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An application of a boundary element method to the solution of static field problems in closed domains is presented in this paper. The fully populated system matrix of the boundary element method is compressed with the fast multipole method. Two approaches of modified transformation techniques are compared and discussed in the context of boundary element methods to further reduce the computational costs of the fast multipole method. The efficiency of the fast multipole method with modified transformations is shown in two numerical examples.

The purpose of this paper is to present an application of augmented reality (AR) in the context of teaching of electrodynamics. The AR visualization technique is applied to electromagnetic fields. Carrying out of numerical simulations as well as preparation of the AR display is shown. Presented examples demonstrate an application of this technique in teaching of electrodynamics.

The 3D electromagnetic fields are computed with the finite element method (FEM) and visualized with an AR display.

AR is a vivid method for visualization of electromagnetic fields. Students as well as experts can easily connect the characteristics of the fields with the physical object.

The focus of the presented work has been on an application of AR in a lecture room. Then, easy handling of a presentation among with low‐hardware requirements is important.

The presented approach is based on low‐hardware requirements. Hence, a presentation of electromagnetic fields with AR in a lecture room can be easily done. AR helps students to understand electromagnetic field theory.

Well‐known methods like FEM and AR have been combined to develop a visualization technique for electromagnetic fields, which can be easily applied in a lecture room.

If the fast multipole method (FMM) is applied in the context of the boundary element method, the efficiency and accuracy of the FMM is significantly influenced by the used hierarchical grouping scheme. Hence, in this paper, a new approach to the grouping scheme is presented to solve numerical examples with problem‐oriented meshes and higher order elements accurately and efficiently. Furthermore, with the proposed meshing strategies the efficiency of the FMM can be additionally controlled.

Aims to show that efficiency and accuracy of integral equation methods (IEMs) in combination with the fast multipole method for the design of a novel magnetic gear.

A novel magnetic gear was developed. Magnetic fields and torque of the gear were simulated based on IEMs. The fast multipole method was applied to compress the matrix of the belonging linear system of equations. A computer cluster was used to achieve numerical results within an acceptable time. A three‐dimensional post‐processing and visualization of magnetic fields enables a deep understanding of the gear.

IEMs are very well suited for the numerical analysis of a magnetic gear. Especially, the treatment of the air gap between the rotating components, which move with significant varying velocities, is relatively easy. Furthermore, a correct computation and visualization of flux lines is possible. A magnetic gear is advantageous for high rotational velocities.

A quasi static numerical simulation has sufficed for an understanding of the principle of the magnetic gear and for the development of a prototype.

IEMs are very suitable for the analysis of complex problems with moving parts. Nowadays, the efficiency is very good even for large problems, since matrix compression techniques are well‐engineered.

The design of a novel magnetic gear is discussed. Well‐known techniques like IEMs, fast multipole method and parallel computing are combined to solve a very large and complex problem.

To show for magnetostatic problems, how the numerically expensive post‐processing with the integral equation method (IEM) can be accelerated with the fast multipole method (FMM) and how this approach can be used to generate post‐processing data that allow for drawing streamlines.

In general, post‐processing with the IEM requires computation of the induced field due to solution variables, the field of permanent magnets and of free currents. For each of the three parts an approach to apply the FMM. With these approaches, large numbers of evaluation points can be used which are needed when streamlines are to be drawn. It is shown that this requires specially tailored meshes.

Post‐processing time can be largely reduced by applying the FMM. Additional memory requirements are acceptable even for high numbers of evaluation points. In order to obtain streamline breaks at material discontinuities, flat volume elements can be used.

The presented application of the FMM is applicable only to static problems.

Application of the FMM during post‐processing allows for a large number of evaluation points which are often required to visualize electromagnetic fields. This approach in combination with specially tailored meshes allows for drawing of streamlines.

The FMM is used not only to solve the field problem, but also for post‐processing which requires using the FMM to compute induced magnetic fields as well as the field due to permanent magnets and free currents. This leads to a speedup which allows for a large number of evaluation points which can be used, e.g. for high‐precision drawing of streamlines.

The application of the fast multipole method reduces the computational costs and the memory requirements of the boundary element method from O(N²) to approximately O(N). In this paper we present that the computational costs can be strongly shortened, when the multipole method is not only used for the solution of the system of linear equations but also for the field computation in arbitrary points.

Various parallelization strategies are investigated to mainly reduce the computational costs in the context of boundary element methods and a compressed system matrix.

Electrostatic field problems are solved numerically by an indirect boundary element method. The fully dense system matrix is compressed by an application of the fast multipole method. Various parallelization techniques such as vectorization, multiple threads, and multiple processes are applied to reduce the computational costs.

It is shown that in total a good speedup is achieved by a parallelization approach which is relatively easy to implement. Furthermore, a detailed discussion on the influence of problem oriented meshes to the different parts of the method is presented. On the one hand the application of problem oriented meshes leads to relatively small linear systems of equations along with a high accuracy of the solution, but on the other hand the efficiency of parallelization itself is diminished.

The presented parallelization approach has been tested on a small PC cluster only. Additionally, the main focus has been laid on a reduction of computing time.

Typical properties of general static field problems are comprised in the investigated numerical example. Hence, the results and conclusions are rather general.

Implementation details of a parallelization of existing fast and efficient boundary element method solvers are discussed. The presented approach is relatively easy to implement and takes special properties of fast methods in combination with parallelization into account.

A boundary element method in terms of the field variables is applied to three‐dimensional electromagnetic scattering problems. Especially, the influence of a dipole excited field on low conducting materials situated very close to the antenna will be discussed. We use higher order edge elements of quadilateral shape for the field approximation on curved surfaces. The tangential components of the unknown field variables are interpolated by vector element functions. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by the comparison of different BEM‐formulations and FEM‐results.

This paper deals with the inverse scattering problem of reconstructing the material properties of perfectly conducting or dielectric cylindrical objects. The material properties are reconstructed from measured far‐field scattering data provided by the Electromagnetics Technology Division, AFRL/SNH, 31 Grenier Street, Hanscom AFB, MA 01731‐3010. The measured data have to be calibrated for use in our reconstruction algorithm. The inverse scattering problem formulated as unconstrained nonlinear optimization problem is numerically solved using an iterative scheme with a variable calibration factor which will be determined during the optimization process. Numerical examples show the successful application of the method to the measured data.

Magnetostatic problems including iron components can be solved by a nonlinear indirect volume integral equation. Its unknowns are scalar field sources. They are evaluated iteratively. In doing so the integral representation of fields has to be calculated. At edges singularities occur. Following a method to calculate the field strength on charged surfaces a way out is presented.