Fast Calderón Preconditioning for the Electric Field Integral Equation

Despite its solid mathematical background, the standard Calderón preconditioning for the electric field integral equation scales poorly with respect to the mesh refinement due to its construction over barycentric meshes. Based on hierarchical matrices, our proposed algorithm optimally splits solution and preconditioner accuracies, significantly reducing computation times and memory requirements while retaining the good properties of the original Calderón preconditioner. Numerical experiments validate our claims for increasingly complex settings, yielding results comparable to those given by algebraic techniques such as near-field preconditioners and providing insights into further research avenues.