Topoprocessor: An efficient computational topology toolbox for h-oriented eddy current formulations

Abstract

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

Lean Cohomology Computation for Electromagnetic Modeling

“…The algorithm presented in this paper is implemented as a part of the TOPOPROCESSOR C++ package [7]. To show how the lean DS algorithm enhancement in TOPOPROCESSOR further advocates for the use of the package, we perform the topological preprocessing required by the h-oriented eddy current formulations in the three industrial test cases already used in [7]. The reader is invited to consult [7] for the pictures of the benrchmarks given that there is no space to represent them here.…”

“…To show how the lean DS algorithm enhancement in TOPOPROCESSOR further advocates for the use of the package, we perform the topological preprocessing required by the h-oriented eddy current formulations in the three industrial test cases already used in [7]. The reader is invited to consult [7] for the pictures of the benrchmarks given that there is no space to represent them here. The performance of the lean DS algorithm is compared with the one of an output equivalent tool provided in GMSH [8], which is an efficient implementation of the standard paradigm based on reducing the complex and computing the Smith Normal Form (SNF) of the reduced matrix.…”

“…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 DS algorithm has been proved to be superior to all the competing approaches to perform the required topological preprocessing in terms of speed and memory consumption (see [7]), while keeping the full generality. The output provided by the fastest version of the DS algorithm consists of lazy generators which span the H 1 (K a ) space, but are not linearly independent.…”

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

“…To achieve good overall performances, it is mandatory to address this topological pre-processing efficiently. With classical algebraic methods like [8] based on reduction of the complex K a followed by a Smith Normal Form (SNF) computation on the reduced complex, finding such non-local basis functions easily becomes the bottleneck of the whole simulation, see [11]. This is the main reason why such rigorous methods to solve this issue did not take off in electromagnetic solvers.…”