Design sensitivities using high-order tetrahedral vector elements

Obtaining design sensitivites for electromagnetic quantities by finite elem ent analysis requires explicit expressions for the derivatives of the local stiffness matrix with respect to design parameters. By expressing the stif fness matrix for a vector tetrahedron in a certain way, the required deriva tives are easily evaluated in terms of universal matrices. The method is va lidated by comparison with exact values or with derivatives obtained by a f inite-difference formula.