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Journal articles on the topic 'Pseudo-spectral based global collocation method'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Izadi, Mohammad, and Hari Mohan Srivastava. "Applications of Modified Bessel Polynomials to Solve a Nonlinear Chaotic Fractional-Order System in the Financial Market: Domain-Splitting Collocation Techniques." Computation 11, no. 7 (2023): 130. http://dx.doi.org/10.3390/computation11070130.

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We propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic fi

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2

Khanduzi, Raheleh, Asyieh Ebrahimzadeh, and Samaneh Panjeh Ali Beik. "Optimal control of fractional integro-differential systems based on a spectral method and grey wolf optimizer." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 10, no. 1 (2020): 55–65. http://dx.doi.org/10.11121/ijocta.01.2020.00753.

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This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned

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Khader, M. M., and Mohammed M. Babatin. "On Approximate Solutions for Fractional Logistic Differential Equation." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/391901.

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A new approximate formula of the fractional derivatives is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. The new spectral Laguerre collocation method is presented for solving fractional Logistic differential equation (FLDE). The properties of Laguerre polynomials approximation are used to

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Ibrahim, Yasser F., Sobhi E. Abd El-Bar, Mohamed M. Khader, and Mohamed Adel. "Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach." Fractal and Fractional 7, no. 4 (2023): 307. http://dx.doi.org/10.3390/fractalfract7040307.

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We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a

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CHAKRABORTY, DEBANANDA, JAE-HUN JUNG, and GAURAV KHANNA. "A MULTI-DOMAIN HYBRID METHOD FOR HEAD-ON COLLISION OF BLACK HOLES IN PARTICLE LIMIT." International Journal of Modern Physics C 22, no. 05 (2011): 517–41. http://dx.doi.org/10.1142/s0129183111016415.

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A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-

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Sánchez, José L. Carrión, Sílvio R. C. de Freitas, and Riccardo Barzaghi. "OFFSET EVALUATION OF THE ECUADORIAN VERTICAL DATUM RELATED TO THE IHRS." Boletim de Ciências Geodésicas 24, no. 4 (2018): 503–25. http://dx.doi.org/10.1590/s1982-21702018000400031.

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Abstract Considering the definition of the International Height Reference System (IHRS) in the geopotential space (Resolution 1/2015, International Association of Geodesy - IAG), among the present main objectives of the international geodetic community is the materialization of IHRS around the world. One fundamental task for this is the offset determination of each national vertical datum related to the IHRS. In this manuscript we establish the relationship between the Ecuadorian Vertical Datum (EVD) and the IHRS in the geopotential space following the foundations of the Resolution 1/2015 IAG.

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Zhang, Jing, Xiaokai Zhu, Te Chen, and Guowei Dou. "Optimal Dynamics Control in Trajectory Tracking of Industrial Robots Based on Adaptive Gaussian Pseudo-Spectral Algorithm." Algorithms 18, no. 1 (2025): 18. https://doi.org/10.3390/a18010018.

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A pseudo-spectral control algorithm based on adaptive Gauss collocation point reconstruction is proposed to efficiently solve the optimal dynamics control problem of industrial robots. A mathematical model for the kinematic relationship and dynamic optimization control of industrial robots has been established. On the basis of deriving the Legendre–Gauss collocation formula, a two-stage adaptive Gauss collocation strategy for industrial robot dynamics control variables was designed to improve the dynamics optimization control effect of industrial robot by improving the solution efficiency of c

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Kim, Chang Ho, and U. Jin Choi. "Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 3 (1998): 408–30. http://dx.doi.org/10.1017/s0334270000009474.

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AbstractWe propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.

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Vergos, Georgios S., Ilias N. Tziavos, Stelios Mertikas, Dimitrios Piretzidis, Xenofon Frantzis, and Craig Donlon. "Local Gravity and Geoid Improvements around the Gavdos Satellite Altimetry Cal/Val Site." Remote Sensing 16, no. 17 (2024): 3243. http://dx.doi.org/10.3390/rs16173243.

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The isle of Gavdos, and its wider area, is one of the few places worldwide where the calibration and validation of altimetric satellites has been carried out during the last, more than, two decades using dedicated techniques at sea and on land. The sea-surface calibration employed for the determination of the bias in the satellite altimeter’s sea-surface height relies on the use of a gravimetric geoid in collocation with data from tide gauges, permanent global navigation satellite system (GNSS) receivers, as well as meteorological and oceanographic sensors. Hence, a high-accuracy and high-reso

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Bhrawy, A. H., M. A. Alghamdi, and D. Baleanu. "Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/513808.

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The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit

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Lovetskiy, Konstantin P., Dmitry S. Kulyabov, and Ali Weddeye Hissein. "Multistage pseudo-spectral method (method of collocations) for the approximate solution of an ordinary differential equation of the first order." Discrete and Continuous Models and Applied Computational Science 30, no. 2 (2022): 127–38. http://dx.doi.org/10.22363/2658-4670-2022-30-2-127-138.

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The classical pseudospectral collocation method based on the expansion of the solution in a basis of Chebyshev polynomials is considered. A new approach to constructing systems of linear algebraic equations for solving ordinary differential equations with variable coefficients and with initial (and/or boundary) conditions makes possible a significant simplification of the structure of matrices, reducing it to a diagonal form. The solution of the system is reduced to multiplying the matrix of values of the Chebyshev polynomials on the selected collocation grid by the vector of values of the fun

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Bhrawy, A. H., and M. A. Alghamdi. "A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/306746.

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We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. A new shifted Legendre-Galerkin basis is constructed which satisfies exactly the homogeneous initial conditions by expanding the unknown variable using a new polynomial basis of functions which is built upon the shifted Legendre polynomials. A new spectral collocation approximation based on the Gauss-Lobatto quadrature nodes of shifted Legendre polynomials is investigated for solving the nonlinear multiterm FDEs. The main advantage of this approxim

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SEO, JEONG-KWEON, and BYEONG-CHUN SHIN. "NUMERICAL SOLUTIONS OF BURGERS EQUATION BY REDUCED-ORDER MODELING BASED ON PSEUDO-SPECTRAL COLLOCATION METHOD." Journal of the Korea Society for Industrial and Applied Mathematics 19, no. 2 (2015): 123–35. http://dx.doi.org/10.12941/jksiam.2015.19.123.

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Wang, Xiao, Juan Wang, Xin Wang, and Chujun Yu. "A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations." Mathematics 10, no. 3 (2022): 296. http://dx.doi.org/10.3390/math10030296.

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Inhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions of two- (2D) and three-dimensional (3D) inhomogeneous elliptic boundary value problems. We describe how one can improve the numerical accuracy by making some extra “reconstruction techniques” before applying the traditional Fourier series approximation. After the particular solutions have been obtained, the resulting homogeneous equation can the

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15

Salam, M. A., Mehran Azeem, and Imran Afzal. "Hermite Based Collocation Method for the Solution of Boundary Layer Flow of Eyring–Powell Fluid." Archives des Sciences 74, no. 3 (2024): 118–22. http://dx.doi.org/10.62227/as/74320.

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Eyring-Powell equations are used in computational fluid mechanics. When Mach number approaches to 0.9 or close to turbulent flow, the Newtonian equations are not accurateenough . In this research work we consider a boundary layer flow of an Eyring-Powell fluid which is non-newtonian and passing over a wedge. We consider Eyring-Powell fluid in an infinite domain and leading nonlinear differential equation are converted into the ordinary differential equations by using similarity transformations. Then we use Pseudo-Spectral method which is actually Hermite based collocation method on this ordina

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Zajkani, Asghar, Abolfazl Darvizeh, and Mansour Darvizeh. "Analytical modelling of high-rate elasto-viscoplastic deformation of circular plates subjected to impulsive loads using pseudo-spectral collocation method." Journal of Strain Analysis for Engineering Design 48, no. 2 (2012): 126–49. http://dx.doi.org/10.1177/0309324712460359.

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An analytical methodology is developed to study dynamic elasto-viscoplastic behaviour of moderately thick circular plates subjected to high-intensity impulsive loads, comprehensively. First, incremental kinematic formulations are derived based on the first-order shear deformation theory to take into account viscous damping and rotary inertia. Geometrical and material non-linearities are applied by the complete von Kármán system and a mixed strain hardening law coupled with a physically based viscoplastic model, respectively. A semi-implicit scheme of return-mapping is employed by the cutting-p

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Wang, Jianing, Linhao Li, Yichen Liu, Jinyu Hu, Xiao Xiao, and Bo Liu. "AI-TFNet: Active Inference Transfer Convolutional Fusion Network for Hyperspectral Image Classification." Remote Sensing 15, no. 5 (2023): 1292. http://dx.doi.org/10.3390/rs15051292.

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The realization of efficient classification with limited labeled samples is a critical task in hyperspectral image classification (HSIC). Convolutional neural networks (CNNs) have achieved remarkable advances while considering spectral–spatial features simultaneously, while conventional patch-wise-based CNNs usually lead to redundant computations. Therefore, in this paper, we established a novel active inference transfer convolutional fusion network (AI-TFNet) for HSI classification. First, in order to reveal and merge the local low-level and global high-level spectral–spatial contextual featu

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Sengupta, Tapan K., Vajjala K. Suman, Prasannabalaji Sundaram, and Aditi Sengupta. "Analysis of Pseudo-spectral Methods Used for Numerical Simulations of Turbulence." WSEAS TRANSACTIONS ON COMPUTER RESEARCH 10 (January 19, 2022): 9–24. http://dx.doi.org/10.37394/232018.2022.10.2.

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Events in turbulent flows computed by direct numerical simulation (DNS) are often calibrated with properties based on homogeneous isotropic turbulence, advanced by Kolmogorov, and given in Turbulence, U. Frisch, Cambridge Univ. Press, UK (1995). However, these computational procedures are not calibrated using numerical analyses in order to assess their strengths and weaknesses for DNS. This is with the exception in "A critical assessment of simulations for transitional and turbulence flows- Sengupta, T.K., In Proc. of IUTAM Symp. on Advances in Computation, Modeling and Control of Transitional

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Yang, Chunlan, Yi Kong, Xuesong Wang, and Yuhu Cheng. "Hyperspectral Image Classification Based on Adaptive Global–Local Feature Fusion." Remote Sensing 16, no. 11 (2024): 1918. http://dx.doi.org/10.3390/rs16111918.

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Labeled hyperspectral image (HSI) information is commonly difficult to acquire, so the lack of valid labeled data becomes a major puzzle for HSI classification. Semi-supervised methods can efficiently exploit unlabeled and labeled data for classification, which is highly valuable. Graph-based semi-supervised methods only focus on HSI local or global data and cannot fully utilize spatial–spectral information; this significantly limits the performance of classification models. To solve this problem, we propose an adaptive global–local feature fusion (AGLFF) method. First, the global high-order a

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DE STEFANO, G., and O. V. VASILYEV. "Stochastic coherent adaptive large eddy simulation of forced isotropic turbulence." Journal of Fluid Mechanics 646 (March 8, 2010): 453–70. http://dx.doi.org/10.1017/s002211200999303x.

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The stochastic coherent adaptive large eddy simulation (SCALES) methodology is a novel approach to the numerical simulation of turbulence, where a dynamic grid adaptation strategy based on wavelet threshold filtering is utilized to solve for the most ‘energetic’ eddies. The effect of the less energetic unresolved motions is simulated by a model. Previous studies have demonstrated excellent predictive properties of the SCALES approach for decaying homogeneous turbulence. In this paper the applicability of the method is further explored for statistically steady turbulent flows by considering lin

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Gil, Jorge, Juan Fernando Rodrigo, Pablo Salvador, Diego Gómez, Julia Sanz, and Jose Luis Casanova. "An Empirical Radiometric Intercomparison Methodology Based on Global Simultaneous Nadir Overpasses Applied to Landsat 8 and Sentinel-2." Remote Sensing 12, no. 17 (2020): 2736. http://dx.doi.org/10.3390/rs12172736.

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The Simultaneous Nadir Overpass (SNO) method was developed by the NOAA/NESDIS to improve the consistency and quality of climate data acquired by different meteorological satellites. Taking advantage of the reduced impact induced by the Bidirectional Reflectance Distribution Function (BRDF), atmospheric effects, illumination and viewing geometries during an SNO, we created a sensor comparison methodology for all spectral targets. The method is illustrated by applying it to the assessment of data acquired by the Landsat 8 (L8), Sentinel-2A (S2A), and Sentinel-2B (S2B) optical sensors. Multiple S

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Yang, Min, Jing Qin, Xiaodan Wang, and Yanfeng Gu. "Research on the Wetland Vegetation Classification Method Based on Cross-Satellite Hyperspectral Images." Journal of Marine Science and Engineering 13, no. 4 (2025): 801. https://doi.org/10.3390/jmse13040801.

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In recent years, the global commercial aerospace industry has flourished, witnessing a rapid surge in customized satellite services. Deep learning has emerged as a pivotal tool for accurately identifying wetland vegetation. However, hyperspectral remote sensing images are often plagued by varying degrees of noise during acquisition, leading to subtle differences in spectral responses. Currently, vegetation classification models are tailored specifically for each hyperspectral sensor, making it challenging to generalize a model designed for one sensor to others. Furthermore, discrepancies in da

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Zhang, Jun, Hao Wu, and Shu Peng. "A KNOWLEDGE-BASED APPROACH ON GLOBELAND30 INCREMENTAL UPDATING: A CASE STUDY OF BUILT-UP AREA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B8 (June 24, 2016): 1335–39. http://dx.doi.org/10.5194/isprs-archives-xli-b8-1335-2016.

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Global land cover/land use product in multiple periods is pivotal to understand the complex drivers and mechanisms in global climate change, and to forecast future land use trends in sustainable development. GlobeLand30, as the world’s first high spatial resolution land cover product (83% accuracy), needs to be continually updated to meet various needs. However, many challenges - such as removing pseudo change to keep consistency of updating - remain unsolved. To deal with high temporal and spatial variability happened within built-up area class and between it and other classes, this paper pre

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Zhang, Jun, Hao Wu, and Shu Peng. "A KNOWLEDGE-BASED APPROACH ON GLOBELAND30 INCREMENTAL UPDATING: A CASE STUDY OF BUILT-UP AREA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B8 (June 24, 2016): 1335–39. http://dx.doi.org/10.5194/isprsarchives-xli-b8-1335-2016.

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Global land cover/land use product in multiple periods is pivotal to understand the complex drivers and mechanisms in global climate change, and to forecast future land use trends in sustainable development. GlobeLand30, as the world’s first high spatial resolution land cover product (83% accuracy), needs to be continually updated to meet various needs. However, many challenges - such as removing pseudo change to keep consistency of updating - remain unsolved. To deal with high temporal and spatial variability happened within built-up area class and between it and other classes, this paper pre

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Ducasse, Etienne, Karine Adeline, Xavier Briottet, Audrey Hohmann, Anne Bourguignon, and Gilles Grandjean. "Montmorillonite Estimation in Clay–Quartz–Calcite Samples from Laboratory SWIR Imaging Spectroscopy: A Comparative Study of Spectral Preprocessings and Unmixing Methods." Remote Sensing 12, no. 11 (2020): 1723. http://dx.doi.org/10.3390/rs12111723.

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Clay minerals play an important role in shrinking–swelling of soils and off–road vehicle mobility mainly due to the presence of smectites including montmorillonites. Since soils are composed of different minerals intimately mixed, an accurate estimation of its abundance is challenging. Imaging spectroscopy in the short wave infrared spectral region (SWIR) combined with unmixing methods is a good candidate to estimate clay mineral abundance. However, the performance of unmixing methods is mineral-dependent and may be enhanced by using appropriate spectral preprocessings. The objective of this p

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Fesenko, O. D., R. O. Bieliakov, H. D. Radzivilov, et al. "METHOD OF IMPROVING THE ACCURACY OF NAVIGATION MEMS DATA PROCESSING OF UAV INERTIAL NAVIGATION SYSTEM." Radio Electronics, Computer Science, Control, no. 3 (October 18, 2022): 196. http://dx.doi.org/10.15588/1607-3274-2022-3-18.

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Context. Modern theory and practice of preparation and conduct of hostilities on land, at sea, in the air, and recently in cyberspace dictates the relentless modernization of military equipment. The development of fundamentally new weapons is carried out considering one of the main requirements – maximum automation of operational processes, which allows combatants to distance themselves from each other as much as possible. Among the newest models of armaments on the battlefield, due to the predominantly positional nature of the armed confrontation, unmanned aerial vehicles (UAVs) have be

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Yu, Qixin, and Dieter Horns. "Searching for photon-ALPs mixing effects in AGN gamma-ray energy spectra." Journal of Cosmology and Astroparticle Physics 2023, no. 05 (2023): 029. http://dx.doi.org/10.1088/1475-7516/2023/05/029.

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Abstract High energy gamma-rays propagating in external magnetic fields may convert into axion-like particles (ALPs). In this case, the observed gamma-ray spectra are modified by the resulting energy-dependent conversion probability. In this study, we use the energy spectra of 20 extra-galactic gamma-ray sources recorded during 10 years of Fermi-LAT observations. We define a test statistics based upon the likelihood ratio to test the hypothesis for a spectral model without vs. a model with photon-ALPs coupling. The conversion probability is calculated for fixed values of the mass and two-photo

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Tabata, Tasuku, Viju O. John, Rob A. Roebeling, Tim Hewison, and Jörg Schulz. "Recalibration of over 35 Years of Infrared and Water Vapor Channel Radiances of the JMA Geostationary Satellites." Remote Sensing 11, no. 10 (2019): 1189. http://dx.doi.org/10.3390/rs11101189.

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Infrared sounding measurements of the Infrared Atmospheric Sounding Interferometer (IASI), Atmospheric Infrared Sounder (AIRS), and High-resolution Infrared Radiation Sounder/2 (HIRS/2) instruments are used to recalibrate infrared (IR; ~11 µm) channels and water vapor (WV; ~6 µm) channels of the Visible and Infrared Spin Scan Radiometer (VISSR), Japanese Advanced Meteorological Imager (JAMI), and IMAGER instruments onboard the historical geostationary satellites of the Japan Meteorological Agency (JMA). The recalibration was performed using a common recalibration method developed by European O

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Cortesi, U., J. C. Lambert, C. De Clercq, et al. "Geophysical validation of MIPAS-ENVISAT operational ozone data." Atmospheric Chemistry and Physics Discussions 7, no. 3 (2007): 5805–939. http://dx.doi.org/10.5194/acpd-7-5805-2007.

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Abstract. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), on-board the European ENVIronmental SATellite (ENVISAT) launched on 1 March 2002, is a middle infrared Fourier Transform spectrometer measuring the atmospheric emission spectrum in limb sounding geometry. The instrument is capable to retrieve the vertical distribution of temperature and trace gases, aiming at the study of climate and atmospheric chemistry and dynamics, and at applications to data assimilation and weather forecasting. MIPAS operated in its standard observation mode for approximately two years, from

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Cortesi, U., J. C. Lambert, C. De Clercq, et al. "Geophysical validation of MIPAS-ENVISAT operational ozone data." Atmospheric Chemistry and Physics 7, no. 18 (2007): 4807–67. http://dx.doi.org/10.5194/acp-7-4807-2007.

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Abstract. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), on-board the European ENVIronmental SATellite (ENVISAT) launched on 1 March 2002, is a middle infrared Fourier Transform spectrometer measuring the atmospheric emission spectrum in limb sounding geometry. The instrument is capable to retrieve the vertical distribution of temperature and trace gases, aiming at the study of climate and atmospheric chemistry and dynamics, and at applications to data assimilation and weather forecasting. MIPAS operated in its standard observation mode for approximately two years, from

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Han, Holly Kyeore, Natalya Gomez, and Jeannette Xiu Wen Wan. "Capturing the interactions between ice sheets, sea level and the solid Earth on a range of timescales: a new “time window” algorithm." Geoscientific Model Development 15, no. 3 (2022): 1355–73. http://dx.doi.org/10.5194/gmd-15-1355-2022.

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Abstract. Retreat and advance of ice sheets perturb the gravitational field, solid surface and rotation of the Earth, leading to spatially variable sea-level changes over a range of timescales O(100−6 years), which in turn feed back onto ice-sheet dynamics. Coupled ice-sheet–sea-level models have been developed to capture the interactive processes between ice sheets, sea level and the solid Earth, but it is computationally challenging to capture short-term interactions O(100−2 years) precisely within longer O(103−6 years) simulations. The standard forward sea-level modelling algorithm assigns

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Liu, Yuxian, and Yan Li. "State‐dependent indirect hp‐pseudospectral method for rigid spacecraft attitude optimal control problem." Asian Journal of Control, February 2, 2024. http://dx.doi.org/10.1002/asjc.3307.

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AbstractThe state‐dependent indirect ‐pseudospectral (SDIHP) method for rigid spacecraft attitude control is presented in this paper. The optimal controller is obtained by the SDIHP method through classifying the attitude optimal control problem as a nonlinear quadratic optimal control problem. In the proposed control scheme, successive state‐dependent coefficient (SDC) parameterization is initially applied to the spacecraft dynamics to derive an available linear system to decrease the calculation cost and speed. Then, the indirect ‐adaptive spectral discretization is developed to convert the

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He, Chen, Dakun Sun, and Xiaofeng Sun. "Stall Inception Analysis of Transonic Compressors With Chordwise and Axial Sweep." Journal of Turbomachinery 140, no. 4 (2018). http://dx.doi.org/10.1115/1.4038873.

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This paper concentrates on the stall inception analysis of transonic compressors with chordwise and axial sweep. A new prediction approach of stall inception is developed based on global stability analysis and immersed boundary theory, which makes it possible to take both the concrete blade geometry and the complicated base flow into consideration. The prediction of stall inception boils down to an eigenvalue problem. Spectral collocation method is adopted to discretize the eigenvalue equations and the eigenvalues are solved by using singular value decomposition method. The developed predictio

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Herrada, M. A., S. Blanco-Trejo, J. Eggers, and P. S. Stewart. "Global stability analysis of flexible channel flow with a hyperelastic wall." Journal of Fluid Mechanics 934 (January 18, 2022). http://dx.doi.org/10.1017/jfm.2021.1131.

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We consider the stability of flux-driven flow through a long planar rigid channel, where a segment of one wall is replaced by a pre-tensioned hyperelastic (neo-Hookean) solid of finite thickness and subject to a uniform external pressure. We construct the steady configuration of the nonlinear system using Newton's method with spectral collocation and high-order finite differences. In agreement with previous studies, which use an asymptotically thin wall, we show that the thick-walled system always has at least one stable steady configuration, while for large Reynolds numbers the system exhibit

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Magnini, Mirco, and Miguel A. Herrada. "Two-dimensional global stability analysis of elongated bubbles moving in a horizontal tube." Physical Review Fluids 10, no. 5 (2025). https://doi.org/10.1103/physrevfluids.10.053603.

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The linear stability of an elongated axisymmetric gas bubble transported by a liquid in a capillary tube is analyzed through the use of numerical simulations. The study focuses on the influence of inertia, characterized by the Reynolds number (Re) and the imposed flow rate, characterized by a capillary number (Cal), on the stability of the bubble tail, which exhibits ripples at high Re. The numerical approach utilizes a boundary-fitted method in a reference frame anchored to the bubble, combined with a mixed spatial discretization based on spectral collocation in the radial direction and finit

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Abdelhakem, Mohamed, Doha Mahmoud, Dumitru Baleanu, and Mamdouh El-kady. "Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems." Advances in Difference Equations 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13662-021-03247-6.

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AbstractIn this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods. Also, this method can be extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified Galerkin spectral method has been used to create direct approximate solutions of linear/nonlinear ordinary fractional d

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Wei, Yi, Xing-Qiu Zhang, Zhu-Yan Shao, Jian-Qiang Gao, and Xiao-Feng Yang. "Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle." Scientific Reports 9, no. 1 (2019). http://dx.doi.org/10.1038/s41598-019-52419-8.

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Abstract The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete globa

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Masoumzadeh, Reza, Mostafa Abbaszadeh, and Mehdi Dehghan. "Isogeometric collocation method to simulate phase-field crystal model." International Journal of Numerical Methods for Heat & Fluid Flow, July 25, 2024. http://dx.doi.org/10.1108/hff-01-2024-0020.

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Purpose The purpose of this study is to develop a new numerical algorithm to simulate the phase-field model. Design/methodology/approach First, the derivative of the temporal direction is discretized by a second-order linearized finite difference scheme where it conserves the energy stability of the mathematical model. Then, the isogeometric collocation (IGC) method is used to approximate the derivative of spacial direction. The IGC procedure can be applied on irregular physical domains. The IGC method is constructed based upon the nonuniform rational B-splines (NURBS). Each curve and surface

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Sun, Yunhao, Zhengxing Dai, Gulou Shen, Xiaohua Lu, Xiang Ling, and Xiaoyan Ji. "Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing." Frontiers in Chemistry 9 (January 24, 2022). http://dx.doi.org/10.3389/fchem.2021.801551.

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To improve the efficiency of electrolyte perturbed-chain statistical associating fluid theory–density functional theory (ePC-SAFT-DFT) calculation of the confined system, in this work, first, the Chebyshev pseudo-spectral collocation method was extended to the spherical pores. Second, it was combined with the Anderson mixing algorithm to accelerate the iterative process. The results show that the Anderson mixing algorithm can reduce the computation time significantly. Finally, based on the accelerated ePC-SAFT-DFT program, a systematic study of the effects of the temperature, pressure, pore si

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Gao, Haiyang, Xinglin Guo, Huajiang Ouyang, and Fang Han. "Crack Identification of Cantilever Plates Based on a Kriging Surrogate Model." Journal of Vibration and Acoustics 135, no. 5 (2013). http://dx.doi.org/10.1115/1.4023813.

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This work presents an effective method to identify the tip locations of an internal crack in cantilever plates based on a Kriging surrogate model. Samples of varying crack parameters (tip locations) and their corresponding root mean square (RMS) of random responses are used to construct the initial Kriging surrogate model. Moreover, the pseudo excitation method (PEM) is employed to speed up the spectral analysis. For identifying crack parameters based on the constructed Kriging model, a robust stochastic particle swarm optimization (SPSO) algorithm is adopted for enhancing the global searching

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Fusi, Lorenzo, and Antonio Giovinetto. "A spectral collocation scheme for the flow of a piezo-viscous fluid in ducts with slip conditions." Theoretical and Computational Fluid Dynamics, July 13, 2024. http://dx.doi.org/10.1007/s00162-024-00713-1.

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AbstractIn this paper we present a numerical scheme based on spectral collocation methods to investigate the flow of a piezo-viscous fluid, i.e., a fluid in which the rheological parameters depend on the pressure. In particular, we consider an incompressible Navier–Stokes fluid with pressure dependent viscosity flowing in: (i) a two-dimensional non-symmetric planar channel; (ii) a three-dimensional axisymmetric non-straight conduit. For both cases we impose the Navier slip boundary conditions that can be reduced to the classical no-slip condition for a proper choice of the slip parameter. We a

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M S, Basavaraj, and Shivaraj Kumar D L. "Optimal Transient Energy Growth Of 2D Perturbation In A Magnetohydrodynamic Plane Poiseuille Flow Of Casson Fluid." Journal of Fluids Engineering, August 5, 2023, 1–55. http://dx.doi.org/10.1115/1.4063117.

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Abstract The study investigates the influence of the Casson fluid parameter and the spanwise uniform magnetic field on the onset of instability against infinitesimal disturbances in an electrically conducting fluid flow between two parallel non-conducting rigid plates. The 4th-order linearized disturbance equation governing stability is solved using the spectral collocation method with Chebyshev-based polynomials. The aim is to analyze in detail the effect of the parameters involved in the problem using both modal and non-modal linear stability analysis. The modal analysis provides accurate va

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Hosseinverdi, Shirzad, and Hermann F. Fasel. "High-Order-Accurate Incompressible Flow Solver for High-Fidelity Numerical Simulations and Linear Stability Analysis." AIAA Journal, February 1, 2023, 1–18. http://dx.doi.org/10.2514/1.j062110.

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The development of high-fidelity versatile incompressible Navier–Stokes solver that is applicable for both direct numerical simulations (DNSs) and linear global stability investigations is presented and discussed. The solver is based on a vorticity–velocity formulation of the Navier–Stokes equations for orthogonal curvilinear grids. A rigorous and efficient approach is proposed that guarantees the divergence-free condition for the velocity and vorticity fields. The code incorporates advanced numerical algorithms including compact finite differences in combination with a pseudo-spectral method,

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Wang, Zi'an, Ganghua Hu, and Zhan Wang. "Dynamics of multi-mode nonlinear internal waves in fluids of great depth." Physics of Fluids 36, no. 4 (2024). http://dx.doi.org/10.1063/5.0206500.

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This paper is mainly concerned with the dynamics of strongly nonlinear internal waves in two-dimensional fluids of great depth. A fully nonlinear model for a three-layer fluid of great depth containing topography, a Miyata–Choi–Camassa (MCC)-type system, is developed based on the generalization of the Ablowitz–Fokas–Musslimani global-relation formulation for free-surface water waves. Mode-1 internal solitary waves are numerically found in the MCC-type equation using the Petviashvili iteration technique and in the full Euler equations based on the boundary integral equation method. The comparis

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Chen, Jingjian, Chunxin Yuan, Jiali Xu, Pengfei Bie, and Zhiqiang Wei. "DF-ParPINN: parallel PINN based on velocity potential field division and single time slice focus." Frontiers in Marine Science 11 (March 14, 2024). http://dx.doi.org/10.3389/fmars.2024.1309775.

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Modified Benney-Luke equation (mBL equation) is a three-dimensional temporal-spatial equation with complex structures, that is a high-dimensional partial differential equation (PDE), it is also a new equation of the physical ocean field, and its solution is important for studying the internal wave-wave interaction of inclined seafloor. For conventional PDE solvers such as the pseudo-spectral method, it is difficult to solve mBL equation with both accuracy and speed. Physics-informed neural network (PINN) incorporates physical prior knowledge in deep neural networks, which can solve PDE with re

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Li Xiang, Liu Yun, Zhu Tian-Xin, and Duan Chuan-Xi. "New rovibrational subbands of Ar-D<sub>2</sub>O complex in the D<sub>2</sub>O bending mode region." Acta Physica Sinica, 2023, 0. http://dx.doi.org/10.7498/aps.72.20221728.

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The intermolecular interactions involving the water molecule play important roles in many fields of physics, chemistry, and biology. High-resolution spectroscopy of Van der Waals complexes formed by a rare gas atom and a water molecule could provide a wealth of information on these intermolecular interactions. The precise experimental data can be used to test the accuracy and efficiency of various theoretical methods for constructing the intermolecular potential energy surfaces and calculating the bound states. In this work, the high-resolution infrared absorption spectrum of the Ar-D<sub&g

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