**Authors:** Andrew F. Peterson and Roberto D. Graglia

**Source:** FERMAT, Volume 18, Article 1, Nov.-Dec., 2016

**Abstract:** This article attempts to organize and review the variety of different types of hierarchical vector bases appropriate for use in solving the common equations of electromagnetic fields on (possibly curved) triangular or quadrilateral domains. Tables are used to illustrate 16 different basis families for triangular domains and 7 families for quadrilateral domains. The choice of a suitable basis may be dictated by the relative linear independence of the set and the ease with which functions can be used on meshes containing both cell shapes. We also consider suitability for use with surface integral equation applications.

**Index Terms:** Basis Functions, Boundary Elements, Electromagnetic Fields, Method of Moments (MoM), Vector Finite Elements.

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