On a Novel Calderón Preconditioning Strategy Based on High-Order Quasi-Helmholtz Projectors

The first of Calderón identities indicates that the operator of the electric field integral equation (EFIE) can potentially act as a preconditioner for itself. However, the discretization of this preconditioning operator via the boundary element method (BEM) requires constructing a dual space commonly defined on a barycentric refinement of the orginal mesh. This contribution introduces a novel Calderón strategy that leverages high-order quasi-Helmholtz projectors. Unlike the standard strategies, which are based on barycentric refinements, a dual space is obtained by combinating functions of higher order. This strategy allows the development of a discretization of the Calderón identity that is suitable for arbitrary order. The well-conditioning of the proposed formulation is investigated, and numerical results are presented to corroborate the theory.