Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin's method with Hermite-Gauss basis functions

1995 ◽  
Vol 13 (8) ◽  
pp. 1795-1800 ◽  
Author(s):  
A. Weisshaar ◽  
J. Li ◽  
R.L. Gallawa ◽  
I.C. Goyal
Keyword(s):  
Optical Waveguide ◽  
Basis Functions ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Waveguide Modes

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.

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