Numerical optimization of an electrostatic device based on the 3D XFEM and genetic algorithm

Avram, Alexandru; Ţopa, Vasile; Purcar, Marius; Munteanu, Călin

doi:10.1109/upec.2014.6934757

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…20 More recent studies have concerned multiple materials and inclusions. [21][22][23] There are also publications covering other fields of engineering, such as fluid flow, 24,25 electrostatics, 26 and magnetic actuators. 27 However, to the authors' best knowledge, there does not seem to be any previous study on level-set-based optimization using finite element methods on fixed meshes for wave propagation problems.…”

Section: Introductionmentioning

confidence: 99%

Acoustic shape optimization using cut finite elements

Bernland

Wadbro

Berggren

2017

Numerical Meth Engineering

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Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.

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