Constrained divergence-conforming bases

In this paper, a technique for automatically generating basis functions suitable for integral equation discretizations is presented. The technique seeks to obtain an optimal basis function from a linear combination of more general functions by enforcing an appropriate set of constraints on the linear combination and then solving for the optimal coefficients. Numerical properties of divergence-conforming constrained bases on quadrilateral meshes are characterized in terms of scattering from perfectly electric conducting structures. Computed data show that the condition numbers of system matrices resulting from the use of the constrained bases are equal to or better than those resulting from the use of other basis sets reported in the literature.