Two requisite tools in the optimal design of electromagnetic devices

Subramaniam, S.; Kanaganathan, S.; Hoole, S. Ratnajeevan H.

doi:10.1109/20.105005

Cited by 17 publications

(1 citation statement)

References 4 publications

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“…Recognizing this problem Subramaniam et al [29] suggest a tunneling function and an assortment of algorithms so that when one fails another may be started to identify the minimum. However, the real cause of the local minima in the object functions, would soon be identified as owing to changes in nodal connections as the shape evolved under synthesis [30,31].…”

Section: Other Early Papers On Optimization In Magneticsmentioning

confidence: 99%

Finite elements, design optimization, and nondestructive evaluation: A review in magnetics, and future directions in GPU-based, element-by-element coupled optimization and NDE

Jayakumar¹,

Thyagarajan²,

Rahunanthan

et al. 2015

JAE

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Most important journal papers in magnetics are selected from conference records with quick review and subject to stringent page limits. The literature as a result is unsatisfactory, inadequately attributing previous works and without sufficient details to replicate work presented. This paper therefore reviews mathematical optimization in synthesis and nondestructive evaluation (NDE) by the finite element method in magnetics. The review identifies the earliest papers. Thereafter this paper proposes and establishes the feasibility of coupled problem optimization using the genetic algorithm to avoid mesh induced minima which hurt gradient based methods. The genetic algorithm, while avoiding the need for derivatives, results in having to undertake even more numerous finite element solutions. Although the genetic algorithm has been applied in optimization, in coupled systems the number of object function evaluations doubles. We there examine the use of graphics processing units (GPUs) to handle the immense computational load. GPUs have recently been introduced in finite element analysis but their memory limits are often not recognized and are critically limiting when parallelizing the several solutions required in optimization. To overcome this limit, element-by-element finite element matrix processing is employed, making coupled problems practicable on GPUs. We overcome the memory limits faced by others.

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Section: Other Early Papers On Optimization In Magneticsmentioning

confidence: 99%

Finite elements, design optimization, and nondestructive evaluation: A review in magnetics, and future directions in GPU-based, element-by-element coupled optimization and NDE

Jayakumar¹,

Thyagarajan²,

Rahunanthan

et al. 2015

JAE

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A structural mapping technique for geometric parametrization in the optimization of magnetic devices

Weeber

Ratnajeevan

Hoole

1992

Numerical Meth Engineering

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SUMMARYThe continuity and differentiability of object functions is a basic prerequisite for the application of gradient methods in optimization. However, for parameters defining the shape of an electromagnetic device, the finite element discretization in the field analysis introduces discontinuities into the object function which slow down the convergence rate . Additionally, depending on the geometric parametrization employed, the optimization frequently yields shape contours that are impracticable for manufacturing purposes. This paper investigates the problems inherent in geometric parametrization and shows that the discontinuities in the object function are caused by changes in mesh topology as the geometric parameters vary; these changes inevitably follow from the use of free meshing algorithms. As a solution to these shortcomings a structural mapping technique is outlined that maps surface displacements onto the parameters of the finite element mesh and obtains the parameter dependent geometric variations without a change in mesh topology. This resulting geometric parametrization'yields continuous object functions without artificial local minima and results in smooth surface contours of the optimized device. Using this new parametrization technique, design sensitivity analysis is shown to be a reliable and essential part in the efficient application of gradient methods for shape optimization.

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