Implementation of the Calderón multiplicative preconditioner for the efie solution with curvilinear triangular patches

The electric field integral equation (EFIE) has been widely used in the moment method (MoM) solution of electromagnetic problems. However, due to the spectrum property of the EFIE operator, the resulting MoM impedance matrix has eigenvalues clustered around the origin and at the infinity as the mesh density increases, leading to a dramatic increase of the matrix condition number. When the object is discretized with a nonuniform mesh, the EFIE impedance matrix becomes even more ill-conditioned and therefore very difficult to be solved efficiently and accurately. To overcome these problems, a preconditioner based on the Calderon identity has been developed in the past. Recently, Andriulli et al. has introduced a multiplicative scheme named as the Calderon multiplicative preconditioner (CMP) to precondition the EFIE operator. In this paper, we implement the CMP for the EFIE solution using curvilinear triangular patches, which enhances the flexibility and accuracy of geometry modeling, and formulate the CMP with a uniform expression for both uniform and nonuniform discretizations.