Fake Conductivity or Cohomology: Which to Use When Solving Eddy Current Problems With $h$ -Formulations?

Dłotko, Paweł; Kapidani, Bernard; Pitassi, Silvano; Specogna, Ruben

doi:10.1109/tmag.2019.2906099

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Since the quasi-static approximation is only valid at low frequencies, these solvers are particularly ill-suited for electrically large conductors [9], [10]. In addition, the simulation of multiply connected geometries usually requires further preprocessing such as the introduction of cutting surfaces or structural loops detection to guarantee the uniqueness of the solution [11], [12].…”

Section: Imentioning

confidence: 99%

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Chhim

Merlini

Rahmouni

et al. 2020

IEEE Open J. Antennas Propag.

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Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell's equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full-wave solvers such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation become highly ill-conditioned and inaccurate in eddy current settings. This work presents a new well-conditioned and stable full-wave formulation which encompasses the simulation of eddy currents. Our method is built upon the PMCHWT equation and thus remains valid over the entire frequency range. Moreover, our scheme is also compatible with structures containing holes and handles (multiply connected geometries). The effectiveness of quasi-Helmholtz projectors is leveraged to obtain a versatile solver, which is computationally efficient and allows for a seamless transition between low and high frequencies. The stability and accuracy of the new method are demonstrated both theoretically and through numerical experiments on canonical and realistic structures.

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Section: Imentioning

confidence: 99%

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Chhim

Merlini

Rahmouni

et al. 2020

IEEE Open J. Antennas Propag.

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“…First, in the full h-formulation, the magnetic field is discretized with edge functions on the whole domain, and a spurious resistivity ρ s is introduced in Ω C c [1]. Despite leading to more unknowns and ill-conditioned matrices [7], this approach is still popular in proprietary softwares, e.g., COMSOL.…”

Section: A Standard H-conform Formulationsmentioning

confidence: 99%

What Formulation Should One Choose for Modeling a 3-D HTS Motor Pole With Ferromagnetic Materials?

Dular¹,

Berger

Geuzaine³

et al. 2022

IEEE Trans. Magn.

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We discuss the relevance of several finite-element formulations for nonlinear systems containing high-temperature superconductors (HTS) and ferromagnetic materials (FM), in the context of a 3D motor pole model. The formulations are evaluated in terms of their numerical robustness and efficiency. We propose a coupled h-φ-a-formulation as an optimal choice, modeling the problem with an a-formulation in the FM and an h-φ-formulation in the remaining domains. While maintaining a low number of degrees of freedom, the h-φ-a-formulation guarantees a robust resolution and strongly reduces the number of iterations required for handling the nonlinearities of HTS and FM compared to standard formulations.

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“…For example, in [20], two different methods are compared: adding a thin conducting layer in the air domains and imposing a discontinuity in φ along a "thin cut" equal to the current inside the conductor. More recently, the use of edge-based cohomology basis functions or "thick cuts" was shown to efficiently make multiply connected domains simply connected [12], [13], [21]- [23]. Although this last method is very promising, a home-brewed or open-source FEM software must be programmed or utilized in order to generate the thick cuts.…”

Section: Introductionmentioning

confidence: 99%

COMSOL implementation of the H-$ϕ$-formulation with thin cuts for modeling superconductors with transport currents

Arsenault,

Alves,

Sirois

2021

Preprint

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Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite element method, the use of vector-dependent variables in non-conducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the non-conducting domains must be made simply connected in order to obey Ampere's law. In this work, we use thin cuts to apply a discontinuity in φ and make the non-conducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite element program, already widely used by the applied superconductivity community. We simulate three different models in 2-D and 3-D using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H-φ-formulation can be up to seven times faster than the standard H-formulation in certain applications of interest.

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Fake Conductivity or Cohomology: Which to Use When Solving Eddy Current Problems With $h$ -Formulations?

Cited by 4 publications

References 11 publications

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

Eddy Current Modeling in Multiply Connected Regions via a Full-Wave Solver Based on the Quasi-Helmholtz Projectors

What Formulation Should One Choose for Modeling a 3-D HTS Motor Pole With Ferromagnetic Materials?

COMSOL implementation of the H-$ϕ$-formulation with thin cuts for modeling superconductors with transport currents

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