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

Abstract : 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.