Accurate solutions of Maxwell's equations around PEC corners and highly curved surfaces using nodal finite elements

A method is presented for computing accurate solutions of Maxwell's equations in the presence of perfect electrical conductors (PECs) with sharp corners and highly curved surfaces using conventional nodal finite elements and a scalar/vector (S/V) potential formulation. This technique approximates the PEC with an impedance boundary condition (IBC) where the impedance is small. Critically, it couples both potentials through this boundary condition, rather than setting the scalar potential to zero. This permits cancellation of the tangential components of the vector potential, resulting in an accurate normal electric field. The cause for the inaccuracies that nodal methods experience In the presence of sharp PEC corners or highly curved PEC surfaces is elucidated. It is then shown how the inclusion of the scalar potential cures these deficiencies permitting accurate solutions. Spectral analysis of the resulting finite element matrices are shown validating the boundary conditions used. Examples are presented comparing a benchmark solution, conventional PEC and IBC boundary conditions, and the new S/V potential IBC on a PEC wedge and PEC ellipse. In both cases the new S/V IBC produces superior results.