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We describe a novel basis of hierarchical, multiscale
functions that are linear combinations of standard Rao-Wilton-
Glisson (RWG) functions. When the basis is used for discretizing
the electric field integral equation (EFIE) for PEC objects it gives
rise to a linear system immune from low-frequency breakdown,
and well conditioned for dense meshes. The proposed scheme can
be applied to any mesh with triangular facets, and therefore it can
be used as if it were an algebraic preconditioner. The properties
of the new system are confirmed by numerical results that show
fast convergence rates of iterative solvers, significantly better than
those for the loop-tree basis. As a byproduct of the basis generation,
a generalization of the RWG functions to nonsimplex cells is
introduced
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