Matthias Jüttner, Andreas Pflug, Markus Wick and Wolfgang M. Rucker
Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes are…
Abstract
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.
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Markus Wick, Matthias Jüttner and Wolfgang M. Rucker
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…
Abstract
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.
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André Buchau, Wolfgang Hafla and Wolfgang M. Rucker
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…
Abstract
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.
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Wolfgang Hafla, André Buchau, Wolfgang M. Rucker, Andreas Weinläder and Antoni Bardakcioglu
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
The presented application of the FMM is applicable only to static problems.
Practical implications
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.
Originality/value
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.
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André Buchau, Wolfgang Rieger and Wolfgang M. Rucker
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…
Abstract
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.
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Friedemann Groh, Wolfgang Hafla, André Buchau and Wolfgang M. Rucker
Magnetostatic problems including iron components can be solved by a nonlinear indirect volume integral equation. Its unknowns are scalar field sources. They are evaluated…
Abstract
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.
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Wolfgang Hafla, André Buchau, Wolfgang M. Rucker, Andreas Weinläder and Benjamin Klotz
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.
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
A quasi static numerical simulation has sufficed for an understanding of the principle of the magnetic gear and for the development of a prototype.
Practical implications
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.
Originality/value
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.
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Wolfgang Hafla, André Buchau and Wolfgang M. Rucker
The paper seeks to solve nonlinear magnetostatic field problems with the integral equation method and different indirect formulations.
Abstract
Purpose
The paper seeks to solve nonlinear magnetostatic field problems with the integral equation method and different indirect formulations.
Design/methodology/approach
To avoid large cancellation errors in cases where the demagnetizing field is high a difference field concept is used. This requires the computation of sources of the scalar potential of the excitation field.
Findings
A new formulation to compute these sources is presented. The improved computational accuracy is demonstrated with numerical examples.
Originality/value
The paper develops a novel formulation for the computation of sources of scalar excitation potential.
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André Buchau, Wolfgang Hafla, Friedemann Groh and Wolfgang M. Rucker
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…
Abstract
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.
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André Buchau, Wolfgang Hafla, Friedemann Groh and Wolfgang M. Rucker
Various parallelization strategies are investigated to mainly reduce the computational costs in the context of boundary element methods and a compressed system matrix.
Abstract
Purpose
Various parallelization strategies are investigated to mainly reduce the computational costs in the context of boundary element methods and a compressed system matrix.
Design/methodology/approach
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.
Findings
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.
Research limitations/implications
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.
Practical implications
Typical properties of general static field problems are comprised in the investigated numerical example. Hence, the results and conclusions are rather general.
Originality/value
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.