Isogeometric Shape Optimization for Electromagnetic Scattering Problems

Nguyen, Dang-Manh; Evgrafov, Anton; Gravesen, Jens

doi:10.2528/pierb12091308

Cited by 44 publications

(27 citation statements)

References 21 publications

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“…Furthermore, Basilevs et al [2] and Scott et al [3] have already demonstrated the efficient usage of IGA in conjunction with T-splines technology [4,5]. Shape optimization, in the context of IGA, has been presented in various works as, e.g., in [6,7,8] for the 2D case and in [9] for the 3D case. In these works, the control points are directly used as shape optimization parameters.…”

Section: Introductionmentioning

confidence: 99%

Ship-hull shape optimization with a T-spline based BEM–isogeometric solver

Κώστας

Ginnis

Politis

et al. 2015

Computer Methods in Applied Mechanics and Engineering

120

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Section: Introductionmentioning

confidence: 99%

Ship-hull shape optimization with a T-spline based BEM–isogeometric solver

Κώστας

Ginnis

Politis

et al. 2015

Computer Methods in Applied Mechanics and Engineering

120

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show abstract

“…To this end, we proceed in a standard way (see e.g. [14]). The derivative of the discrete magnetic field solution with respect to the boundary control points d ij for instance can be found by solving the auxiliary system of linear equations…”

Section: Shape Sensitivity Analysismentioning

confidence: 99%

Iso-geometric shape optimization of magnetic density separators

Nguyen

Evgrafov

Gravesen

et al. 2014

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose – The waste recycling industry increasingly relies on magnetic density separators. These devices generate an upward magnetic force in ferro-fluids allowing to separate the immersed particles according to their mass density. Recently, a new separator design has been proposed that significantly reduces the required amount of permanent magnet material. The purpose of this paper is to alleviate the undesired end-effects in this design by altering the shape of the ferromagnetic covers of the individual poles. Design/methodology/approach – The paper represents the shape of the ferromagnetic pole covers with B-splines and defines a cost functional that measures the non-uniformity of the magnetic field in an area above the poles. The authors apply an iso-geometric shape optimization procedure, which allows us to accurately represent, analyze and optimize the geometry using only a few design variables. The design problem is regularized by imposing constraints that enforce the convexity of the pole cover shapes and is solved by a non-linear optimization procedure. The paper validates the implementation of the algorithm using a simplified variant of the design problem with a known analytical solution. The algorithm is subsequently applied to the problem posed. Findings – The shape optimization attains its target and yields pole cover shapes that give rise to a magnetic field that is uniform over a larger domain. Research limitations/implications – This increased magnetic field uniformity is obtained at the cost of a pole cover shape that differs per pole. This limitation has negligible impact on the manufacturing of the separator. The new pole cover shapes therefore lead to improved performance of the density separation. Practical implications – Due to the larger uniformity the generated field, these shapes should enable larger amounts of waste to be processed than the previous design. Originality/value – This paper treats the shapes optimization of magnetic density separators systematically and presents new shapes for the ferromagnetic poles covers.

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“…In [20] a method for shape optimization using the Winslow functional is introduced. In [21] and [22] the authors use this technique to optimize the domain of interest for special applications such as vibrating membranes or conducting scatterers.…”

Section: Introductionmentioning

confidence: 99%

Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis

Pilgerstorfer

Jüttler

2014

Computer Methods in Applied Mechanics and Engineering

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Isogeometric Analysis (IGA) was introduced by Hughes et al. in 2005 [1] as a new method to bridge the gap between the geometry description and numerical analysis. Similar to the finite element approach, the IGA concept to solve a partial differential equation leads to a (linear) system of equations. The condition number of the coefficient matrix is a crucial factor for the stability of the system. It depends strongly on the domain parameterization, which provides the isogeometric discretization. In this paper we derive a bound for the condition number of the stiffness matrix of the Poisson equation. In particular, we investigate the influence of the domain parameterization and the knot spacing on the stability of the numerical system. The factors appearing in our bound reflect the stability properties of a given domain parameterization.

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Isogeometric Shape Optimization for Electromagnetic Scattering Problems

Cited by 44 publications

References 21 publications

Ship-hull shape optimization with a T-spline based BEM–isogeometric solver

Ship-hull shape optimization with a T-spline based BEM–isogeometric solver

Iso-geometric shape optimization of magnetic density separators

Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis

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