On Operator Filtering for Integral Equations: the High-Order Case

In this work, we extend the standard quasi-Helmholtz filters to high-order discretizations in the context of the boundary element method. This generalization allows preconditioning integral equations such as the electric field integral equation (EFIE) in the h-refinement regime while preserving the accuracy gain of high-order discretizations. The theoretical framework will be corroborated by numerical results that validate the effectiveness of the proposed strategy when stabilizing the refinement-dependent spectral behavior of the high-order discretized EFIE.