A general finite element vector potential formulation of electromagnetics using a time-integrated electric scalar potential

The equations of electromagnetics are formulated for finite-element analysis using a novel time-integrated electric scalar potential in addition to the conventional magnetic vector potential. The resulting matrix equation is fully equivalent to Maxwell´s equations in their general form. The matrices which represent dielectric, conduction, and reluctivity material properties are sparse, banded, symmetric, and positive semidefinite. An initial condition representing electrostatics is also introduced. An analysis of high-frequency charge relaxation in three dimensions is presented to demonstrate formulation generality. With this new formulation, it is possible to treat general behavior, including wave propagation, induction, and charge accumulation, using only four degrees of freedom per grid point in a matrix equation with attractive numerical properties