7. A Mortar Element Method for the Electric Field Integral Equation on Sheets and Junctions

Boundary Element Methods offer an appealing avenue for the modelling of scattering of time-harmonic electromagnetic waves by obstacles. Classic boundary element methods, however, require the construction of a geometrically conforming mesh to model the scatterer’s surface. This conformity requirement poses a number of serious restrictions. It is impossible to create truly local refinements to increase the solution’s accuracy. Parallelisation of the geometry creation and preprocessing turns out to be highly challenging, limiting the scalability of parallel implementations of the boundary element method. In this chapter, a mortar element method for the electric field integral equation is introduced. In this method the regularity constraints on the candidate solutions are relaxed allowing for greater flexibility in the choice of finite element spaces and surface meshes. In particular, the surface meshes are not required to be geometrically conforming, allowing for truly local refinements and parallelisation of the geometry handling. Moreover, the method presented here is fit to deal with structures containing junctions, i.e. lines at which three or more sheets meet. These structures are indispensable to model e.g. fins and wings.