Accuracy of the Mortar Element Electric Field Integral Equation

Scattering of time-harmonic electromagnetic fields by perfect electric conductors can be modelled by the electric field integral equation (EFIE). The EFIE is flexible in that it can be applied to both closed and open structures, and that it can be extended to include the effects of a non-zero surface impedance. Approximate solutions of the EFIE can be computed by application of the boundary element method (BEM). In the BEM, the geometry is approximated by a triangular mesh, and the unknown current is approximated by an expansion in basis functions that are constructed subordinate to that mesh. The classic EFIE requires the candidate solution to have continuous normal components everywhere on the surface. This requires the underlying triangulation to be geometrically conforming. Recently, the mortar element EFIE was introduced. In the mortar element EFIE, the candidate solution is only required to have continuous normal components on subsets of the surface. Global normal continuity is imposed in a weak discreet sense by solution of a saddle point problem. The lack of normal continuity of the solution makes it challenging to assess the accuracy of the mortar element EFIE. In this contribution, an error criterion is designed and applied to the solution of the mortar element EFIE. The accuracy of the solution as a function of the mesh parameter is studied.