SHAPE DESIGN OPTIMIZATION OF POWER FREQUENCY ELECTROMAGNETIC DEVICES USING NUMERICAL METHODS

Abstract

This paper presents the mathematical formulation concerning the solution of inverse electromagnetic problems, i.e. the shape optimization of power frequency electromagnetic devices, based on a combination of numerical methods. The optimization problem is solved using deterministic methods in which the electromagnetic field problem is treated as a subproblem of the optimization process. The field problem is calculated using the finite element (FE) method. Three deterministic approaches are studied in detail, the quadratic extended penalty method (QUA), the augmented Lagrange multiplier (ALM) method and the constrained quasi-Newton method (PLBA-CR). The work highlights the advantages and drawbacks of each approach. The search direction for the optimization is found by two distinct methods, the direct differentiation of the FE matrices and the finite difference (FD) method. In total, three problems are discussed in order to show the power and applicability of the theory presented. The PLBA-CR, when combined with the direct differentiation of the FE matrices, appears to offer important advantages over the other methods. [Vol. 12, No. 1 (1997), Special Issue on International Computational Electromagnetics, pp 117-124]