A fast finite-difference algorithm for topology optimization of permanent magnets

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

doi:10.1063/1.4998532

Cited by 19 publications

(16 citation statements)

References 22 publications

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“…The presented method is based on a highly efficient hybrid finite element–boundary element method (FEM–BEM) approach 7 solving the magnetostatic Maxwell’s problem. In contrast to already presented finite element 3 , 8 and finite differences 9 algorithms using a FEM–BEM approach has the advantage that only the regions of interest need to be discretized reducing the dofs dramatically. Furthermore, in order to efficiently calculate gradients during optimization, the adjoint approach is utilized.…”

Section: Introductionmentioning

confidence: 99%

A topology optimization algorithm for magnetic structures based on a hybrid FEM–BEM method utilizing the adjoint approach

Wautischer

Abert

Bruckner

et al. 2022

Sci Rep

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A method to optimize the topology of hard as well as soft magnetic structures is implemented using the density approach for topology optimization. The stray field computation is performed by a hybrid finite element–boundary element method. Utilizing the adjoint approach the gradients necessary to perform the optimization can be calculated very efficiently. We derive the gradients using a “first optimize then discretize” scheme. Within this scheme, the stray field operator is self-adjoint allowing to solve the adjoint equation by the same means as the stray field calculation. The capabilities of the method are showcased by optimizing the topology of hard as well as soft magnetic thin film structures and the results are verified by comparison with an analytical solution.

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Section: Introductionmentioning

confidence: 99%

A topology optimization algorithm for magnetic structures based on a hybrid FEM–BEM method utilizing the adjoint approach

Wautischer

Abert

Bruckner

et al. 2022

Sci Rep

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“…Such a possibility will be discussed in future work. It is also worth mentioning that additive manufacturing [17,40,41] might be a very convenient route for manufacturing permanent-magnet blocks with curved boundaries. Knowledge of the optimal solution is not only interesting from a theoretical point of view but is also a useful resource for the purpose of producing an efficient design, especially as the optimal solution for a chosen external boundary can be determined with our method.…”

Section: A Underlying Assumptions and Optimization Objectivementioning

confidence: 99%

“…With both frameworks, the shape of the resulting uniformly magnetized blocks is not limited to some parameterized geometrical configurations. Moreover, since the field computation can be performed with numerical methods (typically finite-element methods [18,21,22], or the finite-difference method [17]), both approaches can be used with arbitrary geometries, even when the analytical expression of the field distribution is not known. One of the difficulties of topology-optimization approaches is that the resulting shapes might be characterized by irregular or jagged boundaries.…”

Section: Comparison With Topology Optimizationmentioning

confidence: 99%

“…While our optimization approach is based on analytically proved optimality conditions, the implementation discussed here relies on numerical methods. For this reason, this technique has some similarities with topologyoptimization algorithms [17][18][19][20][21][22][23]. There are no intrinsic limitations to the variety of geometries that can be optimized with the method presented here.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Segmentation of Three-Dimensional Permanent-Magnet Assemblies

Insinga¹,

Smith²,

Bahl³

et al. 2019

Phys. Rev. Applied

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The optimal segmentation of three-dimensional permanent-magnet systems into uniformly magnetized blocks to generate a desired field is a question that has been studied extensively in recent years. We present a procedure that generates the theoretically optimal shape and magnetization direction of all the magnet segments in the system, given only the total number of blocks as a constraint. Materials of arbitrary magnetic permeability can be included in this optimization framework. As an optimization objective we consider any functional that is linear with respect to the magnetic field distribution. We furthermore assume that all magnetic materials obey a linear constitutive relation. We show that with these assumptions calculating an optimal three-dimensional segmentation is equivalent to determining a centroidal Voronoi tessellation. We use the most-well-known and most-straightforward algorithm for the generation of centroidal Voronoi tessellations, known as "Lloyd's method," which can also be thought of as a fixed-point iteration. We show that the procedure is guaranteed to lead to a configuration that is at least locally optimal with respect to the assumed linear objective functional. However, we present results providing a strong indication that for most design problems applying our technique a few times starting from different random configurations is very likely to lead to the globally optimal solution.

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“…In order to reach fields with certain properties, either the shape of the field source or the magnetization distribution within the field generating magnet [3] or both can be optimized. For shape optimization, on/off methods [4,5], in which space points are either magnetic or non-magnetic, or parameterized geometries [6] have been used. Inverse problems, in which the optimal distribution of the magnetization is to be found, are efficiently solved with the adjoint method [7].…”

Section: Introductionmentioning

confidence: 99%

Magnetostatics and micromagnetics with physics informed neural networks

Kovacs,

Exl,

Kornell

et al. 2021

Preprint

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Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at collocation points or the magnetostatic energy, the weights of the neural network are adjusted so that the neural network solution approximates the magnetic vector potential. This way, the magnetic flux density for a given magnetization distribution can be estimated. With the magnetization as an additional unknown, inverse magnetostatic problems can be solved. Augmenting the magnetostatic energy with additional energy terms, micromagnetic problems can be solved. We demonstrate the use of physics informed neural networks for solving magnetostatic problems, computing the magnetization for inverse problems, and calculating the demagnetization curves for two-dimensional geometries.

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A fast finite-difference algorithm for topology optimization of permanent magnets

Cited by 19 publications

References 22 publications

A topology optimization algorithm for magnetic structures based on a hybrid FEM–BEM method utilizing the adjoint approach

A topology optimization algorithm for magnetic structures based on a hybrid FEM–BEM method utilizing the adjoint approach

Optimal Segmentation of Three-Dimensional Permanent-Magnet Assemblies

Magnetostatics and micromagnetics with physics informed neural networks

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