Higher order finite models [computational electromagnetics]

This work reviews the previous work on high-order modelling and on the use of high-order vector bases in computational electromagnetics. Higher-order vector bases on 2D (triangular and quadrilateral) elements, and on 3D elements are considered. Several 3D elements are presented and discussed altogether: the tetrahedron, the pyramidal element, the triangular prism and the brick. Elements of different shape can be used together to form 2D and 3D conformal meshes. The paper also discusses new singular curl- and divergence-conforming vector bases that incorporate the edge conditions and that are particularly suited to approach wedge problems. Use of these high-order bases provides more accurate and efficient numerical solutions of both surface integral and differential problems.