Finite elements, design optimization, and nondestructive
evaluation: A review in magnetics, and future directions in GPU-based, element-by-element coupled optimization and NDE
Affiliations: [a] Department of Electrical and Computer Engineering,
Michigan State University, East Lansing, MI, USA | [b] Department of Mathematics and Statistics, University
of Toledo, Toledo, OH, USA | [c] The US Army Tank Automotive Research Development and
Engineering Center, Warren, MI, USA
Correspondence:
[*]
Corresponding author: S.R.H. Hoole, Department of Electrical and
Computer Engineering, Michigan State University, 2120 Engineering Building, 428
South Shaw Lane, East Lansing, MI 48824-1226, USA. Tel.: +1 517 974 6442; Fax:
+1 517 353 1980; E-mail: [email protected]
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.
