Fast Calderón Preconditioning for the Electric Field Integral Equation

Abstract

Despite its solid mathematical background, standard
Calderon preconditioning for the Electric Field Integral Equation ´
scales poorly with respect to 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
Calderon preconditioner. Numerical experiments validate our ´
claims for increasingly complex settings, yielding results comparable to those given by algebraic techniques such as nearfield preconditioners and providing insights into further research
avenues.