A sequential coupling of optimal topology and multilevel shape design applied to two-dimensional nonlinear magnetostatics

Lukáš, Dalibor; Chalmovianský, Pavel

doi:10.1007/s00791-006-0038-5

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…Thus, the fact that arctan is a non-convex function is not relevant. However, there are other convex penalization functions that was used and tested in (Bendsøe and Sigmund, 2003;Sanogo et al, 2014;Sanogo, 2016;Sanogo and Messine, 2018;Luk aš and Chalmovianský, 2007). But the numerical tests showed that the choice of a convex penalization function appears to be not necessary.…”

Section: Solid Isotropic Materials With Penalization Methods Penalization Methodsmentioning

confidence: 99%

“…The degree of penalization n (Section 3) is set to 100 as in (Luk aš and Chalmovianský, 2007); this seems to be good enough for our application. In order to ensure the convergence toward a solution that provides the desired magnetic field (a solution that respects the constraint), we choose the interior point algorithm of fmincon.…”

Section: Hall Effect Thrustermentioning

confidence: 99%

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Adjoint-based topology optimization to reduce the energy consumption of a Hall effect thruster

Rtimi

Messine

2020

COMPEL

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Purpose The presented study aims to minimize the energy consumed by a Hall effect thruster (HET) under a constraint which makes it possible to generate a specified magnetic field in a target region of the thruster. Design/methodology/approach Herein topology optimization (TO) is used to reduce the energy consumption of an HET while keeping its performance unchanged. The design variables are the current densities in the coils and the distribution of materials in the polar pieces of the thruster. Intermediate values of material distribution are penalized using the solid isotropic material with penalization method to favor binary solutions. By means of the adjoint method, this paper provides the derivatives of the objective and constraint functions with respect to material distribution and current density variables. Findings The TO-based design methodology is developed and validated on a design example involving 2,051 variables. The approach shows its interest and its effectiveness of on a large scale two-criteria problem. Research limitations/implications In this paper, TO is presented as a tool that has allowed to explore new and innovative designs. However, although the design presented is original, its fabrication is not feasible. Despite this, the designs found give a good idea of the starting points for shape and parametric optimization tools. Practical implications Through the HET design problem, TO shows the ability to explore more original design possibilities of a complex magnetostatic design problem and to discover designs that make a HET more efficient with respect to several criteria at the same time. Originality/value A new way to reduce the energy consumption of a HET is presented. To achieve this, an adjoint-based TO method is developed and then implemented in a simple way. This approach shows that, for efficiency purposes, TO is a key tool for extending the state of the art of HET designs.

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Section: Solid Isotropic Materials With Penalization Methods Penalization Methodsmentioning

confidence: 99%

Section: Hall Effect Thrustermentioning

confidence: 99%

Adjoint-based topology optimization to reduce the energy consumption of a Hall effect thruster

Rtimi

Messine

2020

COMPEL

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“…8) before applying the TLM method, we can obtain an ideal guess of Y 0 but with less time consumption. Assuming μ guess is the result from the Newton method, we substitute it into (11) and get all items of matrix C e which can be used to set the value of corresponding TL's admittance.…”

Section: Speed Up Strategiesmentioning

confidence: 99%

Nonlinear Axisymmetric Magnetostatic Analysis for Electromagnetic Device Using TLM-Based Finite-Element Method

2017

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Finite-element method (FEM) has been widely used in industrial applications for many years. With the increase of finite-element model complexity and the number of elements, computation burden has become a serious issue and requires more attention. In this paper, the transmission line method (TLM) is adopted to the solution of FEM-based nonlinear axisymmetric magnetostatic problem and an equivalent finite-element network's circuit model is given. Several methods were investigated to speed up the computation, such as Newton preconditioners, simplification of nonlinear equation solution and parallel computation. Compared with traditional Newton FEM iteration, our results show that the proposed method has more obvious advantages on computational efficiency at the same calculation accuracy. The method is applicable and valuable in the characteristic analysis and design of the magnetic device with a cylindrical structure.

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A shape optimization method for nonlinear axisymmetric magnetostatics using a coupling of finite and boundary elements

Lukáš

Postava

Životský

2012

Mathematics and Computers in Simulation

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A sequential coupling of optimal topology and multilevel shape design applied to two-dimensional nonlinear magnetostatics

Cited by 4 publications

References 18 publications

Adjoint-based topology optimization to reduce the energy consumption of a Hall effect thruster

Adjoint-based topology optimization to reduce the energy consumption of a Hall effect thruster

Nonlinear Axisymmetric Magnetostatic Analysis for Electromagnetic Device Using TLM-Based Finite-Element Method

A shape optimization method for nonlinear axisymmetric magnetostatics using a coupling of finite and boundary elements

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