A New Preconditioner for the EFIE Based on Primal and Dual Graph Laplacian Spectral Filters (2004.12802v1)

Abstract: The Electric Field Integral Equation (EFIE) is notorious for its ill-conditioning both in frequency and h-refinement. Several techniques exist for fixing the equation conditioning problems based on hierarchical strategies, Calderon techniques, and related technologies. This work leverages on a new approach, based on the construction of tailored spectral filters for the EFIE components which allow the block renormalization of the EFIE spectrum resulting in a provably constant condition number for the equation. This is achieved without the need for a barycentric refinement and with low computational overhead compared with other schemes. In particular, only sparse matrices are required in addition to the EFIE original matrix. Numerical results will show the robustness of our scheme and its application to the solution of realistic problems.