Wolfgang Hafla

Efficient integral equation method for the solution of 3-D magnetostatic problems

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.

Parallelization of a Fast Multipole Boundary Element Method with Cluster OpenMP

Parallelization of a boundary element method for the solution of problems, which are based on a Laplace equation, is considered. The fast multipole method is applied to compress the belonging linear system of equations. The well-known parallelization standard OpenMP is used on shared memory computers and the new standard Cluster OpenMP is used on computer clusters. Both standards are based on multithreading and exploit multicore processors very efficiently. Cluster OpenMP is an enhancement of OpenMP. There, multiprocessing on a computer cluster is hidden by virtual threads, which use a virtual shared memory on a distributed memory computer.

Accuracy investigations of boundary element methods for the solution of Laplace equations

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 Greens 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

Simulation Based Development of a Valve Actuator for Alternative Drives Using BEM-FEM Code

The importance of natural gas engines is increasing due to low CO2 emissions. To optimize these engines, a direct injection valve has been developed that works with low pressure and is triggered purely electrical. The development of this valve has been supported by numerical simulations using a coupled boundary-element-method-finite-element-method (BEM-FEM) code. This paper deals with the interaction of theoretical considerations, numerical simulations, and measurements on the realized device. In order to achieve the prescribed electromagnetic forces, numerous aspects were considered. The exciting coil, the armature, and the stator geometry is of basic interest. Several concepts have been investigated. Finally, a simple but powerful concept is realized. The simulation results have been compared to measurements on the lately constructed valve.

Parallelized computation of compressed BEM matrices on multiprocessor computer clusters

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 i...

Fast and efficient 3D boundary element method for closed domains

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.

Improved grouping scheme and meshing strategies for the fast multipole method

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.

Consideration of Scalar Magnetic Hysteresis With the Integral Equation Method

Magnetic field problems can be accurately solved with the integral equation method in combination with a total scalar potential approach. However, only nonhysteretic magnetic material has been considered so far. Therefore, in this paper a novel formulation is presented that allows for the coupling of hysteresis models with the integral equation method. It has been investigated with the scalar hysteresis Product Model.

Magnetic field computation with integral equation method and energy-controlled relaxation

The magnetic field integral equation method is applied to linear and nonlinear magnetostatic problems. Two drawbacks of this method, the slow convergence rate and the dense system matrix, are tackled. The convergence behavior is improved by a novel algorithm that determines adaptive relaxation factors at every iteration step by an energy minimum principle. The dense matrix is compressed with the fast multipole method

Accuracy improvement in nonlinear magnetostatic field computations with integral equation methods and indirect total scalar potential formulations

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.