FEMSTER: an object oriented class library of discrete differential forms

The FEMSTER finite element class library described in this paper is unique in several aspects. First, it is based upon the language of differential forms. This language provides a unified description of a great variety of PDEs and thus leads us directly to a concise and abstract interface to finite element methods. This language also unifies the seemingly disparate Lagrange, H(curl) and H(div) basis functions that are used in computational electromagnetics. Secondly, FEMSTER utilizes higher-order elements, bases, and integration rules. Higher-order elements are important for accurate modeling of curved surfaces. The use of higher-order basis functions reduces the demands put upon mesh generation, e.g. a billion element mesh is no longer required for a numerically converged solution. The FEMSTER class library is ideally suited for researchers who wish to experiment with unstructured-grid, higher-order solution of Poisson's equation, the Helmholtz equation, Maxwell equations, and related PDEs that employ the standard gradient, curl, and divergence operators.