Hybrid Formulation of the Equation Systems of the 3-D PEEC Model Based on Graph Algorithms

This paper presents a new hybrid nodal-mesh formulation of the equation systems of the 3-D partial element equivalent circuit (PEEC) method for the solution of combined electromagnetic and circuit (EM-CKT) problems. Traditional electromagnetic solution methods suffer from singularity of the system matrix due to the decoupling of the charge and currents at low frequencies. Based on the hypothesis that charges reside only on the surface of conductors and that current density is solenoidal inside them, a novel scheme is developed fully exploiting the physical properties of charges and currents. An elegant and efficient algorithm, based on graph theory, is proposed to automatically search independent loops on three dimensional rectangular grids such as those arising in volumetric PEEC formulation. The most significant outcome is that the proposed approach allows to reduce the number of unknowns while preserving the accuracy at low frequency down to DC. The method is validated through numerical results that confirm the accuracy of the proposed formulation from DC-to-daylight and its capability to provide memory saving.