Pyramid Elements for Finite Methods

Modern finite methods electromagnetic (EM) solvers model complex geometries using hybrid three-dimensional meshes composed of cells of different shapes, namely a mixture of tetrahedra, hexahedrons (bricks), triangular prisms, and pyramids.In particular, square-based pyramids are used to connect tetrahedral and hexahedral mesh schemes or, in combination with triangular prisms, to glue brick meshes of different densities.Pyramids are also useful when using h-adaptive techniques that require iterative refinement of the mesh on a zone-by-zone basis, which is easier if hybrid meshes are allowed [1].In all cases, to obtain conforming meshes, the quadrilateral and triangular faces of a pyramidal element must match those of the other differently shaped elements that have quadrilateral and triangular faces.In this regard, we note that while there is little to add on how to define and use tetrahedral, prismatic and brick elements for applications of finite methods [1], much remains to be clarified and validated regarding pyramids, for which the literature is more recent, less extensive, less coherent and, at times, discordant (see [2,3,4] and the references therein).