Magnetostatics with edge elements: a numerical investigation in the choice of the tree

On solving the Magnetostatic problem with edge elements a spanning tree technique must be employed so that uniqueness of the magnetic vector potential is ensured and solution is possible. It is shown that the choice of the tree affects very much the accuracy of the approximation. The use of an arbitrary tree results in poor convergence with reduced accuracy or even in inability to solve the problem. On the other hand employment of optimal tree structures results in very good convergence of the ICCG and increased accuracy. An algorithm for constructing nearly optimal tree structures is developed and applied in the solution of various problems