H-$\Phi$ Field Formulation With Lumped Sources and Unbounded Domains

We consider a H-Φ field formulation to solve 3-D frequency-domain eddy-current problems. This formulation uses vector and scalar tetrahedral finite elements within, respectively, the conductive and nonconductive domains. It can handle multiply-connected regions and eliminates the need to compute the source current density and source magnetic field before the actual simulation. We propose three ways to couple finite elements with the multiple multipole program (MMP) and solve this H-Φ variational form on an unbounded domain. The MMP is a method that uses exact solutions of the homogeneous equations as basis functions (the so-called “multipoles”). The desired behavior at infinity is given by the chosen multipoles-this eliminates the need for artificially truncating the computational domain. Interface conditions between the finite-element method (FEM) and MMP domains allow to express the coupled FEM-MMP problem.