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Article
Publication date: 1 January 1983

Ch. HAFNER and R. BALLISTI

We present a semi‐analytic approach based on a multipole expansion for the solution of two‐dimensional, linear electrostatic problems with piecewise homogeneous regions. This…

313

Abstract

We present a semi‐analytic approach based on a multipole expansion for the solution of two‐dimensional, linear electrostatic problems with piecewise homogeneous regions. This method, called multiple multipole method, leads to more accurate solutions and requires less computation time than the usual numerical methods, especially in such problems where the capacitance of a system of electrodes with different dielectric rods in between, both of arbitrary cross section, is to be calculated with precision.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 2 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 January 1992

Jan Sroka and Jacek Starzyński

In the paper establishing the benchmark tests for open boundary problems as it has been done in other branches of electromagnetic field calculations is proposed. Consideration is…

69

Abstract

In the paper establishing the benchmark tests for open boundary problems as it has been done in other branches of electromagnetic field calculations is proposed. Consideration is given to what input and output data should be defined for the benchmark problems. In the appendix one proposal for benchmark problems is presented.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 11 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 April 1995

S. Brillante, R.J. Hill, P.J. Leonard and P. Pozzobon

A two‐dimensional electromagnetic field model of a railway track and traction line is used to determine the equivalent track distributed transmission line parameters in the…

62

Abstract

A two‐dimensional electromagnetic field model of a railway track and traction line is used to determine the equivalent track distributed transmission line parameters in the frequency range DC to 30kHz. The model is solved using the finite‐element method to find the minimum energy condition for two conditions: current excitation to obtain the resistance and inductance, and voltage excitation for the conductance and capacitance. The results have been confirmed using practical test data, and their application is illustrated in a time‐domain circuit simulation to model interference between power and signalling currents in a 750V DC electric railway.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 14 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 February 1994

J. SROKA, J. KORYTKOWSKI and J. STARZYŃSKI

An extension of the coupling of the generalized multipole technique, adapted to the infinite domain, with the standard finite elements in the examined area, to problems with…

51

Abstract

An extension of the coupling of the generalized multipole technique, adapted to the infinite domain, with the standard finite elements in the examined area, to problems with rotational symmetry is presented. The multipole expansion in the infinite domain is the superposition of three‐dimensional multipoles distributed uniformly at several circles. The circles build multipole rings. The theoretical basis for building the multipole rings and for taking symmetry into account are given. The method is verified by calculating electrostatic and magnetostatic problems for which analytical solutions exist. Verification encompasses potential distribution as well as calculation of equivalent lumped parameters, i.e. capacitance and inductance.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 13 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 March 1985

Ch. HAFNER and G. KLAUS

The MMP method, which was already successfully applied to two‐dimensional electrostatic problems, is extended in this paper to solve dynamic cases. Different techniques are…

105

Abstract

The MMP method, which was already successfully applied to two‐dimensional electrostatic problems, is extended in this paper to solve dynamic cases. Different techniques are introduced to get better results and to save computation time. Some waveguide and scattering calculations show the possibilities of this method.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 4 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 8 March 2011

Jianhua Dai, Helder Pinheiro, Jonathan P. Webb and Igor Tsukerman

The purpose of this paper is to extend the generalized finite‐difference calculus of flexible local approximation methods (FLAME) to problems where local analytical solutions are…

256

Abstract

Purpose

The purpose of this paper is to extend the generalized finite‐difference calculus of flexible local approximation methods (FLAME) to problems where local analytical solutions are unavailable.

Design/methodology/approach

FLAME uses accurate local approximations of the solution to generate difference schemes with small consistency errors. When local analytical approximations are too complicated, semi‐analytical or numerical ones can be used instead. In the paper, this strategy is applied to electrostatic multi‐particle simulations and to electromagnetic wave propagation and scattering. The FLAME basis is constructed by solving small local finite‐element problems or, alternatively, by a local multipole‐multicenter expansion. As yet another alternative, adaptive FLAME is applied to problems of wave propagation in electromagnetic (photonic) crystals.

Findings

Numerical examples demonstrate the high rate of convergence of new five‐ and nine‐point schemes in 2D and seven‐ and 19‐point schemes in 3D. The accuracy of FLAME is much higher than that of the standard FD scheme. This paves the way for solving problems with a large number of particles on relatively coarse grids. FLAME with numerical bases has particular advantages for the multi‐particle model of a random or quasi‐random medium.

Research limitations/implications

Irregular stencils produced by local refinement may adversely affect the accuracy. This drawback could be rectified by least squares FLAME, where the number of stencil nodes can be much greater than the number of basis functions, making the method more robust and less sensitive to the irregularities of the stencils.

Originality/value

Previous applications of FLAME were limited to purely analytical basis functions. The present paper shows that numerical bases can be successfully used in FLAME when analytical ones are not available.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 2
Type: Research Article
ISSN: 0332-1649

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