Extension to Nonconforming Meshes of the Combined Current and Charge Integral Equation

We bring out some mathematical properties of the current and charge boundary integral equation when it is posed on a surface without geometrical singularities. This enables us to show that it is then possible to solve this equation by a boundary element method that requires no interelement continuity. In particular, this property allows the use of meshes on various parts of the surface obtained independently of each other. The extension to surfaces with geometrical singularities showed that acute dihedral angles can lead to inaccuracies in the results. We built a two-dimensional version of this equation which brought out that the wrong results are due to spurious oscillations concentrating around the singular points of the geometry. Noticing that the system linking the current and the charge is a saddle-point problem, we have tried augmenting the approximation of the charge to stabilize the numerical scheme. We show that this stabilization procedure, when coupled with a refinement of the mesh in the proximity of the geometrical singularities, obtained by a simple subdivision of the triangles, greatly reduces the effect of these instabilities.