André Buchau

Fast BEM computations with the adaptive multilevel fast multipole method

Since the storage requirements of the BEM are proportional to N/sup 2/, only relative small problems can be solved on a PC or a workstation. In this paper we present an adaptive multilevel fast multipole method for the solution of electrostatic problems with the BEM. We will show, that in practice the storage requirements and the computational costs are approximately proportional to N and therefore even large three dimensional problems can be solved on a relative small computer.

Comparison between different approaches for fast and efficient 3-D BEM computations

Fast methods like the fast multipole method or the adaptive cross approximation technique reduce the memory requirements and the computational costs of the boundary-element method (BEM) to approximately O(N). In this paper, both fast methods are applied in combination with BEM-finite-element method coupling to nonlinear magnetostatic problems.

Augmented reality in teaching of electrodynamics

Purpose – The purpose of this paper is to present an application of augmented reality (AR) in the context of teaching of electrodynamics. The AR visualization technique is applied to electromagnetic fields. Carrying out of numerical simulations as well as preparation of the AR display is shown. Presented examples demonstrate an application of this technique in teaching of electrodynamics.Design/methodology/approach – The 3D electromagnetic fields are computed with the finite element method (FEM) and visualized with an AR display.Findings – AR is a vivid method for visualization of electromagnetic fields. Students as well as experts can easily connect the characteristics of the fields with the physical object.Research limitations/implications – The focus of the presented work has been on an application of AR in a lecture room. Then, easy handling of a presentation among with low‐hardware requirements is important.Practical implications – The presented approach is based on low‐hardware requirements. Hence, ...

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.

Preconditioned fast adaptive multipole boundary-element method

The application of the fast multipole method reduces the computational costs and the memory requirements in boundary-element method (BEM) computations from O(N/sup 2/) to approximately O(N). The computation of the near-field interactions can be done very efficiently, when all conventional BEM integrations are stored in one sparse matrix. Furthermore, we will show, how the system of linear equations can be preconditioned, when the fast multipole method is used, and how the preconditioner reduces the computational costs significantly.

BEM computations using the fast multipole method in combination with higher order elements and the Galerkin method

A new approach to the adaptive multilevel fast multipole method in combination with higher order elements and the Galerkin method is presented. As the computational costs and the memory requirements are approximately proportional to the number of unknowns, very large static problems with complex geometrical configuration can be solved on a small 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

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.