Vector potential expanded by edge basis functions associated with loops on finite-element facets

Abstract

Edge basis functions associated with loops forming fundamental sets on finite element facets rather than with single edges are introduced. It is shown that using these to approximate vector potentials results in less linearly interdependent equations than with usual edge basis functions. Furthermore, the conditioning of the matrix in the Galerkin equations system obtained is demonstrated to be substantially better than when using a tree-cotree gauge.