Hybrid FE/BI modeling of commensurate and non-commensurate 3D doubly periodic structures

By applying appropriate periodicity conditions, the computational domain of infinite periodic structures can be reduced down to a single unit cell. Fully three-dimensional modeling can be achieved by using hybrid finite element (FE)/boundary integral (BI) methods. Both of these methods are based on FE modeling employing tetrahedral meshes and a spectral domain Floquet mode expansion of the BI fields. We propose a hybrid FE/BI method employing distorted triangular prismatic elements for volume tesselation and a mixed potential integral equation (MPIE) formulation in the spatial domain for mesh truncation. The triangular prismatic elements provide for full geometrical adaptability in the plane of the triangles and structured meshing along the depth of the cell, For the evaluation of the spatial periodic Green´s function the Ewald acceleration technique is applied.