Magnetic vector potential tree edge values for boundary elements

An efficient boundary integral equation solution for magnetic field problems is presented, based on a novel magnetic vector potential formulation and using edge elements and tree-cotree spanning. A zero normal component of this vector potential A and the condition for its line integral along any closed path on the boundary are imposed such that the continuity of the normal component of the magnetic flux density is rigorously satisfied. The unknowns employed are the tangential components of ∇×A and only the tree edge element values. Multiply connected domains are easily dealt with by introducing certain pairs of cotree edges in the set of tree edges, which are used to construct the cuts that transform a multiply connected domain into a simply connected one. The line integrals of A along the cut loops are determined by the respective magnetic fluxes. The stiffness matrix can easily be obtained. Three illustrative examples are given.