Search

Purpose The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Design/methodology/approach The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Findings The three-phase symmetry reduces the simulated geometry to the sixth part of one pole. The motion transforms to a frequency offset in the angular Fourier series decomposition. The calculation overhead of the Fourier integrals is negligible. The air impedance approximation increases the accuracy and yields a convergence speed of three iterations per decade. Research limitations/implications Only linear materials and two-dimensional geometries are shown for clearness. Researchers are encouraged to adopt recent harmonic balance findings and to evaluate the performance and accuracy of both formulations for larger applications. Practical implications This method offers fast-frequency domain simulations in the optimization process of rotating machines and so an efficient way to treat time-dependent effects such as eddy-currents or voltage-driven coils. Originality/value This paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

Purpose Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering. Design/methodology/approach The formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation. Findings Using confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model. Research limitations/implications This approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately. Practical implications This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications. Originality/value The novelty of the paper is the proposed formulation for the coupling of both methods.

Purpose The high calculation effort for accurate material loss simulation prevents its observation in most magnetic devices. This paper aims at reducing this effort for time periodic applications and so for the steady state of such devices. Design/methodology/approach The vectorized Jiles-Atherton hysteresis model is chosen for the accurate material losses calculation. It is transformed in the frequency domain and coupled with a harmonic balanced finite element solver. The beneficial Jacobian matrix of the material model in the frequency domain is assembled based on Fourier transforms of the Jacobian matrix in the time domain. A three-phase transformer is simulated to verify this method and to examine the multi-harmonic coupling. Findings A fast method to calculate the linearization of non-trivial material models in the frequency domain is shown. The inter-harmonic coupling is moderate, and so, a separated harmonic balanced solver is favored. The additional calculation effort compared to a saturation material model without losses is low. The overall calculation time is much lower than a time-dependent simulation. Research limitations/implications A moderate working point is chosen, so highly saturated materials may lead to a worse coupling. A single material model is evaluated. Researchers are encouraged to evaluate the suggested method on different material models. Frequency domain approaches should be in favor for all kinds of periodic steady-state applications. Practical implications Because of the reduced calculation effort, the simulation of accurate material losses becomes reasonable. This leads to a more accurate development of magnetic devices. Originality/value This paper proposes a new efficient method to calculate complex material models like the Jiles-Atherton hysteresis and their Jacobian matrices in the frequency domain.

Purpose Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes are essential. This paper is comparing experimental results of different interpolation methods for a segregated coupling with monolithic approaches, implemented using a global and a local nearest neighbour method. The results show the significant influence of discretisation for multiphysics simulation. Design/methodology/approach Applying disparate meshes to the monolithic as well as the segregated calculation of finite element problems and evaluating the related numerical error is content of the contribution. This is done by an experimental evaluation of a source and a material coupling applied to a multiphysics problem. After an introduction to the topic, the evaluated multiphysics model is described based on two bidirectional coupled problems and its finite element representation. Afterwards, the considered methods for approximating the coupling are introduced. Then, the evaluated methods are described and the experimental results are discussed. A summary concludes this work. Findings An experimental evaluation of the numerical errors for different multiphysics coupling methods using disparate meshes is presented based on a bidirectional electro-thermal simulation. Different methods approximating the coupling values are introduced and challenges of applying these methods are given. It is also shown, that the approximation of the coupling integrals is expensive. Arguments for applying the different methods to the monolithic and the segregated solution strategies are given and applied on the example. The significant influence of the mesh density within the coupled meshes is shown. Since the projection and the interpolation methods do influence the result, a careful decision is advised. Originality/value In this contribution, existing coupling methods are described, applied and compared on their application for coupling disparate meshes within a multiphysics simulation. Knowing their performance is relevant when deciding for a monolithic or a segregated calculation approach with respect to physics dependent contrary discretisation requirements. To the authors’ knowledge, it is the first time these methods are compared with a focus on an application in multiphysics simulations and experimental results are discussed.

Purpose The purpose of this paper is to present the design and the numerical calculation of the electromagnetic heating system for the ablation therapy. Hence, the heating of the tumor cells must be processed very carefully to achieve a localized coagulative necrosis and to avoid too high temperatures inside the tissue. Design/methodology/approach The non-invasive method of the ablation therapy is implemented due to the inductive power transmission between the generator and implant. The ferromagnetic implant has a small size and can be placed intravenously into tumor cells. High-frequency driving currents are necessary to obtain high induced eddy currents within the ferromagnetic implant. Findings Finite element analysis has been used for the design and numerical calculation of the electromagnetic heating system. The electromagnetic analysis is done in the time domain due to the nonlinearity of the ferromagnetic implant. Magnetic fields are computed based on a magnetic vector potential formulation. The thermal analysis is done in the time domain as well. The temperature computation in biological tissue is based on a heat balance equation. Research limitations/implications This paper is focused on the design and simulation of the inductive system for the ablation therapy. Practical implications The designed system can be practically implemented. It can be used for the clinical study of the immune response by the thermal ablation therapy. Originality/value The common method of thermal ablation is combined with an inductive power transmission. It enables a repetitive application of this method to study the immune response.

Purpose – The purpose of this paper is to present an accurate and efficient hybrid method for the calculation of the inductance of a coil and its inductance change due to deformed turns using numerical methods. Design/methodology/approach – The paper opted for finite element method coupled with analytical method (FCA) to accurately calculate the inductance of a coil, which is used as reference value. An algorithm with a power function is presented to approximate the partial inductance matrix with the purpose of obtaining the percentage change of the inductance due to deformed turns by using the partial element equivalent circuit (PEEC) with an approximated model and an optimization process. The presented method is successfully validated by the numerical results. Findings – The paper provides a systematic investigation of the inductance of an arbitrary shaped coil and shows how to accurately and efficiently evaluate the inductance change of a coil due to its deformed turns. It suggests that the inductance of a coil can be accurately calculated by using FCA and its percentage change due to deformed turns can be efficiently calculated by using the PEEC_Approximation. Research limitations/implications – As this research is for the magnetostatics, the skin- and proximity-effects have not been taken into account. Practical implications – The paper includes implication for the worst-case analysis of the coil’s inductance due to mechanical damage or manufacturing tolerance. Originality/value – This paper fulfills an identified need to study how the inductance change of a coil can be obtained accurately and efficiently.

For the calculation of eddy current problems using integral formulations, compression techniques are needed due to the fully populated system matrix. As the system matrix is ill-conditioned, even low compression leads to very high errors and is in most cases unsolvable with classical iterative solvers like CG or GMRES. By using regularization techniques, the condition number is enormously reduced, so that high compression rates can be achieved. In this paper the efficiency of the Block Wavelet Compression combined with the Tikhonov regularization is shown by 3-D eddy current problems. The use of the so called Block Wavelet Compression is presented for the first time for eddy current problems using integral formulations.

PurposeThe 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.Design/methodology/approachThe 3D electromagnetic fields are computed with the finite element method (FEM) and visualized with an AR display.FindingsAR 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.Research limitations/implicationsThe 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.Practical implicationsThe 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.Originality/valueWell‐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.

PurposeTo 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.Design/methodology/approachIn 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.FindingsPost‐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.Research limitations/implicationsThe presented application of the FMM is applicable only to static problems.Practical implicationsApplication 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.Originality/valueThe 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.

PurposeAims 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.Design/methodology/approachA 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.FindingsIEMs 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.Research limitations/implicationsA quasi static numerical simulation has sufficed for an understanding of the principle of the magnetic gear and for the development of a prototype.Practical implicationsIEMs 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.Originality/valueThe 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.

Boundary element methods (BEMs) are approved methods for an efficient numerical solution of problems, which are based on a Laplace equation. Here, the solution of electrostatic field problems, steady current flow field problems, and magnetostatic field problems is considered. Focus of this paper is on investigations of accuracy of direct formulations, which are based on Green's theorem. Different types of coupling of computational domains are examined with respect to accuracy and convergence behavior of iterative solvers of the linear system of equations. Furthermore, the influence of singular and nearly singular integrals and the influence of matrix compression techniques to the accuracy of the solution are observed

PurposeVarious parallelization strategies are investigated to mainly reduce the computational costs in the context of boundary element methods and a compressed system matrix.Design/methodology/approachElectrostatic 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.FindingsIt 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.Research limitations/implicationsThe 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.Practical implicationsTypical properties of general static field problems are comprised in the investigated numerical example. Hence, the results and conclusions are rather general.Originality/valueImplementation 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.

Nonlinear three-dimensional (3-D) magnetostatic field problems are solved using integral equation methods (IEM). Only the nonlinear material itself has to be discretized. This results in a system of nonlinear equations with a relative small number of unknowns. To keep computational costs low the fully dense system matrix is compressed with the fast multipole method. The accuracy of the applied indirect IEM formulation is improved significantly by the use of a difference field concept and a special treatment of singularities at edges. An improved fixed point solver is used to ensure convergence of the nonlinear problem.

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.

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.

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.

The application of the fast multipole method reduces the computational costs and the memory requirements in boundary-element method (BEM) computations from O(N/sup 2/) to approximately O(N). The computation of the near-field interactions can be done very efficiently, when all conventional BEM integrations are stored in one sparse matrix. Furthermore, we will show, how the system of linear equations can be preconditioned, when the fast multipole method is used, and how the preconditioner reduces the computational costs significantly.

This work deals with the comparison of two identification procedures of Scalar and Vector Preisach Model. The first one is to assume a Preisach function and determine the different parameters with the knowledge of the remanence and the coercivity. The second one is to measure the Everett function directly.

This paper deals with the coupling of a parallelized differential (FEM) and a parallelized integral approach (BEM) under control of a master process within the framework of a preconditioned iterative solver. Applying a domain decomposition scheme splits the problem into separate FEM and BEM parts preserving the typical advantages of both methods. Therefore an independent parallelization with respect to the special properties of both methods is possible. The limitations that arise on sequential computers when performing 3D transient analysis of nonlinear eddy current problems especially with motion can be overcome with this approach. The parallel implementations are discussed with focus on a strategy that keeps substantial parts of the parallelization separated from the numerical algorithm. The numerical modeling of an electromagnetic valve is presented as an example.

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.

A new approach to the adaptive multilevel fast multipole method in combination with higher order elements and the Galerkin method is presented. As the computational costs and the memory requirements are approximately proportional to the number of unknowns, very large static problems with complex geometrical configuration can be solved on a small computer.

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.

Die Anwendung der BEM-FEM Kopplung zur numerischen Behandlung von Abschirmproblemen wird vorgestellt. Dazu werden die Potentialgleichungen hergeleitet und ein Verfahren diskutiert, das die Erfullung der Eichbedingung sicherstellt. Ausgehend von der “schwachen Form” des Randwertproblems wird die Kopplung zwischen finiten Elementen (FEM) und Randelementen (BEM) ausfuhrlich abgeleitet. Zur iterativen Behandlung nichtlinearer Medien wird ein modifiziertes M(B)-Verfahren vorgestellt. Als Beispiel wird das TEAM Problem 21 (TestingElectromagneticAnalysisMethods) untersucht.

A new method for the evaluation of singular boundary element integrals over three-dimensional isoparametric boundary elements of higher order is presented. This new procedure represents a Gaussian quadrature technique using polar coordinates for the calculation of the Gaussian points and the weighting coefficients. This method permits an efficient integration of singular kernels of order O(1/r) on curved surfaces. For a numerical example the proposed integration scheme is compared with other methods (subdivision technique, double exponential formula method, modified Gauss-quadrature) showing high efficiency and accuracy. The actual computation can be easily included in any existing computer code.