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Article
Publication date: 16 February 2022

Thomas Reum and Hannes Toepfer

The purpose of this paper is to show the applicability of a discrete Hodge operator in the context of the De Rham cohomology to bicomplex-valued electromagnetic wave…

Abstract

Purpose

The purpose of this paper is to show the applicability of a discrete Hodge operator in the context of the De Rham cohomology to bicomplex-valued electromagnetic wave propagation problems. It was applied in the finite element method (FEM) to get a higher accuracy through conformal discretization. Therewith, merely the primal mesh is needed to discretize the full system of Maxwell equations.

Design/methodology/approach

At the beginning, the theoretical background is presented. The bicomplex number system is used as a geometrical algebra to describe three-dimensional electromagnetic problems. Because we treat rotational field problems, Whitney edge elements are chosen in the FEM to realize a conformal discretization. Next, numerical simulations regarding practical wave propagation problems are performed and compared with the common FEM approach using the Helmholtz equation.

Findings

Different field problems of three-dimensional electromagnetic wave propagation are treated to present the merits and shortcomings of the method, which calculates the electric and magnetic field at the same spatial location on a primal mesh. A significant improvement in accuracy is achieved, whereas fewer essential boundary conditions are necessary. Furthermore, no numerical dispersion is observed.

Originality/value

A novel Hodge operator, which acts on bicomplex-valued cotangential spaces, is constructed and discretized as an edge-based finite element matrix. The interpretation of the proposed geometrical algebra in the language of the De Rham cohomology leads to a more comprehensive viewpoint than the classical treatment in FEM. The presented paper may motivate researchers to interpret the form of number system as a degree of freedom when modeling physical effects. Several relationships between physical quantities might be inherently implemented in such an algebra.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 27 July 2018

Bojana Nikolic, Bojan Dimitrijevic, Tino Hutschenreuther and Hannes Toepfer

The purpose of this paper is to analyze a signal propagation in highly metalized environments, which has not been extensively studied in the literature. Having in mind a…

Abstract

Purpose

The purpose of this paper is to analyze a signal propagation in highly metalized environments, which has not been extensively studied in the literature. Having in mind a large number of such applications, better understanding and possibly finding a way of improving communication in these conditions would be highly beneficial.

Design/methodology/approach

The analysis is performed in a simulation environment developed by the authors, based on finite difference time domain (FDTD) method, to identify effects that have decisive influence on electromagnetic (EM) wave propagation in the aforementioned conditions. The analysis of the EM field at the reception is modified so that a multiple-field sampling is performed, and maximal values are further used. In practical realizations, this procedure could be implemented by using multiple antennas and selective combining at the reception.

Findings

Results show that the existence of metal objects (in the observed case, these are railway tracks), in combination with the appropriate choice of antenna parameters, can be favorably used to improve signal reception. The contribution is manifested through the reduction of the pathloss.

Research limitations/implications

In the performed analysis, one should be aware of the limitations that the FDTD method brings. Those limitations are related to the size of the computational domain and discretization mesh refinement (possibility of modeling geometry in fine details).

Originality/value

Originality of this paper consists of the introduced modification in the analysis of signal propagation in heavily metalized environment. Namely, a multiple-field sampling in the reception zone (in one plane, dimensions λ × λ = 12.5 cm X 12.5 cm) is performed using several probes in simulation environment. In this way, a qualitative analysis is performed more efficiently, which made it is possible to distinguish and identify different propagation mechanisms.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 17 August 2018

Rafael Psiuk, Alisa Artizada, Daniel Cichon, Hartmut Brauer, Hannes Toepfer and Albert Heuberger

This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses…

Abstract

Purpose

This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses on the magnetic field-based football goal detection system called as GoalRef, where a primary loop generates a magnetic field around the goal. The passive loops are integrated in the football, and a goal is deduced from induced voltages in loop antennas mounted on the goal frame.

Design/methodology/approach

Based on the law of Biot–Savart, the magnetic vector potential of a primary current loop is calculated. The induced voltages in secondary loops are derived by Faraday’s Law. Expressions to calculate induced voltages in elliptically shaped loops and their magnetic field are also presented.

Findings

The induced voltages in secondary loops close to the primary loop are derived by either numerically integrating the primary magnetic flux density over the area of the secondary loop or by integrating the primary magnetic vector potential over the boundary of that loop. Both approaches are examined and compared with respect to accuracy and calculation time. It is shown that using the magnetic vector potential instead of the magnetic flux density can decrease the processing time by a factor of around 100.

Research limitations/implications

Environmental influences like conductive or permeable obstacles are not considered in the model.

Practical implications

The model can be used to investigate the theoretical behavior of inductively coupled systems.

Originality/value

The proposed model provides a flexible, fast and accurate tool for calculations of inductively coupled systems, where the loops can have arbitrary shape, position and orientation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 11 May 2020

Thomas Reum and Hannes Toepfer

The purpose of this paper is to present the advantageous applicability of the bicomplex analysis in the context of the Finite Element Method (FEM). This method can be…

Abstract

Purpose

The purpose of this paper is to present the advantageous applicability of the bicomplex analysis in the context of the Finite Element Method (FEM). This method can be applied for wave propagation problems in various environments.

Design/methodology/approach

In this paper, the bicomplex number system is introduced and accordingly the differential equation for time-harmonic Maxwell’s equations in homogeneous media is derived in detail. Besides that, numerical simulations of wave propagation are performed and compared to the traditional approach based on classical FEM related to the Helmholtz equation. The appropriate error norm is investigated for different discretizations.

Findings

The results show that the use of bicomplex analysis in FEM leads to the higher accuracy of the electromagnetic field determination compared to the traditional Helmholtz approach. By using the bicomplex-valued formulation, the complex-valued electric and magnetic fields can be found directly and no additional FEM calculations are necessary to get the whole field.

Originality/value

The direct bicomplex formulation overcomes the use of the second order derivatives, which leads to the higher accuracy. In general, accurate calculations of the wave propagation in FEM is still an open problem and the approach described in this paper is a contribution to this class of problems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 28 October 2014

Hartmut Brauer, Konstantin Porzig, Judith Mengelkamp, Matthias Carlstedt, Marek Ziolkowski and Hannes Toepfer

The purpose of this paper is to present a novel electromagnetic non-destructive evaluation technique, so called Lorentz force eddy current testing (LET). This method can…

Abstract

Purpose

The purpose of this paper is to present a novel electromagnetic non-destructive evaluation technique, so called Lorentz force eddy current testing (LET). This method can be applied for the detection and reconstruction of defects lying deep inside a non-magnetic conducting material.

Design/methodology/approach

In this paper the technique is described in general as well as its experimental realization. Besides that, numerical simulations are performed and compared to experimental data. Using the output data of measurements and simulations, an inverse calculation is performed in order to reconstruct the geometry of a defect by means of sophisticated optimization algorithms.

Findings

The results show that measurement data and numerical simulations are in a good agreement. The applied inverse calculation methods allow to reconstruct the dimensions of the defect in a suitable accuracy.

Originality/value

LET overcomes the frequency dependent skin-depth of traditional eddy current testing due to the use of permanent magnets and low to moderate magnetic Reynolds numbers (0.1-1). This facilitates the possibility to detect subsurface defects in conductive materials.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 12 July 2011

Olaf Wetzstein, Thomas Ortlepp, Hermann F. Uhlmann and Hannes Toepfer

Josephson junctions act as active elements in superconducting electronics. The behavior of this nonlinear element is characterized by the relation between current and the…

Abstract

Purpose

Josephson junctions act as active elements in superconducting electronics. The behavior of this nonlinear element is characterized by the relation between current and the quantum mechanical phase‐difference. For an accurate device modeling, detailed knowledge about this relation is necessary. This paper aims to discuss these issues.

Design/methodology/approach

To obtain detailed information, a method for DC measurement of the current‐phase relation suitable for all kinds of superconducting circuit elements was accomplished.

Findings

The authors developed a linear transformation algorithm to calculate the current‐phase relation from the measured data.

Research limitations/implications

It turns out that in future designs additional connections and special test structures are required to gain more knowledge about inductance values required for the algorithm.

Originality/value

Based on the inverse calculation of that algorithm, the authors found a 7 percent deviation of the current‐phase relation of a standard superconductor/insulator/superconductor Josephson junction from the predicted sine‐wave behavior. Furthermore, the paper suggests to use this method to evaluate the current‐phase relation of new Josephson elements such as a superconductor/ferromagnet/superconductor junction. Therefore, the authors will deposit the new element directly on the chip with the test setup fabricated with standard Nb‐technology.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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