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1 – 10 of 14Thorsten Steinmetz, Stefan Kurz and Markus Clemens
The paper aims at proposing a uniform and demonstrative description of two well‐known and widely used approximations of slowly time‐varying electromagnetic fields, i.e. the…
Abstract
Purpose
The paper aims at proposing a uniform and demonstrative description of two well‐known and widely used approximations of slowly time‐varying electromagnetic fields, i.e. the electro‐quasistatic and the magneto‐quasistationary approximation to Maxwell's equations.
Design/methodology/approach
Under both approximations, the orders of magnitude of the relative errors of the dominant fields are analyzed by using three characteristic time constants. These time constants are determined by considering the material properties, the characteristic length scale and the characteristic time scale.
Findings
Limiting curves which show the domains of applicability of the two approximations are retrieved from the estimation of their relative errors. The relation between the domains of validity of the electro‐quasistatic and magneto‐quasistationary approximations was found and depicted in a combined diagram.
Research limitations/implications
The study is restricted to slowly time‐varying electromagnetic fields. Heuristic and local estimates based on local material properties were used for the analysis. Rigorous estimations of the errors (e.g. also considering the field problem's topology) of the magneto‐quasistationary approximation are already known in the literature. A rigorous estimation of the error of the electro‐quasistatic approximation is, therefore, suggested for future research.
Originality/value
The combined diagram showing the domains of validity of both approximations considered here in a uniform way is novel. It gives rise to an intuitive and easily accessible understanding of their applicability.
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Fotios Kasolis and Markus Clemens
This paper aims to develop an automated domain decomposition strategy that is based on the presence of nonlinear field grading material, in the context of model order reduction…
Abstract
Purpose
This paper aims to develop an automated domain decomposition strategy that is based on the presence of nonlinear field grading material, in the context of model order reduction for transient strongly nonlinear electro-quasistatic (EQS) field problems.
Design/methodology/approach
The paper provides convincing empirical insights to support the proposed domain decomposition algorithm, a numerical investigation of the performance of the algorithm for different snapshots and model order reduction experiments.
Findings
The proposed method successfully decomposes the computational domain, while the resulting reduced models are highly accurate. Further, the algorithm is computationally efficient and robust, while it can be embedded in black-box model reduction implementations.
Originality/value
This paper fulfills the demand to effectively perform model order reduction for transient strongly nonlinear EQS field problems.
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Sebastian Böhmelt, Nils Kielian, Michael Hagel, Marcus Stiemer, Marvin-Lucas Henkel and Markus Clemens
The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in…
Abstract
Purpose
The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in biology. The numerical scheme is analyzed and first applications are discussed.
Design/methodology/approach
The scheme is based on a finite element discretization of the individual domains obtained by decomposition and a physically consistent inter-domain coupling realized via Robin boundary conditions. The proposed algorithms can efficiently be implemented on a highly parallelized computing grid.
Findings
The feasibility and applicability of the method is proven. Further, a couple of technical details are found that increase the efficiency of the method.
Originality/value
The presented method offers an enhanced geometrical flexibility and extensibility to simulate larger cell systems with higher model resolution compared to other methods presented in the literature. The presented analysis provides an understanding of the balanced coupling scheme for large EQS systems.
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Giovanni Miano, Fabio Villone and Walter Zamboni
To study optical resonances in metallic nanoparticles.
Abstract
Purpose
To study optical resonances in metallic nanoparticles.
Design/methodology/approach
The metallic nanoparticle is modeled as a dielectric body dispersive in frequency with assigned dielectric constant. The electric field is expressed as function of the charge distribution through an integral formulation. By imposing the boundary conditions on the nanoparticle surface, the equations for the induced charge in the nanoparticle is obtained. The numerical solution of such equations allows to treat arbitrary geometries and to estimate the effects of deviations from ideality on the resonance values.
Findings
Plasmon resonances in metallic nanoparticles can be safely studied with an electro‐quasistatic approximation. The resonance frequencies depend greatly on the details of the geometry of the nanoparticles.
Research limitations/implications
The free‐space wavelength is supposed to be much greater than the largest characteristic dimension of the nanoparticles. Consequently, a electro‐quasistatic model is used to evaluate the distribution of the charges induced in the metallic nanoparticle.
Originality/value
Two methods are presented for the evaluation of the resonance frequencies starting from the numerical solution for a given geometry.
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Daniel Weida, Thorsten Steinmetz and Markus Clemens
The purpose of this paper is to analyze the accuracy of finite element method simulations for high voltage equipment featuring resistive field grading.
Abstract
Purpose
The purpose of this paper is to analyze the accuracy of finite element method simulations for high voltage equipment featuring resistive field grading.
Design/methodology/approach
In such simulations, the order of the mesh used and the polynomial order of the ansatz functions are varied while maintaining mesh and simulation parameters. The resulting accuracy of the simulations is analyzed by an error convergence study which shows the relative errors against the number of degrees of freedom the computational time and the memory consumption.
Findings
Simulation results of simplified benchmark geometry and applications to large‐scale 3D high voltage equipment are presented herein.
Originality/value
The impact of the order of the mesh and the Ansatz functions are studied for realistic high voltage setups. The paper helps the user of simulation software to choose adequate simulation parameters.
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Hendrik Hensel and Markus Clemens
Gas insulated systems, such as gas insulated lines (GIL), use insulating gas, mostly sulfur hexalfluoride (SF6), to enable a higher dielectric strength compared to e.g. air…
Abstract
Purpose
Gas insulated systems, such as gas insulated lines (GIL), use insulating gas, mostly sulfur hexalfluoride (SF6), to enable a higher dielectric strength compared to e.g. air. However, under high voltage direct current conditions, charge accumulation and electric field stress may occur, which may lead to partial discharge or system failure. Therefore, numerical simulations are used to design the system and determine the electric field and charge distribution. Although the gas conduction shows a more complex current–voltage characteristic compared to solid insulation, the electric conductivity of the SF6 gas is set as constant in most works. The purpose of this study is to investigate different approaches to address the conduction in the gas properly for numerical simulations.
Design/methodology/approach
In this work, two approaches are investigated to address the conduction in the insulating gas and are compared to each other. One method is an ion-drift-diffusion model, where the conduction in the gas is described by the ion motion in the SF6 gas. However, this method is computationally expensive. Alternatively, a less complex approach is an electro-thermal model with the application of an electric conductivity model for the SF6 gas. Measurements show that the electric conductivity in the SF6 gas has a nonlinear dependency on temperature, electric field and gas pressure. From these measurements, an electric conductivity model was developed. Both methods are compared by simulation results, where different parameters and conditions are considered, to investigate the potential of the electric conductivity model as a computationally less expensive alternative.
Findings
The simulation results of both simulation approaches show similar results, proving the electric conductivity for the SF6 gas as a valid alternative. Using the electro-thermal model approach with the application of the electric conductivity model enables a solution time up to six times faster compared to the ion-drift-diffusion model. The application of the model allows to examine the influence of different parameters such as temperature and gas pressure on the electric field distribution in the GIL, whereas the ion-drift-diffusion model enables to investigate the distribution of homo- and heteropolar charges in the insulation gas.
Originality/value
This work presents numerical simulation models for high voltage direct current GIL, where the conduction in the SF6 gas is described more precisely compared to a definition of a constant electric conductivity value for the insulation gas. The electric conductivity model for the SF6 gas allows for consideration of the current–voltage characteristics of the gas, is computationally less expensive compared to an ion-drift diffusion model and needs considerably less solution time.
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Keywords
Andreas Barchanski, Markus Clemens, Herbert De Gersem, Till Steiner and Thomas Weiland
Improved numerical calculation techniques for low‐frequency current density distributions within high‐resolution anatomy models caused by ambient electric or magnetic fields or…
Abstract
Purpose
Improved numerical calculation techniques for low‐frequency current density distributions within high‐resolution anatomy models caused by ambient electric or magnetic fields or direct contact to potential drops using the finite integration technique (FIT).
Design/methodology/approach
The methodology of calculating low‐frequency electromagnetic fields within high‐resolution anatomy models using the FIT is extended by a local grid refinement scheme using a non‐matching‐grid formulation domain. Furthermore, distributed computing techniques are presented. Several numerical examples are analyzed using these techniques.
Findings
Numerical simulations of low‐frequency current density distributions may now be performed with a higher accuracy due to an increased local grid resolution in the areas of interest in the human body voxel models when using the presented techniques.
Originality/value
The local subgridding approach is introduced to reduce the number of unknowns in the very large‐scale linear algebraic systems of equations that have to be solved and thus to reduce the required computational time and memory resources. The use of distributed computation techniques such as, e.g. the use of a parallel solver package as PETSc follows the same goals.
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Yuqing Xie, Lin Li and Shuaibing Wang
To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal…
Abstract
Purpose
To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal decomposition (POD) and centroidal Voronoi tessellation (CVT) have been used to solve many engineering problems. The purpose of this paper is to investigate the computational principle, accuracy and efficiency of the POD-based and the CVT-based reduced-order method when dealing with quasi-magnetostatic problems.
Design/methodology/approach
The paper investigates computational features of the reduced-order method based on POD and CVT methods for quasi-magnetostatic problems. Firstly the construction method for the POD and the CVT reduced-order basis is introduced. Then, a reduced model is constructed using high-fidelity finite element solutions and a Galerkin projection. Finally, the transient quasi-magnetostatic problem of the TEAM 21a model is studied with the proposed reduced-order method.
Findings
For the TEAM 21a model, the numerical results show that both POD-based and CVT-based reduced-order approaches can greatly reduce the computational time compared with the full-order finite element method. And the results obtained from both reduced-order models are in good agreement with the results obtained from the full-order model, while the computational accuracy of the POD-based reduced-order model is a little higher than the CVT-based reduced-order model.
Originality/value
The CVT method is introduced to construct the reduced-order model for a quasi-magnetostatic problem. The computational accuracy and efficiency of the presented approaches are compared.
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Mariana Ion, Herbert De Gersem, Markus Wilke and Thomas Weiland
To propose trigonometric interpolation in combination with the sliding‐surface technique for modeling rotation in electrical machine models discretised by the finite integration…
Abstract
Purpose
To propose trigonometric interpolation in combination with the sliding‐surface technique for modeling rotation in electrical machine models discretised by the finite integration technique (FIT).
Design/methodology/approach
Locked‐step, linear and trigonometric interpolation techniques are developed for coupling the stator and rotor model parts of an electrical machine model.
Findings
Linear and trigonometric interpolation should be preferred over the locked‐step approach. Three‐machine models with sliding‐surface coupling discretised by the FIT result in efficient and reliable models.
Originality/value
The introduction of sliding‐surface techniques in the FIT, the trigonometric interpolation used in combination, the application of the FIT for simulating electrical machines.
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Galina Benderskaya, Herbert De Gersem, Wolfgang Ackermann and Thomas Weiland
To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.
Abstract
Purpose
To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.
Design/methodology/approach
The numerical integration of an electrotechnical problem is commonly carried out using adaptive time stepping. For one particular selected time step, Runge‐Kutta (RK) adaptive integration methods deliver two approximations to the solution with different order of approximation. The difference between both is used to estimate the local error.
Findings
Standard error‐controlled RK time integration fails for electromagnetic problems with sinusoidal excitation when the adaptive time step selection relies upon the comparison of a main solution and an embedded solution where the difference of orders is one. This problem is overcome when the embedded solution differs by two orders of approximations. Such embedded solution is efficiently constructed by putting appropriate order conditions on the coefficients of the Butcher table.
Originality/value
Using the technique proposed in the paper, electromagnetic problems with sinusoidal dynamics can also be effectively tackled.
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