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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.

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.

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.

This paper is focused on the design and simulation of the inductive system for the ablation therapy.

The designed system can be practically implemented. It can be used for the clinical study of the immune response by the thermal ablation therapy.

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.

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.

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.

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.

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.

This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications.

The novelty of the paper is the proposed formulation for the coupling of both methods.

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.

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.

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.

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.

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.

This paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

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.

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.

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.

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.

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.

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.

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.

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.

Because of the reduced calculation effort, the simulation of accurate material losses becomes reasonable. This leads to a more accurate development of magnetic devices.

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.

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 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.

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.

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.

The paper seeks to solve nonlinear magnetostatic field problems with the integral equation method and different indirect formulations.

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.

A new formulation to compute these sources is presented. The improved computational accuracy is demonstrated with numerical examples.

The paper develops a novel formulation for the computation of sources of scalar excitation potential.