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

This paper reviews mathematical optimization in synthesis and nondestructive evaluation (NDE) by the finite element method in magnetics because background work has been inadequately attributed in the literature. The review identifies the earliest papers and reports new work in nondestructive evaluation and GPU-based matrix solution to save time and memory. Although the genetic algorithm has been applied in optimization, in coupled systems the number of object function evaluations doubles. We therefore examine the use of graphics processing units (GPUs) to handle the immense computational load. GPU 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 element-by-element processing, however, and achieve a GPU speedup of 147 by Jacobi conjugate gradients while forming the matrix of coefficients and of 80(and growing indefinitely) by Gauss iterations without forming the matrix for situations where memory is scarce such as genetic algorithm optimization where several copies of the matrix have to be held on threads.