Primal and dual graph haar bases for the hierarchical regularization of the EFIE on unstructured meshes

When the Electric Field Integral Equation (EFIE) is discretized with a stable basis, such as the RWG basis functions, the resulting system matrix is, in general, ill-conditioned. Hierarchical bases can be used as preconditioner to overcome this issue. For a complete regularization of the EFIE, they require, however, a structured mesh (i.e., a mesh resulting from a dyadic refinement), which limits the applicability and generality of the method. In this work, we present a hierarchical bases preconditioner that can be applied to any unstructured mesh. Numerical results demonstrate the effectiveness of our approach.