R. Dyczijedlinger et O. Biro, A JOINT VECTOR AND SCALAR POTENTIAL FORMULATION FOR DRIVEN HIGH-FREQUENCY PROBLEMS USING HYBRID EDGE AND NODAL FINITE-ELEMENTS, IEEE transactions on microwave theory and techniques, 44(1), 1996, pp. 15-23
An advanced A-V method employing edge-based finite elements for the ve
ctor potential A and nodal shape functions for the scalar potential V
is proposed. Both gauged and ungauged formulations are considered. The
novel scheme is particularly well suited for efficient iterative solv
ers such as the preconditioned conjugate gradient method, since it lea
ds to significantly faster numerical convergence rates than pure edge
element schemes. In contrast to nodal finite element implementations,
spurious solutions do not occur and the inherent singularities of the
electromagnetic fields in the vicinity of perfectly conducting edges a
nd corners are handled correctly. Several numerical examples are prese
nted to verify the suggested approach.