Preconditioning the surface integral equation formulations for the fast solution of penetrable bodies composed of arbitrary materials

The majority of the surface integral equation (SIE) formulations have balancing problems due to the very different scales of the equivalent electric and magnetic currents. As a result of this, the impedance matrix usually has an ill-condition number because of the imbalance between the different blocks, and the use of a preconditioner for a correct balancing between these blocks is necessary. In this work, a very efficient preconditioner formulation is implemented, that operates on the left and right sides of the impedance matrix. The proposed preconditoner improves the impedance matrix balance, and thus the condition number, without altering the SIE formulation. This double preconditioner is simple and the complexity is O(N), with N the number of unknowns.