Multilevel Gauging for Edge Elements

Abstract

The vector potential of a solenoidal vector field, if it exists, is not unique in general. Any procedure that aims to determine such a vector potential typically involves a decision on how to fix it. This is referred to by the term gauging. Gauging is an important issue in computational electromagnetism, whenever discrete vector potentials have to be computed. In this paper a new gauging algorithm for discrete vector potentials is introduced that relies on a hierarchical multilevel decomposition. With minimum computational effort it yields vector potentials whose L ²-norm does not severely blow up. Thus the new approach compares favorably to the widely used co-tree gauging.