T-Ω formulation with higher order hierarchical basis functions for non simply connected conductors

Abstract

This paper presents in detail the extension of the -Ω formulation for eddy currents based on higher-order hierarchical basis functions so that it can automatically deal with conductors of arbitrary topology. To this aim, we supplement the classical hierarchical basis functions with nonlocal basis functions spanning the first de Rham cohomology group of the insulating region. Such nonlocal basis functions may be efficiently and automatically found in negligible time with the recently introduced Dłotko-Specogna (DS) algorithm. The approach presented in this paper merges techniques together which to some extent already existed in literature but they were never grouped together and tested as a single unit.

Lean Cohomology Computation for Electromagnetic Modeling

“…For eddy current formulations based on the magnetic scalar potential in K a , a set of representatives that span the first cohomology basis [1] of K a , denoted as H 1 (K a ), are required, see for example [2]- [4]. The recent attempts to efficiently solve eddy-current problems based on this formulation have allowed the computational topology [1] in general, and computational cohomology in particular, to made its way into commercial [5], [6] and research [7], [8] electromagnetic simulation software.…”

“…The author of [3] never proved or claimed that the algorithm produces a cohomology basis as output. Moreover, how the algorithm is documented inside [3] does not enable to solve the issues raised in [6].…”