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Efficient Cohomology Computation for Electromagnetic Modeling

Paweł Dłotko1, Ruben Specogna2
Jagiellonian University, Institute of Computer Science, Łojasiewicza 6, 30348 Kraków, Poland, dlotko@ii.uj.edu.pl.
Università di Udine, Dipartimento di Ingegegneria Elettrica, Gestionale e Meccanica (DIEGM), via delle Scienze 208, 33100 Udine, Italy, ruben.specogna@uniud.it.

Computer Modeling in Engineering & Sciences 2010, 60(3), 247-278. https://doi.org/10.3970/cmes.2010.060.247

Abstract

The systematic potential design is of high importance in computational electromagnetics. For example, it is well known that when the efficient eddy-current formulations based on a magnetic scalar potential are employed in problems which involve conductive regions with holes, the so-calledthick cutsare needed to make the boundary value problem well defined. Therefore, a considerable effort has been invested over the past twenty-five years to develop fast and general algorithms to compute thick cuts automatically. Nevertheless, none of the approaches proposed in literature meet all the requirements of being automatic, computationally efficient and general. In this paper, an automatic, computationally efficient and provably general algorithm is presented. It is based on a rigorous algorithm to compute a cohomology basis of the insulating region with state-of-art reductions techniques-the acyclic sub-complex technique, among others-expressly designed for cohomology computations over simplicial complexes. Its effectiveness is demonstrated by presenting a number of practical benchmarks. The automatic nature of the proposed approach together with its low computational time enable the routinely use of cohomology computations in computational electromagnetics.

Keywords

Cell Method (CM), Finite Integration Technique (FIT), Finite Element Method (FEM), eddy-currents, potential design, thick cuts, computational cohomology, reduction methods, acyclic sub-complex technique.

Cite This Article

Dłotko, P., Specogna, R. (2010). Efficient Cohomology Computation for Electromagnetic Modeling. CMES-Computer Modeling in Engineering & Sciences, 60(3), 247–278.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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