No abstract

No abstract

No abstract

Solving eddy current problems formulated by using a magnetic scalar potential in the insulator requires a topological pre-processing to find the so called first cohomology basis of the insulating region, which may result being very time consuming for challenging industrially driven problems. The physics-inspired Dłotko-Specogna (DS) algorithm was shown to be superior to alternatives in performing such a topological pre-processing. Yet, the DS algorithm is particularly fast when it produces as output not a regular cohomology basis but a so called lazy one, which contains the regular one but it keeps also some additional redundant elements. Having a regular basis may be advantageous over the lazy basis if a technique to produce it would take about the same time as the computation of a lazy basis. In literature such a technique is missing. This paper covers this gap by introducing modifications to the DS algorithm to compute a regular basis of the first cohomology group in practically the same time as the generation of a lazy cohomology basis. The speedup of this modified DS algorithm with respect to the best alternative reaches more than two orders of magnitudes on challenging benchmark problems. This demonstrates the potential impact of the proposed contribution in the low-frequency computational electromagnetics community and beyond.

When solving eddy-current problems containing topologically non-trivial conductors with formulations using the magnetic scalar potential in the insulators, cohomology is recognized to be the only safe tool to obtain a well posed problem. This paper presents an efficient implementation of the recently introduced DS algorithm to compute the first lazy cohomology group generators of a tetrahedral mesh. The code will be available for download on request for non-profit use. Secondly, for the first time, the computational time required by the proposed toolbox for the topological pre-processing is compared with another freely available alternative on the same input mes