paper is devoted to the problem of processing of tomographic images using wavelet analysis. The features of image processing techniques, indications were analyzed. Wavelets are a signal waveform of limited duration that has an average value of zero. Wavelets are comparable to a sine wave, and they are the basis of Fourier analysis. Wavelet analysis method allows to processing of tomographic images using a large time interval, where more accurate information about the low frequency region and shorter when information is needed on high frequency. The characteristic features of the settings wavelet transforms are described. Their bad choice reduces the reliability of detection of changes in the structure of signals when changing system state. The key stages of the reconstruction tomography images in DICOM format using the method of wavelet analysis were examined; algorithm of noise reduction was investigated. Practical area of application of wavelet analysis doesn´t limited to digital signal processing; it also covers physical experiments, numerical methods and other areas of physics and mathematics. By being able to analyze the non-stationary signals, wavelet analysis has become a powerful alternative Fourier transform in medical applications.
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Podsiadlo, P., and G. W. Stachowiak. "Multi-scale representation of tribological surfaces." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 216, no. 6 (June 1, 2002): 463–79. http://dx.doi.org/10.1243/135065002762355361.

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Many numerical surface topography analysis methods exist today. However, even for the moderately complicated topography of a tribological surface these methods can provide only limited information. The reason is that tribological surfaces often exhibit a non-stationary and multi-scale nature while the numerical methods currently used work well with surface data exhibiting a stationary random process and provide surface descriptors closely related to a scale at which surface data were acquired. The suitability of different methods, including Fourier transform, windowed Fourier transform, Cohen's class distributions (especially the Wigner-Ville distribution), wavelet transform, fractal methods and a hybrid fractal-wavelet method, for the analysis of tribological surface topographies is investigated in this paper. The method best suited to this purpose has been selected.
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Boyd, John P. "Limited-Area Fourier Spectral Models and Data Analysis Schemes: Windows, Fourier Extension, Davies Relaxation, and All That." Monthly Weather Review 133, no. 7 (July 1, 2005): 2030–42. http://dx.doi.org/10.1175/mwr2960.1.

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Abstract Regional spectral models have previously periodized and blended limited-area data through ad hoc low-order schemes justified by intuition and empiricism. By using infinitely differentiable “window functions” or “bells” borrowed from wavelet theory, one can periodize with preservation of spectral accuracy. Similarly, it is shown through a mixture of theory and numerical examples that Davies relaxation for blending limited-area and global data in one-way nested forecasting can be performed using the same C∞ bells as employed for the Fourier blending.“The relative success of empirical methods . . . may be used as partial justification to allow us to make the daring approximation that the data on a limited area domain may be decomposed into a trend and a periodic perturbation, and to proceed with Fourier transformation of the latter.” Laprise (2003, p. 775)
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Sonekar, Parikshit, and Mira Mitra. "A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2113 (October 14, 2009): 263–81. http://dx.doi.org/10.1098/rspa.2009.0369.

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In this paper, a wavelet-based method is developed for wave-propagation analysis of a generic multi-coupled one-dimensional periodic structure (PS). The formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite-element (FE) or other numerical methods. Here, unlike its conventional definition, the dynamic stiffness matrix is obtained in the wavelet domain through a Daubechies wavelet transform. The proposed numerical scheme enables both time- and frequency-domain analysis of PSs under arbitrary loading conditions. This is in contrast to the existing Fourier-transform-based analysis that is restricted to frequency-domain study. Here, the dispersion characteristics of PSs, especially the band-gap features, are studied. In addition, the method is implemented to simulate time-domain wave response under impulse loading conditions. The two examples considered are periodically simply supported beam and periodic frame structures. In all cases, the responses obtained using the present periodic formulation are compared with the response simulated using the FE model without the periodicity assumption, and they show an exact match. This validates the accuracy of the periodic assumption to obtain the time- and frequency-domain wave responses up to a high-frequency range. Apart from this, the proposed method drastically reduces the computational cost and can be implemented for homogenization of PSs.
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Qian, Xu, Yaming Chen, and Songhe Song. "Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time." Communications in Computational Physics 15, no. 3 (March 2014): 692–711. http://dx.doi.org/10.4208/cicp.120313.020813a.

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AbstractIn this paper, we propose a wavelet collocation splitting (WCS) method, and a Fourier pseudospectral splitting (FPSS) method as comparison, for solving one-dimensional and two-dimensional Schrödinger equations with variable coefficients in quantum mechanics. The two methods can preserve the intrinsic properties of original problems as much as possible. The splitting technique increases the computational efficiency. Meanwhile, the error estimation and some conservative properties are investigated. It is proved to preserve the charge conservation exactly. The global energy and momentum conservation laws can be preserved under several conditions. Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.
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Du, Shuangxing, Dominic A. Hudson, W. Geraint Price, Pandeli Temarel, Ruizhang Chen, and Yousheng Wu. "Wavelet Analysis of Loads on a Flexible Ship Model Traveling in Large-Amplitude Waves." Journal of Ship Research 52, no. 04 (December 1, 2008): 249–62. http://dx.doi.org/10.5957/jsr.2008.52.4.249.

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This study describes an application of a Daubechies wavelet function to analyze measured ship model data. The records of a self-propelled, flexible model of the S175 containership moving in waves are analyzed by fast Fourier transform (FFT) and wavelet methods. It is shown that the high-frequency component of the recorded rigid body motions can be omitted without substantially affecting the main features of the data set relating to dynamic loads. The decomposition of the bending moment time history into low-and high-frequency components allows the time of impact occurrence and its amplitude to be easily detected. Such quantities provide important information for the development of generic and realistic transient impact (e.g., slamming, green water) force models for ships traveling in waves.
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Chen, Jian Hui. "An Improved EMD Method and its Application in Nonstationary Signals Analysis." Advanced Materials Research 429 (January 2012): 313–17. http://dx.doi.org/10.4028/www.scientific.net/amr.429.313.

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Empirical mode decomposition (EMD) method based on HHT has exhibited unique advantages such as adaptability and highly efficiency in many nonlinear, nonstationary signals processing applications. It breaks the uncertainty principle limit, but the traditional EMD still has its deficiencies. In this article, we construct a new wavelet which has excellent decomposing-frequency performance and energy concentration, and then an improved EMD method based on this wavelet is presented. Results of numerical simulation show the validity and efficiency of the method proposed in paper are better than traditional one. Furthermore, some foreseeable trends of time-frequency distribution technologies are described. The systems in reality, strictly speaking, tend to non-linear, so most practical signals are non-stationary random signals. Nonlinear, nonstationary signals analysis is a very significant and difficult problem in almost all technical fields such as automation, communication, aerospace- engineering, biomedicine, structural fault diagnosis and so on. Owed to the rapid development of large scale integrated circuit technology and artificial intelligence, the exploration of signal processing theories have got a sharply impetus. A series of new modern signal processing theories and methods have appeared to meet the need of time-frequency joint analysis of nonlinear, non-Gaussian and non-stationary signals, including discrete short-time Fourier transform, wavelet transform, Hilbert-Huang transform and so on. Time-frequency joint analysis can observe the evolution of the signal in the time domain and the frequency domain simultaneously, provide local time-frequency characteristics of the signal.
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Babajanian Bisheh, Hossein, Gholamreza Ghodrati Amiri, and Ehsan Darvishan. "Ensemble Classifiers and Feature-Based Methods for Structural Damage Assessment." Shock and Vibration 2020 (December 19, 2020): 1–14. http://dx.doi.org/10.1155/2020/8899487.

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In this paper, a new structural damage detection framework is proposed based on vibration analysis and pattern recognition, which consists of two stages: (1) signal processing and feature extraction and (2) damage detection by combining the classification result. In the first stage, discriminative features were extracted as a set of proposed descriptors related to the statistical moment of the spectrum and spectral shape properties using five competitive time-frequency techniques including fast S-transform, synchrosqueezed wavelet transform, empirical wavelet transform, wavelet transform, and short-time Fourier transform. Then, forward feature selection was employed to remove the redundant information and select damage features from vibration signals. By applying different classifiers, the capability of the feature sets for damage identification was investigated. In the second stage, ensemble-based classifiers were used to improve the overall performance of damage detection based on individual classifiers and increase the number of detectable damages. The proposed framework was verified by a suite of numerical and full-scale studies (a bridge health monitoring benchmark problem, IASC-ASCE SHM benchmark structure, and a cable-stayed bridge in China). The results showed that the proposed framework was superior to the existing single classifier and could assess the damage with reduced false alarms.
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Chen, Binqiang, Qixin Lan, Yang Li, Shiqiang Zhuang, and Xincheng Cao. "Enhancement of Fault Feature Extraction from Displacement Signals by Suppressing Severe End Distortions via Sinusoidal Wave Reduction." Energies 12, no. 18 (September 15, 2019): 3536. http://dx.doi.org/10.3390/en12183536.

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Displacement signals, acquired by eddy current sensors, are extensively used in condition monitoring and health prognosis of electromechanical equipment. Owing to its sensitivity to low frequency components, the displacement signal often contains sinusoidal waves of high amplitudes. If the digitization of the sinusoidal wave does not satisfy the condition of full period sampling, an effect of severe end distortion (SED), in the form of impulsive features, is likely to occur because of boundary extensions in discrete wavelet decompositions. The SED effect will complicate the extraction of weak fault features if it is left untreated. In this paper, we investigate the mechanism of the SED effect using theories based on Fourier analysis and wavelet analysis. To enhance feature extraction performance from displacement signals in the presence of strong sinusoidal waves, a novel method, based on the Fourier basis and a compound wavelet dictionary, is proposed. In the procedure, ratio-based spectrum correction methods, using the rectangle window as well as the Hanning window, are employed to obtain an optimized reduction of strong sinusoidal waves. The residual signal is further decomposed by the compound wavelet dictionary which consists of dyadic wavelet packets and implicit wavelet packets. It was verified through numerical simulations that the reconstructed signal in each wavelet subspace can avoid severe end distortions. The proposed method was applied to case studies of an experimental test with rub impact fault and an engineering test with blade crack fault. The analysis results demonstrate the proposed method can effectively suppress the SED effect in displacement signal analysis, and therefore enhance the performance of wavelet analysis in extracting weak fault features.
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Stanković, Ljubiša, Jonatan Lerga, Danilo Mandic, Miloš Brajović, Cédric Richard, and Miloš Daković. "From Time–Frequency to Vertex–Frequency and Back." Mathematics 9, no. 12 (June 17, 2021): 1407. http://dx.doi.org/10.3390/math9121407.

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The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral form of the vertex–frequency analysis, and it will be considered in this paper since the spectral domain for signal localization is well ordered and thus simpler for application to the graph signals. The localized graph Fourier transform is defined based on its counterpart, the short-time Fourier transform, in classical signal analysis. We consider various spectral window forms based on which these transforms can tackle the localized signal behavior. Conditions for the signal reconstruction, known as the overlap-and-add (OLA) and weighted overlap-and-add (WOLA) methods, are also considered. Since the graphs can be very large, the realizations of vertex–frequency representations using polynomial form localization have a particular significance. These forms use only very localized vertex domains, and do not require either the graph Fourier transform or the inverse graph Fourier transform, are computationally efficient. These kinds of implementations are then applied to classical time–frequency analysis since their simplicity can be very attractive for the implementation in the case of large time-domain signals. Spectral varying forms of the localization functions are presented as well. These spectral varying forms are related to the wavelet transform. For completeness, the inversion and signal reconstruction are discussed as well. The presented theory is illustrated and demonstrated on numerical examples.
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Dissertations / Theses on the topic "Numerical analysis – Numerical methods in Fourier analysis – Wavelets"

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Huang, Ning Ying. "Numerical methods for early-exercise option pricing via Fourier analysis." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148270.

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Ismail, Atikah. "Fourier spectral methods for numerical modeling of ionospheric processes." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-03142009-040454/.

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Napov, Artem. "Algebraic analysis of V-cycle multigrid and aggregation-based two-grid methods." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210175.

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This thesis treats two essentially different subjects: V-cycle schemes are considered in Chapters 2-4, whereas the aggregation-based coarsening is analysed in Chapters 5-6. As a matter of paradox, these two multigrid ingredients, when combined together, can hardly lead to an optimal algorithm. Indeed, a V-cycle needs more accurate prolongations than the simple piecewise-constant one, associated to aggregation-based coarsening. On the other hand, aggregation-based approaches use almost exclusively piecewise constant prolongations, and therefore need more involved cycling strategies, K-cycle [Num.Lin.Alg.Appl. vol.15(2008), pp.473-487] being an attractive alternative in this respect.



Chapter 2 considers more precisely the well-known V-cycle convergence theories: the approximation property based analyses by Hackbusch (see [Multi-Grid Methods and Applications, 1985, pp.164-167]) and by McCormick [SIAM J.Numer.Anal. vol.22(1985), pp.634-643] and the successive subspace correction theory, as presented in [SIAM Review, vol.34(1992), pp.581-613] by Xu and in [Acta Numerica, vol.2(1993), pp.285-326.] by Yserentant. Under the constraint that the resulting upper bound on the convergence rate must be expressed with respect to parameters involving two successive levels at a time, these theories are compared. Unlike [Acta Numerica, vol.2(1993), pp.285-326.], where the comparison is performed on the basis of underlying assumptions in a particular PDE context, we compare directly the upper bounds. We show that these analyses are equivalent from the qualitative point of view. From the quantitative point of view,

we show that the bound due to McCormick is always the best one.



When the upper bound on the V-cycle convergence factor involves only two successive levels at a time, it can further be compared with the two-level convergence factor. Such comparison is performed in Chapter 3, showing that a nice two-grid convergence (at every level) leads to an optimal McCormick's bound (the best bound from the previous chapter) if and only if a norm of a given projector is bounded on every level.



In Chapter 4 we consider the Fourier analysis setting for scalar PDEs and extend the comparison between two-grid and V-cycle multigrid methods to the smoothing factor. In particular, a two-sided bound involving the smoothing factor is obtained that defines an interval containing both the two-grid and V-cycle convergence rates. This interval is narrow when an additional parameter α is small enough, this latter being a simple function of Fourier components.



Chapter 5 provides a theoretical framework for coarsening by aggregation. An upper bound is presented that relates the two-grid convergence factor with local quantities, each being related to a particular aggregate. The bound is shown to be asymptotically sharp for a large class of elliptic boundary value problems, including problems with anisotropic and discontinuous coefficients.



In Chapter 6 we consider problems resulting from the discretization with edge finite elements of 3D curl-curl equation. The variables in such discretization are associated with edges. We investigate the performance of the Reitzinger and Schöberl algorithm [Num.Lin.Alg.Appl. vol.9(2002), pp.223-238], which uses aggregation techniques to construct the edge prolongation matrix. More precisely, we perform a Fourier analysis of the method in two-grid setting, showing its optimality. The analysis is supplemented with some numerical investigations.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

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Szubert, Damien. "Physics and modelling of unsteady turbulent flows around aerodynamic and hydrodynamic structures at high Reynold number by numerical simulation." Phd thesis, Toulouse, INPT, 2015. http://oatao.univ-toulouse.fr/15129/2/szubert_1.pdf.

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This thesis aims at analysing the predictive capabilities of statistical URANS and hybrid RANS-LES methods to model complex flows at high Reynolds numbers and carrying out a physical analysis of the near-region turbulence and coherent structures. This study handles configurations included in the European research programmes ATAAC (Advanced Turbulent Simulation for Aerodynamics Application Challenges) and TFAST (Transition Location Effect on Shock Wave Boundary Layer Interaction). First, the detached flow in a configuration of a tandem of cylinders, positionned behind one another, is investigated at Reynolds number 166000. A static case, corresponding to the layout of the support of a landing gear, is initially considered. The fluid-structure interaction is then studied in a dynamic case where the downstream cylinder, situated in the wake of the upstream one, is given one degree of freedom in translation in the crosswise direction. A parametric study of the structural parameters is carried out to identify the various regimes of interaction. Secondly, the physics of the transonic buffet is studied by means of time-frequency analysis and proper orthogonal decomposition (POD), in the Mach number range 0.70–0.75. The interactions between the main shock wave, the alternately detached boundary layer and the vortices developing in the wake are analysed. A stochastic forcing, based on reinjection of synthetic turbulence in the transport equations of kinetic energy and dissipation rate by using POD reconstruction, has been introduced in the so-called organised-eddy simulation (OES) approach. This method introduces an upscale turbulence modelling, acting as an eddy-blocking mechanism able to capture thin shear-layer and turbulent/non-turbulent interfaces around the body. This method highly improves the aerodynamic forces prediction and opens new ensemble-averaged approaches able to model the coherent and random processes at high Reynolds number. Finally, the shock-wave/boundary-layer interaction (SWBLI) is investigated in the case of an oblique shock wave at Mach number 1.7 in order to contribute to the so-called "laminar wing design" studies at European level. The performance of statistical URANS and hybrid RANS-LES models is analysed with comparison, with experimental results, of integral boundary-layer values (displacement and momentum thicknesses) and wall quantities (friction coefficient). The influence of a transitional boundary layer on the SWBLI is featured.
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Smital, Petr. "Analýza obrazu pro korekci elektronových mikroskopů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-219238.

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This thesis describes the physical nature of corrections of an electron microscope and mathematical methods of image processing required for their complete automation. The corrections include different types of focusing, astigmatism correction, electron beam centring, and image stabilisation. The mathematical methods described in this thesis include various methods of measuring focus and astigmatism, with and without using the Fourier transform, edge detection, histogram operations, and image registration, i.e. detection of spatial transformations in images. This thesis includes detailed descriptions of the mathematical methods, their evaluation using an “offline” application, descriptions of the algorithms of their implementation into an actual electron microscope and results of their testing on the actual electron microscope, in the form of a video footage grabbed from its control computer’s screen.
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Kottmann, Jakob Siegfried. "Coupled-Cluster in Real Space." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19357.

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In dieser Arbeit werden Algorithmen für die Berechnung elektronischer Korrelations- und Anregungsenergien mittels der Coupled-Cluster Methode auf adaptiven Gittern entwickelt und implementiert. Die jeweiligen Funktionen und Operatoren werden adaptiv durch Multiskalenanalyse dargestellt, was eine Basissatz unabängige Beschreibung mit kontrollierter numerischer Genauigkeit ermöglicht. Gleichungen für die Coupled-Cluster Methode werden in einem verallgemeinerten Rahmen, unabhängig von virtuellen Orbitalen und globalen Basissätzen, neu formuliert. Hierzu werden die amplitudengewichteten Anregungen in virtuelle Orbitale ersetzt durch Anregungen in n-Elektronenfunktionen, welche durch Gleichungen im n-Elektronen Ortsraum bestimmt sind. Die erhaltenen Gleichungen können, analog zur Basissatz abh¨angigen Form, mit leicht angepasster Interpretation diagrammatisch dargestellt werden. Aufgrund des singulären Coulomb Potentials werden die Arbeitsgleichungen mit einem explizit korrelierten Ansatz regularisiert. Coupled-Cluster singles mit genäherten doubles (CC2) und ähnliche Modelle werden, für geschlossenschalige Systeme und in regularisierter Form, in die MADNESS Bibliothek (eine allgemeine Bibliothek zur Darstellung von Funktionen und Operatoren mittels Multiskalenanalyse) implementiert. Mit der vorgestellten Methode können elektronische CC2 Paarkorrelationsenergien und Anregungsenergien mit bestimmter numerischer Genauigkeit unabhängig von globalen Basissätzen berechnet werden, was anhand von kleinen Molekülen verifiziert wird
In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules.
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Bashier, Eihab Bashier Mohammed. "Fitted numerical methods for delay differential equations arising in biology." Thesis, 2009. http://hdl.handle.net/11394/3134.

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Philosophiae Doctor - PhD
Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.
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Books on the topic "Numerical analysis – Numerical methods in Fourier analysis – Wavelets"

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Michel, Volker. Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball. Boston: Birkhäuser Boston, 2013.

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Numerical analysis of wavelet methods. Amsterdam: Elsevier, 2003.

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Gasquet, Claude. Fourier analysis and applications: Filtering, numerical computation, wavelets. New York: Springer, 1999.

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Gasquet, C. Fourier analysis and applications: Filtering, numerical computation, wavelets. New York, N.Y: Springer, 1999.

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Applied functional analysis: Numerical methods, wavelet methods, and image processing. New York: M. Dekker, 2004.

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1950-, Joppich W., ed. Practical Fourier analysis for multigrid methods. Boca Raton, FL: Chapman & Hall/CRC, 2005.

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Mercier, Bertrand. An introduction to the numerical analysis of spectral methods. Berlin: Springer-Verlag, 1989.

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Hitzer, Eckhard. Quaternion and Clifford Fourier Transforms and Wavelets. Basel: Springer Basel, 2013.

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Nievergelt, Yves. Wavelets Made Easy. New York, NY: Springer New York, 2013.

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Imaging, multi-scale, and high-contrast partial differential equations: Seoul ICM 2014 Satellite Conference, August 7-9, 2014, Daejeon, Korea. Providence, Rhode Island: American Mathematical Society, 2016.

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Book chapters on the topic "Numerical analysis – Numerical methods in Fourier analysis – Wavelets"

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Plonka, Gerlind, Daniel Potts, Gabriele Steidl, and Manfred Tasche. "Multidimensional Fourier Methods." In Numerical Fourier Analysis, 159–230. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04306-3_4.

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Plonka, Gerlind, Daniel Potts, Gabriele Steidl, and Manfred Tasche. "Chebyshev Methods and Fast DCT Algorithms." In Numerical Fourier Analysis, 305–76. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04306-3_6.

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Nome, Morten A., and Tor Sørevik. "Discrete Fourier Analysis on Lattice Grids." In Numerical Methods and Applications, 251–60. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10692-8_28.

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Tijhuis, Anton G. "Fourier Methods Applicable in the Numerical Solution of Electromagnetic Time-Domain Scattering Problems." In Recent Advances in Fourier Analysis and Its Applications, 273–309. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0665-5_18.

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Ahmad, Muneer. "A Biologically-Inspired Computational Solution for Protein Coding Regions Identification in Noisy DNA Sequences." In Advances in Environmental Engineering and Green Technologies, 201–16. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9792-8.ch010.

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Biologically inspired computational solutions for protein coding regions identification are termed as optimized solutions that could enhance regions of interest in noisy DNA signals contrary to contemporary identification. Exponentially growing genomic data needs better protein translation. The solutions proposed so far rely on statistical, digital signal processing and Fourier transforms approaches lacking the reflection for optimal biologically inspired identification of coding regions. This paper presents a peculiar biologically inspired solution for coding regions identification based on wavelet transforms with notion of a peculiar indicator sequence. DNA signal noise has been reduced considerably and exon peaks can be discriminated from introns significantly. A comparative analysis performed over datasets commonly used for protein coding identification revealed the outperformance of proposed solution in power spectral density estimation graphs and numerical discrimination measure's calculations. The significant results achieved depict 75% reduction in computational complexity than Binary indicator sequence method and 32% to 266% improvement than other methods in literature (as a comparison with standard NCBI range). The significance in results has been achieved by efficiently denosing the target DNA signal employing wavelets and peculiar indicator sequence.
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Plastino, A., and M. T. Martin. "Generalized Information Measures and the Analysis of Brain Electrical Signals." In Nonextensive Entropy. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195159769.003.0020.

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The traditional way of analyzing brain electrical activity, on the basis of electroencephalogram (EEG) records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature that hardly allows for a systematic protocol. In order to overcome this undesirable feature, a quantitative EEG analysis has been developed over the years that introduces objective measures. These reflect not only characteristics of the brain activity itself, but also clues concerning the underlying associated neural dynamics. The processing of information by the brain is reflected in dynamical changes of the electrical activity in (i) time, (ii) frequency, and (iii) space. Therefore, the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency. In the present work we introduce new information tools based on the wavelet transform for the assessment of EEG data. In particular, different complexity measures are utilized…. The traditional electroencephalogram (EEG) tracing is now interpreted in much the same way as it was 50 years ago. More channels are used now and much more is known about clinical implication of the waves, but the basic EEG display and quantification of it are quite similar to those of its predecessors. The clinical interpretation of EEG records is made by a complex process of visual pattern recognition and the association with external and evident characteristics of clinical symptomatology. Analysis of EEG signals always involves the queries of quantification, i.e., the ability to state objective data in numerical and/or graphic form that simplify the analysis of long EEG time series. Without such measures, EEG appraisal remains subjective and can hardly lead to logical systematization [36]. Spectral decomposition of the EEG by computing the Fourier transform has been used since the very early days of electroencephalography. The rhythmic nature of many EEG activities lends itself naturally to this analysis. Fourier transform allows separation of various rhythms and estimation of their frequencies independently of each other, a difficult task to perform visually if several rhythmic activities occur simultaneously. Spectral analysis can also quantify the amount of activity in a frequency band.
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Johnson, Michael L., and Michelle Lampl. "[4] Artifacts of fourier series analysis." In Part B: Numerical Computer Methods, 51–68. Elsevier, 1994. http://dx.doi.org/10.1016/s0076-6879(94)40043-1.

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Goriely, Alain. "6. Can you picture that? X‐rays, DNA, and photos." In Applied Mathematics: A Very Short Introduction, 85–101. Oxford University Press, 2018. http://dx.doi.org/10.1093/actrade/9780198754046.003.0006.

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Applied mathematics is also concerned with the manipulation and analysis of signals and data. In our digital world, where huge amounts of data are routinely collected, transmitted, processed, analysed, compressed, encrypted, decrypted, and stored, efficient mathematical methods and numerical algorithms are needed. ‘Can you picture that? X-rays, DNA, and photos’ outlines how applied mathematics is used to extract information from this data using the examples of computed tomography, X-ray crystallography, and the compression of digital image files. Modern developments have seen the discovery of new methods to extract information and process it efficiently. Examples are the theory of wavelets and compressed sensing, which has been implemented in Magnetic Resonance Imaging scanners.
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Conference papers on the topic "Numerical analysis – Numerical methods in Fourier analysis – Wavelets"

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Černá, Dana, Václav Finěk, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Construction of Orthonormal Wavelets Using Symbolic Algebraic Methods." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241329.

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Postnikov, Eugene B. "Preface of the "Symposium on wavelets and related multiscale methods"." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825590.

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Brugnano, L., M. Calvo, J. I. Montijano, and L. Rández. "Fourier methods for oscillatory differential problems with a constant high frequency." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992149.

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Adam, A. M. A., E. B. M. Bashier, M. H. A. Hashim, and K. C. Patidar. "Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992716.

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Takacs, Stefan. "Using Cylindrical Algebraic Decomposition and Local Fourier Analysis to Study Numerical Methods: Two Examples." In 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2014. http://dx.doi.org/10.1109/synasc.2014.14.

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Daneshmand, Farhang, Abdolaziz Abdollahi, Mehdi Liaghat, and Yousef Bazargan Lari. "Free Vibration Analysis of Frame Structures Using BSWI Method." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68417.

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Vibration analysis for complicated structures, or for problems requiring large numbers of modes, always requires fine meshing or using higher order polynomials as shape functions in conventional finite element analysis. Since it is hard to predict the vibration mode a priori for a complex structure, a uniform fine mesh is generally used which wastes a lot of degrees of freedom to explore some local modes. By the present wavelets element approach, the structural vibration can be analyzed by coarse mesh first and the results can be improved adaptively by multi-level refining the required parts of the model. This will provide accurate data with less degrees of freedom and computation. The scaling functions of B-spline wavelet on the interval (BSWI) as trial functions that combines the versatility of the finite element method with the accuracy of B-spline functions approximation and the multiresolution strategy of wavelets is used for frame structures vibration analysis. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. To verify the proposed method, the vibrations of a cantilever beam and a plane structures are studied in the present paper. The analyses and results of these problems display the multi-level procedure and wavelet local improvement. The formulation process is as simple as the conventional finite element method except including transfer matrices to compute the coupled effect between different resolution levels. This advantage makes the method more competitive for adaptive finite element analysis. The results also show good agreement with those obtained from the classical finite element method and analytical solutions.
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Karmazin, Alexander, Evgenia Kirillova, Wolfgang Seemann, and Pavel Syromyatnikov. "Analysis of Spatial Steady-State Vibrations of a Layered Anisotropic Plate Using the Green’s Functions." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-25430.

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Spatial steady-state harmonic vibrations of a layered anisotropic plate excited by the distributed sources are considered. The work is based on the classical methods of the integral Fourier transforms and integral representations of the Green’s functions. In Fourier transform domain, the displacement vector is represented in terms of the Green’s matrix transform and the transform of the surface load vector. The two-dimensional inverse Fourier transform of the displacement vector is computed by reducing double integral to the iterated one with integrating along a contour, which deviates from the real axis while bypassing the real poles, and with subsequent integrating along the wave propagation angle. Three numerical algorithms of computing related iterated integrals are presented. The features of the application of these algorithms for the near- and far-field zones of the source are discussed. All of presented methods are compared for the numerical examples of vibrations on the surface of 24-layer symmetrical composite.
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Dickmann, Hans-Peter, Thomas Secall Wimmel, Jaroslaw Szwedowicz, Dietmar Filsinger, and Christian H. Roduner. "Unsteady Flow in a Turbocharger Centrifugal Compressor: 3D-CFD-Simulation and Numerical and Experimental Analysis of Impeller Blade Vibration." In ASME Turbo Expo 2005: Power for Land, Sea, and Air. ASMEDC, 2005. http://dx.doi.org/10.1115/gt2005-68235.

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Experimental investigations on a single stage centrifugal compressor showed that measured blade vibration amplitudes vary considerably along a constant speed line from choke to surge. The unsteady flow has been analysed to obtain detailed insight into the excitation mechanism. Therefore, a turbocharger compressor stage impeller has been modeled and simulated by means of Computational Fluid Dynamics (CFD). Two operating points at off-design conditions were analysed. One was close to choke and the second one close to the surge line. Transient CFD was employed, since only then a meaningful prediction of the blade excitation, caused by the unsteady flow situation, can be expected. Actually, it was observed that close to surge a steady state solution could not be obtained; only transient CFD could deliver a converged solution. The CFD results show the effect of the interaction between the inducer casing bleed system and the main flow. Additionally, the effect of the non-axisymmetric components, such as the suction elbow and the discharge volute, was analysed. The volute geometry itself had not been modeled. It turned out to be sufficient to impose a circumferentially asymmetric pressure distribution at the exit of the vaned diffuser to simulate the volute. Volute and suction elbow impose a circumferentially asymmetric flow field, which induces blade excitation. To understand the excitation mechanism, which causes the measured vibration behavior of the impeller, the time dependent pressure distribution on the impeller blades was transformed into the frequency domain by Fourier decomposition. The complex modal pressure data were imposed on the structure that was modeled by Finite Element Methods (FEM). Following state-of-the-art calculations to analyze the free vibration behavior of the impeller, forced response calculations were carried out. Comparisons with the experimental results demonstrate that this employed methodology is capable of predicting the impeller’s vibration behavior under real engine conditions. Integrating the procedure into the design of centrifugal compressors will enhance the quality of the design process.
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Yao, Dan, Jie Tian, Yadong Wu, and Hua Ouyang. "Circumferential Mode Analysis of Axial Compressor Tip Flow Using Fourier Transform and Proper Orthogonal Decomposition." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76258.

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Rotating instability (RI) of a single-stage axial compressor was studied by both numerical and experimental methods. A circumferential mode decomposition method based on spatial Fourier transform was used to analyze the circumferential pressure distribution of the tip flow. Circumferential mode characteristics were captured both on blade passing frequency (BPF) and rotational instability frequency (RIF) under several flow conditions. The characteristic spectrum of RI with broadband hump existed in a large range of flow conditions. Both frequency range and dominant circumferential mode number decreased with flow rate, while circumferential angular velocity of RI increased at the same time. On the other hand, a proper orthogonal decomposition (POD) method was applied to obtain the mode component of tip flow. The feature of tip flow was analyzed with the help of POD mode vector and mode amplitude. The influence of the decrease on the spatial monitor points in POD method was analyzed using CFD data to analysis the potential error from experimental results. It is expected to deeply understand the mechanism of the rotating instability and rotor-stator interaction phenomenon by spatial FT and POD methods in this study.
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Wang, Junzhen, and Yanfeng Shen. "Numerical Investigation of Nonlinear Lamb Wave Time Reversing for Fatigue Crack Detection." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10881.

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Abstract This paper presents a numerical study on nonlinear Lamb wave time reversing for fatigue crack detection. An analytical framework is initially presented, modeling Lamb wave generation, propagation, wave crack linear and nonlinear interaction, and reception. Subsequently, a 3D transient dynamic coupled-field finite element model is constructed to simulate the pitch-catch procedure in an aluminum plate using the commercial finite element software (ANSYS). The excitation frequency is carefully selected, where only single Lamb wave mode will be generated by the Piezoelectric Wafer Active Sensor (PWAS). The fatigue cracks are modelled nucleating from both sides of a rivet hole. In addition, contact dynamics are considered to capture the nonlinear interactions between guided waves and the fatigue cracks, which would induce Contact Acoustic Nonlinearity (CAN) into the guided waves. Then the conventional and virtual time reversal methods are realized by finite element simulation. Advanced signal processing techniques are used to extract the distinctive nonlinear features. Via the Fast Fourier Transform (FFT) and time-frequency spectral analysis, nonlinear superharmonic components are observed. The reconstructed signals attained from the conventional and virtual time reversal methods are compared and analyzed. Finally, various Damage Indices (DIs), based on the difference between the reconstructed signal and the excitation waveform as well as the amplitude ratio between the superharmonic and the fundamental frequency components are adopted to evaluate the fatigue crack severity. The DIs could provide quantitative diagnostic information for fatigue crack detection. This paper finishes with summary, concluding remarks, and suggestions for future work.
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