Efficient post‐processing with the integral equation method

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

The presented application of the FMM is applicable only to static problems.

Practical implications

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.

Originality/value

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.

Citation

Hafla, W., Buchau, A., Rucker, W.M., Weinläder, A. and Bardakcioglu, A. (2007), "Efficient post‐processing with the integral equation method", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 3, pp. 873-887. https://doi.org/10.1108/03321640710751280