Relevant bibliographies by topics / Spectral collocation

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

Academic literature on the topic 'Spectral collocation'

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

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Journal articles on the topic "Spectral collocation"

1

Hussaini, M. Y., D. A. Kopriva, and A. T. Patera. "Spectral collocation methods." Applied Numerical Mathematics 5, no. 3 (May 1989): 177–208. http://dx.doi.org/10.1016/0168-9274(89)90033-0.

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Zayernouri, Mohsen, and George Em Karniadakis. "Fractional Spectral Collocation Method." SIAM Journal on Scientific Computing 36, no. 1 (January 2014): A40—A62. http://dx.doi.org/10.1137/130933216.

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Li, Yiqun, Boying Wu, and Melvin Leok. "Spectral-collocation variational integrators." Journal of Computational Physics 332 (March 2017): 83–98. http://dx.doi.org/10.1016/j.jcp.2016.12.007.

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Heinrichs, Wilhelm. "Spectral Collocation on Triangular Elements." Journal of Computational Physics 145, no. 2 (September 1998): 743–57. http://dx.doi.org/10.1006/jcph.1998.6052.

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Gu, Zhendong, and Yanping Chen. "Piecewise Legendre spectral-collocation method for Volterra integro-differential equations." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 231–49. http://dx.doi.org/10.1112/s1461157014000485.

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Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in$h^{m}N^{-m}$-version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.
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Chantawansri, Tanya L., Su-Mi Hur, Carlos J. García-Cervera, Hector D. Ceniceros, and Glenn H. Fredrickson. "Spectral collocation methods for polymer brushes." Journal of Chemical Physics 134, no. 24 (June 28, 2011): 244905. http://dx.doi.org/10.1063/1.3604814.

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Hessari, Peyman, Sang Dong Kim, and Byeong-Chun Shin. "Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/780769.

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The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface. The spectral element collocation method is then employed to complex geometries; that is, we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain. We give some numerical experiments to show efficiency of our algorithm and its spectral convergence.
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WELLS, J. C., V. E. OBERACKER, M. R. STRAYER, and A. S. UMAR. "SPECTRAL PROPERTIES OF DERIVATIVE OPERATORS IN THE BASIS-SPLINE COLLOCATION METHOD." International Journal of Modern Physics C 06, no. 01 (February 1995): 143–67. http://dx.doi.org/10.1142/s0129183195000125.

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We discuss the basis-spline collocation method for the lattice solution of boundary-value differential equations, drawing particular attention to the difference between lattice and continuous collocation methods. Spectral properties of the basis-spline lattice representation of the first and second spatial derivatives are studied for the case of periodic boundary conditions with homogeneous lattice spacing and compared to spectra obtained using traditional finite-difference schemes. Basis-spline representations are shown to give excellent resolution on small-length scales and to satisfy the chain rule with good fidelity for the lattice-derivative operators using high-order splines. Application to the one-dimensional Dirac equation shows that very high-order spline representations of the Hamiltonian on odd lattices avoid the notorious spectral-doubling problem.
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Ma, Xian, Yongxian Wang, Xiaoqian Zhu, Wei Liu, Wenbin Xiao, and Qiang Lan. "A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations." Entropy 23, no. 9 (September 18, 2021): 1227. http://dx.doi.org/10.3390/e23091227.

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The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.
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Ma, Xian, Yongxian Wang, Xiaoqian Zhu, Wei Liu, Qiang Lan, and Wenbin Xiao. "A Spectral Method for Two-Dimensional Ocean Acoustic Propagation." Journal of Marine Science and Engineering 9, no. 8 (August 19, 2021): 892. http://dx.doi.org/10.3390/jmse9080892.

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The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.
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Dissertations / Theses on the topic "Spectral collocation"

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Kattelans, Thorsten. "The least squares spectral collocation method for incompressible flows." Berlin Köster, 2009. http://d-nb.info/997987812/04.

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Yuan, Huifang. "Spectral collocation methods for the fractional PDEs in unbounded domain." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/558.

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This thesis is concerned with a particular numerical approach for solving the fractional partial differential equations (PDEs). In the last two decades, it has been observed that many practical systems are more accurately described by fractional differential equations (FDEs) rather than the traditional differential equation approaches. Consequently, it has become an important research area to study the theoretical and numerical aspects of various types of FDEs. This thesis will explore high order numerical methods for solving FDEs numerically. More precisely, spectral methods which exhibits exponential order of accuracy will be investigated. The method consists of expanding the solution with proper global basis functions and imposing collocation conditions on the Gauss quadrature points. In this work, Hermite and modified rational functions are employed to serve as basis functions for solutions that decay exponentially and algebraically, respectively. The main emphasis of this thesis is to propose the spectral collocation method for FDEs posed in unbounded domains. Components of the differentiation matrix involving fractional Laplacian are derived which can then be computed recursively using the properties of confluent hypergeometric function or hypergeometric function. The first part of the thesis introduces preliminaries useful for other parts of the thesis. Review of the relevant definitions and properties of special functions such as Hermite functions, Bessel functions, hypergeometric functions, Gegenbauer polynomials, mapped Jacobi polynomials, modified rational functions are presented. Fractional Sobolev space is introduced and some lemmas on interpolation approximation in the fractional Sobolev space are also included. In the second part of the thesis, we present the spectral collocation method based on Hermite functions. Two bases are used, namely, the over-scaled Hermite function and generalized Hermite function, which are orthogonal functions on the whole line with appropriate weight functions. We will show that the fractional Laplacian of these two kinds of Hermite functions can be represented by confluent hypergeometric function. Behaviors of the condition numbers for the resulting spectral differentiation matrices with respect to the number of expansion terms are investigated. Moreover, approximation in two-dimensional space using the tensorized bases, application to multi-term problems and use of scaling to match different decay rate are also considered. Convergence analysis for generalized Hermite function are derived and numerical errors for two bases are analyzed. The third part of the thesis deals with the spectral collocation method based on modified rational functions. We first give a brief introduction for computation of the fractional Laplacian using modified rational functions, which is represented by hypergeometric functions. Then the differentiation matrix involving the fractional Laplace operator is given. Convergence analysis for modified Chebyshev rational functions and modified Legendre rational functions are derived and numerical experiments are carried out.
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Cameron, James M. "Spectral collocation and path-following methods for reaction-diffusion equations in one and two space dimensions." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1346.

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Merle, Matthieu. "Approches numériques pour l'analyse globale d'écoulements pariétaux en régime subsonique." Thesis, Paris, ENSAM, 2015. http://www.theses.fr/2015ENAM0026/document.

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Dans le cadre de l'étude des écoulements ouverts, deux types de dynamiques coexistent. Les écoulements de type oscillateur qui présentent une fréquence propre d'oscillation indépendante des perturbations extérieures (dynamique intrinsèque), ainsi que les écoulements de type amplificateur sélectif de bruit comme les écoulements de jets ou de couches limites décollées, caractérisés par une plus large gamme de fréquences dépendantes essentiellement de bruit extérieur (dynamique extrinsèque). Les études de couches limites décollées en régime incompressible ont montré un lien entre le phénomène auto-entretenu de basse fréquence qui apparaît et l'interaction non normale des modes globaux instables existants pour ce type de configuration. L'objectif de ce travail consiste à étendre cette interprétation lorsque l'écoulement est en régime subsonique. Dans ce but, un travail d'adaptation des conditions aux limites non-réfléchissantes aux problèmes de stabilité globale a été réalisé. Une méthode de zone absorbante de type Perfectly Matched Layer a été implémentée dans un code de simulation numérique utilisant des méthodes de collocation spectrale. Une méthode de décomposition de domaine adaptée aux calculs des solutions stationnaires ainsi qu'aux problèmes de stabilité globale a également été utilisée pour permettre la validation des conditions aux limites implémentées sur un cas d'écoulement rayonnant de cavité ouverte. Enfin, les études de stabilité d'un écoulement de couche limite décollée derrière une géométrie de type bosse ont été réalisées. L'étude des instabilités bidimensionnelles, responsables du phénomène basse fréquence (flapping), et réalisées en régime subsonique montre que le mécanisme observé en régime incompressible est aussi observé en régime subsonique. La stabilité de cet écoulement vis-à-vis de perturbations tri-dimensionnelles, et plus particulièrement les instabilités centrifuges ont aussi été étudiées en fonction du nombre de Mach
In open flows context, there are generally two types of dynamic : oscillators, such as cylinder flow, exhibit a well defined frequency insensitive to external perturbations (intrinsic dynamics) and noise amplifiers, such as boundary layers, jets or in some cases the separated flows, which are characterized by wider spectrum bands that depend essentially on the external noise (dynamic extrinsic). Previous studies have shown that separated flows are subject to self-induced oscillations of low frequency in incompressible regime. These studies have revealed links between the interaction of non-normal modes and low oscillations in an incompressible boundary-layer separation and it will be to establish the validity of this interpretation in a compressible regime. In this regard, non-reflecting boundary conditions have been developed to solve the eigenvalue problem formed by linearised Navier-Stokes equations. An absorbing region known as Perfectly Matched Layer has been implemented in order to damp acoustic perturbations which are generated when the compressibility of the flow is considered. A multi-domain approach using spectral collocation discretisation has also been developed in order to study the influence of this absorbing region on the stability analysis of an open cavity flow which is known to generate acoustic perturbations. Finally, we focused on separated boundary layer induced by a bump geometry in order to understand what are the effects of compressibility on the bidimensional low frequency phenomenon and also on transverse instabilities which are known to be unstable for a lots of separated flows
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Alici, Haydar. "Pseudospectral Methods For Differential Equations: Application To The Schrodingertype Eigenvalue Problems." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1086198/index.pdf.

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In this thesis, a survey on pseudospectral methods for differential equations is presented. Properties of the classical orthogonal polynomials required in this context are reviewed. Differentiation matrices corresponding to Jacobi, Laguerre,and Hermite cases are constructed. A fairly detailed investigation is made for the Hermite spectral methods, which is applied to the Schrö
dinger eigenvalue equation with several potentials. A discussion of the numerical results and comparison with other methods are then introduced to deduce the effciency of the method.
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Karkar, Sami. "Méthodes numériques pour les systèmes dynamiques non linéaires : application aux instruments de musique auto-oscillants." Phd thesis, Aix-Marseille Université, 2012. http://tel.archives-ouvertes.fr/tel-00742651.

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Ces travaux s'articulent autour du calcul des solutions périodiques dans les systèmes dynamiques non linéaires, au moyen de méthodes numériques de continuation. La recherche de solutions périodiques se traduit par un problème avec conditions aux limites périodiques, pour lequel nous avons implémenté deux méthodes d'approximation : - Une méthode spectrale dans le domaine fréquentiel : l'équilibrage harmonique d'ordre élevé, qui repose sur une formulation quadratique des équations. Nous proposons en outre une formulation originale permettant d'étendre cette méthode aux cas de non-linéarités non rationnelles. - Une méthode pseudo-spectrale par éléments dans le domaine temporel : la collocation à l'aide fonctions polynômiales par morceaux. Ces méthodes transforment le problème continu en un système d'équations algébriques non linéaires, dont les solutions sont calculées par continuation à l'aide de la méthode asymptotique numérique. L'ensemble de ces outils, intégrés au code de calcul MANLAB et complétés d'une analyse linéaire de stabilité, sont alors utilisés pour l'étude des régimes périodiques d'une classe particulière de systèmes dynamiques non linéaires : les instruments de musique auto-oscillants. Un modèle physique non-régulier de clarinette est étudié en détail : à partir de la branche de solutions statiques et ses bifurcations, on calcule les différentes branches de solutions périodiques, ainsi que leur stabilité et leurs bifurcations. Ce modèle est ensuite adapté au cas du saxophone, pour lequel on intègre une caractérisation acoustique expérimentale, afin de mieux tenir compte de la géométrie complexe de l'instrument. Enfin, nous étudions un modèle physique simplifié de violon, avec une non-régularité liée frottement de Coulomb. Cette dernière application illustre ainsi la polyvalence des outils développés face aux différents types de non-régularité.
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Singh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.

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The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods that are highly efficient in the semiclassical regime. Our analysis takes place in the Lie algebra generated by multiplicative operators and polynomials of the differential operator. This Lie algebra is completely characterised by Jordan polynomials in the differential operator, which constitute naturally symmetrised differential operators. Combined with the $\mathbb{Z}_2$-graded structure of this Lie algebra, the symmetry results in skew-Hermiticity of the exponents for Zassenhaus-style splittings, resulting in unitary evolution and numerical stability. The properties of commutator simplification and height reduction in these Lie algebras result in a highly effective form of $\textit{asymptotic splitting:} $exponential splittings where consecutive terms are scaled by increasing powers of the small semiclassical parameter. This leads to high accuracy methods whose costs grow quadratically with higher orders of accuracy. Time-dependent potentials are tackled by developing commutator-free Magnus expansions in our Lie algebra, which are subsequently split using the Zassenhaus algorithm. We present two approaches for developing arbitrarily high-order Magnus--Zassenhaus schemes${-}$one where the integrals are discretised using Gauss--Legendre quadrature at the outset and another where integrals are preserved throughout. These schemes feature high accuracy, allow large time steps, and the quadratic growth of their costs is found to be superior to traditional approaches such as Magnus--Lanczos methods and Yoshida splittings based on traditional Magnus expansions that feature nested commutators of matrices. An analysis of these operatorial splittings and expansions is carried out by characterising the highly oscillatory behaviour of the solution.
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Ehrenstein, Uwe. "Méthodes spectrales de résolution des équations de Stokes et de Navier-Stokes : application à des écoulements de convection double diffusive." Nice, 1986. http://www.theses.fr/1986NICE4056.

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Résolution des équations en formulation fonction de courant tourbillon. Pour le problème de Stokes périodique, les équations sont approchées par les séries de Fourier, polynômes de Tchebychev en espace et par des schémas aux différences finies en temps ; stabilité des systèmes résultants. Application des méthodes de Tau-Tchebychev et collocation-Tchebychev au problème de Stokes stationnaire et non périodique. Application de l'algorithme de collocation-Tchebychev aux équations de Navier-Stokes instationnaires puis aux équations des écoulements de convection double-diffusive
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Azaiez, Majdi. "Calcul de la pression dans le problème de stokes pour des fluides visqueux incompressibles par une méthode spectrale de collocation." Paris 11, 1991. http://www.theses.fr/1990PA112364.

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Dans ce memoire nous presentons une methode spectrale de collocation pour resoudre les equations de stokes pour des fluides visqueux incompressibles, et en particulier pour satisfaire, a la precision spectrale la contrainte de continuite. On presente d'abord un solveur de helmholtz et on donne ensuite une premiere discretisation des equations de stokes utilisant, pour la vitesse et la pression, des polynomes de meme degre. Enfin on presente une methode d'approximation ameliorant la premiere
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Zakaria, Abdellatif. "Étude de divers schémas pseudo-spectraux de type collocation pour la résolution des équations aux dérivées partielles : application aux équations de Navier-stokes." Nice, 1985. http://www.theses.fr/1985NICE4022.

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On présente un ensemble de schémas pseudo spectraux de type collocation, basés sur des approximations spatiales en polynômes de Tchebychev et s'appliquant a la résolution des problèmes instationnaires. On étudie la stabilité numérique de ces schémas dans le cas d'une équation de diffusion, d'advection-diffusion et d'advection. On considère une méthode mixte spectrale aux différences finies, bien adaptée aux problèmes non linéaires stationnaires. On l'applique a la résolution des équations de Navier-Stokes pour les mouvements stationnaires d'un fluide visqueux incompressible
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Books on the topic "Spectral collocation"

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Hussaini, M. Yousuff. Spectral collocation methods. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Parter, Seymour V. Preconditioning Legendre spectral collocation approximations to elliptic problems. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1993.

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Quarteroni, Alfio. Domain decomposition preconditioners for the spectral collocation method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, Institute for Computer Applications in Science and Engineering, 1988.

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Quarteroni, Alfio. Domain decomposition preconditioners for the spectral collection method. Hampton, Va: ICASE, 1988.

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Bernardi, Christine. Single-grid spectral collocation for the Navier-Stokes equations. Hampton, Va: ICASE, 1988.

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Landriani, G. Sacchi. A multidomain spectral collocation method for the Stokes problem. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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Landriani, G. Sacchi. A multidomain spectral collocation method for the Stokes problem. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1989.

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Landriani, G. Sacchi. A multidomain spectral collocation method for the Stokes problem. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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Macaraeg, Michele G. A spectral collocation solution to the compresssible stability Eigenvalue problem. Hampton, Va: Langley Research Center, 1988.

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Solomonoff, Alex. Global collocation methods for approximation and the solution of partial differential equations. Hampton, Va: ICASE, 1986.

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Book chapters on the topic "Spectral collocation"

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Cavoretto, R., A. De Rossi, M. Donatelli, and S. Serra-Capizzano. "Spectral Analysis for Radial Basis Function Collocation Matrices." In Numerical Mathematics and Advanced Applications 2009, 237–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11795-4_24.

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Cheng, Lizheng, and Hongping Li. "The Chebyshev spectral collocation method of nonlinear Burgers equation." In Advances in Energy Science and Equipment Engineering II, 1557–60. Taylor & Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742: CRC Press, 2017. http://dx.doi.org/10.1201/9781315116174-136.

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Gheorghiu, Călin-Ioan. "Spectral Collocation Solutions to a Class of Pseudo-parabolic Equations." In Numerical Methods and Applications, 179–86. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10692-8_20.

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Liu, Zeting, Shujuan Lv, and Xiaocui Li. "Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher’s Equation." In Theory, Methodology, Tools and Applications for Modeling and Simulation of Complex Systems, 245–52. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2663-8_26.

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Bhoraniya, Rameshkumar, Pinank Patel, Ramdevsinh Jhala, and Rajendrasinh Jadeja. "Theoretical Approach to Chebyshev Spectral Collocation Method and Its Mathematical Implementation." In Numerical Methods for Energy Applications, 165–83. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-62191-9_7.

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Pindza, Edson, Kailash C. Patidar, and Edgard Ngounda. "Rational Spectral Collocation Method for Pricing American Vanilla and Butterfly Spread Options." In Finite Difference Methods,Theory and Applications, 323–31. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20239-6_35.

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Xu, Zhenli, and Houde Han. "Spectral Collocation Technique for Absorbing Boundary Conditions with Increasingly High Order Approximation." In Computational Science – ICCS 2007, 267–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72590-9_38.

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Imai, H., Y. Shinohara, and T. Miyakoda. "On Spectral Collocation Methods in Space and Time for Free Boundary Problems." In Computational Mechanics ’95, 798–803. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79654-8_131.

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Bäck, Joakim, Fabio Nobile, Lorenzo Tamellini, and Raul Tempone. "Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison." In Lecture Notes in Computational Science and Engineering, 43–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15337-2_3.

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Brugiapaglia, Simone. "A Compressive Spectral Collocation Method for the Diffusion Equation Under the Restricted Isometry Property." In Lecture Notes in Computational Science and Engineering, 15–40. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48721-8_2.

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Conference papers on the topic "Spectral collocation"

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Djeddi, Reza, and Kivanc Ekici. "Modified Spectral Operators for Time-Collocation and Time-Spectral Solvers." In 54th AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-1311.

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Fahroo, Fariba, and I. Ross. "Trajectory optimization by indirect spectral collocation methods." In Astrodynamics Specialist Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2000. http://dx.doi.org/10.2514/6.2000-4028.

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Ma, Jing, Yasong Sun, and Benwen Li. "Parametric Study of Simultaneous Radiative Transfer in Plane-Parallel Scattering Medium With Variable Refractive Index by Spectral Collocation Method." In ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ht2013-17689.

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In this work, a spectral collocation method is developed to simulate radiative transfer in a refractive planar medium. The space and angular domains of radiative intensity are discretized by Chebyshev polynomials, and the angular derivative term and the integral term of radiative transfer equation are approximated by spectral collocation method. The spectral collocation method can provide exponential convergence and obtain high accuracy even using few nodes. There is a very satisfying correspondence between the spectral collocation results and available data in literatures. Influence of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the emissivity of boundary are investigated for the plane-parallel scattering medium with variable refractive index.
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Rizales, Johnny J. M., Paulo T. T. Esperanc¸a, and Andre´ Belfort Bueno. "Simulation of Flow Around Circular Cylinder Using a Collocation Spectral Method." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67152.

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The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for low Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.
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Faria, Adriana, Milton Biage, and Paulo Junior. "Collocation spectral elements method for simulation of reactive mixing layer." In Fluids 2000 Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2000. http://dx.doi.org/10.2514/6.2000-2481.

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Ayton, Lorna J., Matthew Colbrook, and Athanassios Fokas. "The Unified Transform: A Spectral Collocation Method for Acoustic Scattering." In 25th AIAA/CEAS Aeroacoustics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-2528.

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Christiansen, Torben B., Harry B. Bingham, Allan P. Engsig-Karup, Guillaume Ducrozet, and Pierre Ferrant. "Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10861.

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A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichlet-to-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes.
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Deshmukh, Venkatesh. "Spectral Collocation-Based Optimization in Parameter Estimation for Nonlinear Time-Varying Dynamical Systems." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35262.

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A constructive optimization algorithm using Chebyshev spectral collocation and quadratic programming is proposed for unknown parameter estimation in nonlinear time-varying dynamic system models to be constructed from available data. The parameters to be estimated are assumed to be identifiable from the data which also implies that the assumed system models with known parameter values have a unique solution corresponding to every initial condition and parameter set. The nonlinear terms in the dynamic system models are assumed to have a known form, and the models are assumed to be parameter affine. Using an equivalent algebraic description of dynamical systems by Chebyshev spectral collocation and data, a residual quadratic cost is set up which is a function of unknown parameters only. The minimization of this cost yields the unique solution for the unknown parameters since the models are assumed to have a unique solution for a particular parameter set. An efficient algorithm is presented step-wise and is illustrated using suitable examples.
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Kabakian, Adour. "A three-dimensional spectral collocation time-domain solver for electromagnetic wave scattering." In 36th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-980.

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Yin, Yan-hong, Ao Sun, and Tian-jun Wang. "Spectral collocation methods for a class of nonlinear singular boundary value problems." In 2013 International Conference on Advanced Mechatronic Systems (ICAMechS). IEEE, 2013. http://dx.doi.org/10.1109/icamechs.2013.6681715.

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