A novel shape design sensitivity formula for magnetostatic problems is derived analytically using the material derivative concept in continuum mechanics. In order to express the design sensitivity as a function of shape variation only, the adjoint variable is defined. Since the formula is expressed as boundary integration of state and adjoint variables over a deformed boundary, the boundary-element method (BEM) is used to evaluate the variables accurately on the boundary. The proposed algorithm is applied to the pole-shape optimization of a quadrupole magnet, through which the validity is proved.>
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Koh et al. (1993) studied this question.
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