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The purpose of this paper is to investigate the accuracy of different force calculation methods and their impact on mechanical deformations. For this purpose, a micrometer scaled actuator is considered, which consists of a micro‐coil and of a permanent magnet (PM) embedded in a deformable elastomeric layer.

For the magnetic field evaluation a hybrid numerical approach (finite element method/boundary element method (FEM/BEM) coupling and a FEM/BEM/Biot‐Savart approach) is used, whereas FEM is implemented for the mechanical deformation analysis. Furthermore, for the magneto‐mechanical coupling several force calculation methods, namely the Maxwell stress tensor, the virtual work approach and the equivalent magnetic sources methods, are considered and compared to each other and to laboratory measurements.

The numerically evaluated magnetic forces and the measured ones are in good accordance with each other with respect to the normal force acting on the PM. Nevertheless, depending on the used method the tangential force components differ from each other, which leads to slightly different mechanical deformations.

Since the force calculations are compared to measurement data, it is possible to give a suggestion about their applicability. The mechanical behavior of the actuator due to the acting forces is solely calculated and therefore only an assumption concerning the deformation can be given.

A new kind of micrometer scaled actuator is numerically investigated by using two different hybrid approaches for the magnetic field evaluation. Based on those, the results of several force calculation methods are compared to measurement data. Furthermore, a subsequent structural analysis is performed, which shows slightly different mechanical deformations depending on the used force calculation method.

For the spatial reconstruction of a two phase flow, as it might occur in a pipe, the main problem has always been the blurring of the resulting images.

In this paper, we present a method where blurring is implicitly avoided by the use of level sets. The level set method describes the iteratively evolving interface between different materials. The underlying field problem is solved with the boundary element method formulated in the region, where the degrees of freedom are present and the finite element method in all other regions.

Finally reconstruction results of an electrical capacitance tomography sensor are presented to show the validity of the method.

Presents a method where blurring is avoided by the use of level sets.

Electrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be demanding if the underlying numerical scheme is solely based on a domain discretization, such as in the case of the finite element method (FEM). This paper aims to present a coupling scheme based on FEM together with boundary element methods (BEMs) that neither hinges on re-meshing techniques nor deals with a special treatment of sliding interfaces. While the numerics are certainly more involved, the reward is obvious: the modeling costs decrease and the application engineer is provided with an easy-to-use, versatile and accurate simulation tool.

The authors present the implementation of a FEM-BEM coupling scheme in which the unbounded air region is handled by the BEM, while only the solid parts are discretized by the FEM. The BEM is a convenient tool to tackle unbounded exterior domains, as it is based on the discretization of boundary integral equations (BIEs) that are defined only on the surface of the computational domain. Hence, no meshing is required for the air region. Further, the BIEs fulfill the decay and radiation conditions of the electromagnetic fields such that no additional modeling errors occur.

This work presents an implementation of a FEM-BEM coupling scheme for electromagnetic field simulations. The coupling eliminates problems that are inherent to a pure FEM approach. In detail, the benefits of the FEM-BEM scheme are: the decay conditions are fulfilled exactly, no meshing of parts of the exterior air region is necessary and, most importantly, the handling of moving parts is incorporated in an intriguingly simple manner. The FEM-BEM formulation in conjunction with a state-of-the-art preconditioner demonstrates its potency. The numerical tests not only reveal an accurate convergence behavior but also prove the algorithm to be suitable for industrial applications.

The presented FEM-BEM scheme is a mathematically sound and robust implementation of a theoretical work presented a decade ago. For the application within an industrial context, the original work has been extended by higher-order schemes, periodic boundary conditions and an efficient treatment of moving parts. While not intended to be used under all circumstances, it represents a powerful tool in case that high accuracies together with simple mesh-handling facilities are required.

The boundary element method (BEM) and the finite element method (FEM) may be computationally expensive if complex problems are to be solved; thus there is the need of implementing them on fast computer architectures, especially parallel computers. Because these methods are complementary to each other, the coupling of FEM and BEM is widely used. In this paper, the coupling of displacement‐based FEM and collocation BEM and its implementation on a distributed memory system (Parsytec MultiCluster2) is described. The parallelization is performed by data partitioning which leads to a very high efficiency. As model problems, we assume linear elasticity for the boundary element method and elastoplasticity for the finite element method. The efficiency of our implementation is shown by various test examples. By numerical examples we show that a multiplicative Schwarz method for coupling BEM with FEM is very well suited for parallel implementation.

This paper aims to extend an efficient method to solve the global system of linear algebraic equations in the hybrid finite element method – boundary element method (FEM‐BEM) solution of open‐boundary skin effect problems. The extension covers the cases in which the skin effect problem is set in a truncated domain in which no homogeneous Dirichlet conditions are imposed.

The extended method is based on use of the generalized minimal residual (GMRES) solver, which is applied virtually to the reduced system of equations in which the unknowns are the nodal values of the normal derivative of the magnetic vector potential on the fictitious truncation boundary. In each step of the GMRES algorithm the FEM equations are solved by means of the standard complex conjugate gradient solver, whereas the BEM equations are not solved but used to perform fast matrix‐by‐vector multiplications. The BEM equations are written in a non‐conventional way, by making the nodes for the potential non‐coinciding with the nodes for its normal derivative.

The paper shows that the method proposed is very competitive with respect to other methods to solve open‐boundary skin effect problems.

The paper illustrates a new method to solve efficiently skin effect problems in open boundary domains by means of the hybrid FEM‐BEM method.

The purpose of this paper is to present a hybrid numerical simulation approach for the calculation of potential and electric field distribution considering charge and dielectric constant.

Each numerical method has its own advantages and disadvantages. The idea is to overcome the disadvantages of the corresponding numerical method by coupling with other numerical methods. An augmented finite element method (FEM), linear FEM and boundary element method are used with an efficient coupling.

The simulation model of microstructured devices is not so simple. During the simulation various types of problems will occur. It is found that by using several numerical methods these problems can be overcome and the calculation can be performed efficiently.

The present approach can be applied in 2D cases. But, in 3D cases the calculation of augmented FEM in a spherical coordinate becomes quite elaborate.

The proposed hybrid numerical simulation approach can be applied for the simulation of the electrostatic force microscope (EFM) which is a very high‐resolution measuring tool in nanotechnology. This approach can be applied also to other micro‐electro‐mechanical systems.

Since the scanning process of the EFM is dynamic, it requires the updating of the FEM mesh in each calculation time step. In the present paper, the mesh updating is achieved by an arbitrary Lagrangian‐Eulerian (ALE) method. The proposed numerical approach can be applied for the simulation of the EFM including this remeshing algorithm ALE.

The development of electrical machines is nowadays closely related to the knowledge of the electromagnetic fields throughout the different parts of a machine. Although a machine is often of complicated geometrical structure and of different, mostly nonlinear materials, modern numerical methods and the related software allow calculation of the fields in 2D models and several 3D cases precisely enough in order to derivate from them quantities like energy density distribution, the torque behaviour and characteristics like load and no load. The paper will at first compare numerical methods suited for electromagnetic field calculation in electrical machines. The following topic deals with adaptive mesh generation playing an important role to save computer memory and cpu time. Then examples like a Switched Reluctance Machine, an Asynchronous Machine and a Stepping Motor are shown concerning the results of field calculation. It is shown that anisotropy may have to be taken into account, and finally it is shown that field calculation enables the shape optimization of a machine.

The state space method (SSM) is good at analyzing the interfacial physical quantities in laminated materials, while it has difficulty in calculating the mechanical quantities of interior points, which can be easily evaluated by the boundary element method (BEM). However, the material has to be divided into many subdomains when the traditional BEM is applied to analyze the functionally graded material (FGM), so that the computational amount will be increased enormously. This study aims to couple these two methods to strengthen their advantages and overcome their disadvantages.

Herein, a state space BEM in which the SSM is coupled by the BEM is proposed to analyze the elasticity of FGMs, where one BEM domain is set and the others belong to SSM domains. The discretized elements occur only on the boundary of the BEM domain and at the interfaces between different SSM domains. In SSM domains, the horizontal interfaces of FGMs are discretized by linear elements and the variables along the vertical direction are yielded by the precise integration method.

The accuracy of the proposed method is verified by comparing the present results with the ones from the finite element method (FEM). It is found that the present method can provide accurate displacements and stresses in the FGMs by fewer freedom degrees in comparison with the FEM. In addition, the present method can provide continuous interfacial stresses at the interfaces between different material domains, while the interfacial stresses by the FEM are discontinuous.

The system equations of the state space BEM are built by combining the boundary integral equation with the state equations according to the continuity conditions at the interfaces. The mechanical parameters of any inner point can be evaluated by the boundary integral equation after the unknowns on the boundaries and interfaces are determined by the system equation.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The purpose of this study is the formulation of an efficient method to compute and analyse the scattering characteristics of cracks or grooves in a conducting object, where the size of the crack is significantly larger than the wavelength of an incident plane wave.

A hybrid finite element-boundary element procedure is formulated for the computation of the scattering properties of the object, where the fast multipole method is used in the boundary integral formulation. The basic fast multipole procedure is enhanced by utilising a fast Fourier transform-based convolution algorithm for the computation of the interactions between groups of source and field elements.

The algorithm accelerates the evaluation of the group interactions and enables the reduction of the memory requirements without introducing an additional approximation into the procedure.

The fast multipole method with convolution algorithm shows to be more efficient for the computation of scattering problems with a large number of unknowns than the conventional procedure.