Calculation of radiative transfer by galerkin's method

1973 ◽  
Vol 13 (2) ◽  
pp. 157-168 ◽  
Author(s):  
Yu.D. Shmyglevskii
Keyword(s):  
Radiative Transfer ◽  
Galerkin’S Method ◽  
Galerkin's Method

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

Galerkin’s method revisited and corrected in the problem of Jaworski and Dowell

2021 ◽  
Vol 155 ◽  
pp. 107604
Author(s):  
Isaac Elishakoff ◽  
Marco Amato ◽  
Alessandro Marzani
Keyword(s):  
Galerkin’S Method ◽  
Galerkin's Method

Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

1999 ◽  
Author(s):  
Keh-Yang Lee ◽  
Anthony A. Renshaw
Keyword(s):  
Solution Technique ◽  
Distributed Parameter ◽  
Moving Mass ◽  
Eigenfunction Expansions ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Mass Problem ◽  
Linearly Independent ◽  
Large Numbers ◽  
Speed Accuracy

Abstract A new solution technique is developed for solving the moving mass problem for nonconservalive, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of terms because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented in the method proposed here by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, 1997). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. A set of real differential ordinary equations in time are derived which require exactly as much work to solve as Galerkin’s method with a set of real, linearly independent trial functions. Results indicate that the proposed method is competitive with traditional Galerkin’s method in terms of speed, accuracy and convergence.

scholarly journals Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method

2012 ◽  
Vol 34 (3) ◽  
pp. 139-156 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Axial Compression ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Method Effects ◽  
Circular Cylindrical Shells

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection.  Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper  [13] which were solved by Ritz energy method.

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