Adaptive improvement of magnetic fields using hierarchal tetrahedral finite elements

By using hierarchal tetrahedral finite elements, the polynomial order can be increased in poorly discretized regions of a mesh and an improved solution obtained for the magnetic field. An algorithm is proposed which estimates the error in each tetrahedron, by calculating the discontinuity of the normal component of flux density, and automatically adjusts the orders accordingly. Results are presented for an infinite sheet of copper carrying a time-harmonic current, an iron-core magnet excited by a DC coil, and the Bath Plate at 50 Hz. Setting all the elements to the highest order available gives the greatest accuracy, but almost the same accuracy can be obtained with fewer degrees of freedom after several adaptive steps. The cumulative CPU time of these steps is roughly the same as that of the highest-order solution, but significantly less memory is needed, and the adaptive route has the added advantage that it can be stopped at intermediate points if the computer resources run out