Construction and assessment of hierarchical edge elements for three- dimensional computations of eddy currents

摘要

This thesis considers the feasibility of doing calculations to optimize electrical machines without the need to build expensive prototypes. It deals with the construction and assessment of new, hierarchical, hexahedral edge elements for three-dimensional computations of eddy currents with the electric vector potential formulation. The new elements, five in all, gave up to second-order approximations for both the magnetic field and the current density. Theoretical arguments showed these elements to be more economical for a given polynomial order of the approximated fields than the serendipity family of nodal elements. Further it was pointed out how the support of a source field computed by using edge elements could be made very small provided that a proper spanning tree was used in the edge element mesh. This was exploited for the voltage forcing technique, where source fields were used as basis functions, with unknown total currents in voltage forced conductors as degrees of freedom. The practical assessment of the edge elements proved the accuracy to improve with increasing polynomial order, both for local and global quantities. The most economical element was, however, one giving only complete first-order approximations for both fields. Further, the edge elements turned out to be better than the nodal elements also in practice. For the voltage forcing technique, source field basis functions which had small support, resulted in large reduction of the CPU-time for solving the main equation system, compared to source fields which had large support. The new elements can be used in a p- type adaptive scheme, and they should also be applicable for other tangentially continuous field problems. 67 refs., 34 figs., 10 tabs.