Since the storage requirements of the BEM are proportional to 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 and therefore even large three dimensional problems can be solved on a relative small computer.Index Terms-Boundary element methods, fast multipole method, iterative methods, Laplace equations.

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PurposeThe 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/approachThe 3D electromagnetic fields are computed with the finite element method (FEM) and visualized with an AR display.FindingsAR 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/implicationsThe 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 implicationsThe presented approach is based on low‐hardware requirements. Hence, a presentation of electromagnetic fields with AR in a lecture room can be easily done. AR helps students to understand electromagnetic field theory.Originality/valueWell‐known methods like FEM and AR have been combined to develop a visualization technique for electromagnetic fields, which can be easily applied in a lecture room.

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A meshfree postprocessing for the computation of field lines suggests itself in the case of fast boundary element methods. Field values are only calculated and stored in points, which are absolutely necessary for field line computations. Hence, the total amount of processed data is dramatically reduced in comparison to a mesh-based approach along with precomputed field values in all mesh nodes. An automatic and robust domain detection method enables reliable identifications of intersections of field lines with domain boundaries even in the case of complex-shaped surfaces. A combination of automatic domain detection and adaptive step size control of the underlying Runge-Kutta-Fehlberg method results in correctly and efficiently computed field lines, including sharp bends at domain boundaries.Index Terms-Boundary element methods (BEMs), field line computation, meshfree postprocessing, multiple domains.