Investigation on Dual Finite-Element Method in Terms of Scalar Potential Through Interpolation

The complementarity of dual finite-element methods (FEMs), which use Whitney nodal and edge elements on the primal mesh, has been exploited to accelerate convergence of energy related quantities, such as impedances. However, the edge-based dual FEM formulation utilizes degrees-of-freedom in terms of vector potential, and requests prebuilt links between charged domains. It leads to increase in complexity and computation costs. To avoid such complexities, the dual FEM in terms of scalar potential on the dual mesh through interpolation is investigated in this paper. The shape functions are constructed through interpolation founded on barycentric coordinates, like Sibson coordinates. A comparison between different FEMs is performed with electrostatic examples.