Boundary edge elements and spanning tree technique in three‐dimensional electromagnetic field computation

Abstract

AbstractThe boundary discretization of the curl‐free vector variable such as the magnetic field h and the divergence‐free variable such as the surface current density k is discussed. Instead of introducing the scalar variables, the vector variables h and k are discretized by the curl‐conform and the div‐conform triangular edge elements, respectively. The degrees of freedom are associated with the boundary edges. In order to ensure the null curl of h and the null divergence of k, a spanning tree technique is used to identify the independent edges. The triangular edge elements contain the first‐order nodal elements when expressing h or k by the scalar variables. The use of edge elements permits one to solve multiply connected problems if the independent edges are well identified, i.e. the necessary cuts are introduced in multiply connected domains. An automatic tree generation algorithm is presented. It permits one to determine automatically the additional edges on the necessary loops (cuts) of a multiply connected region. Some tree generation examples are illustrated. A numerical application to a three‐dimensional multiply connected eddy current problem is reported at the end of the paper.