FIGURE 44.2 Permanent magnet motor. and a suitable edge variable basis function form for solving this equation by finite elements using tetrahedral elements is h(r)=a+b×r (448) here r is the position vector and a and b, respectively, are vectors dependent on the geometry of the element. The basis function expansion is given by ∑h(r)H (449) where h is the vector basis function for edge e, and H is the value of the field along an element edge(se Fig 44.3). The functions, Eqs. (44.8)and (44.9), have the property of being divergence free, and most important they ensure that the tangential component of H is continuous while allowing for the possibility of a discontinuity in the normal component In nonconducting regions where the field can be economically modeled by a scalar potential, standard nodal elements can be used. At the interface the edge elements couple exactly with the nodal An alternative procedure is to solve the field equations in their integral form, see also Chapter 43. For example in magnetostatics, the magnetization vector M given by M=(H-1)H can be used instead of H to derive an egral equation over all ferromagnetic domains of the problem, i.e.,© 2000 by CRC Press LLC and a suitable edge variable basis function form for solving this equation by finite elements using tetrahedral elements is h(r) = a + b ¥ r (44.8) where r is the position vector and a and b, respectively, are vectors dependent on the geometry of the element. The basis function expansion is given by H = ( he(r)He (44.9) where he is the vector basis function for edge e, and He is the value of the field along an element edge (see Fig. 44.3). The functions, Eqs. (44.8) and (44.9), have the property of being divergence free, and most important they ensure that the tangential component of H is continuous while allowing for the possibility of a discontinuity in the normal component. In nonconducting regions where the field can be economically modeled by a scalar potential, standard nodal elements can be used. At the interface the edge elements couple exactly with the nodal elements. Integral Methods An alternative procedure is to solve the field equations in their integral form, see also Chapter 43. For example, in magnetostatics, the magnetization vector M given by M = (m – 1)H can be used instead of H to derive an integral equation over all ferromagnetic domains of the problem, i.e., FIGURE 44.2 Permanent magnet motor