Overdetermined Surface Integral Equation with Fully Orthogonal Non-Conforming Basis Functions

An overdetermined frequency domain electromagnetic surface integral equation formulation of the second kind is applied with fully orthogonal non-conforming basis functions. The surface integral equation of the equivalent surface current and charge densities is derived from the surface integral representation of the normalized Picard's extended Maxwell system. The unknown surface current and charge densities are expanded elementwise using non-conforming polynomial type scalar shape functions and constant vectors. Higher order basis functions are used for better accuracy and larger element sizes. The shape functions and vectors are fully orthogonal in order to achieve fast converge of iterative solution methods with higher order bases. An overdetermined MFIE type integral equation formulation of the second kind is derived by testing all of the unknown and known components of the integral representation on the surfaces in order to overcome the internal resonances and to enforce all of the continuities of the surface fields weakly. Stability, accuracy and numerical efficiency of the overdetermined integral equation is analyzed with numerical experiments.