Accelerating calderón multiplicative preconditioner with multi-grade adaptive cross approximation algorithm

In this paper, a multi-grade-oriented accelerating strategy with adaptive cross approximation (ACA) algorithm is presented for enhancing the efficiency of Calderón multiplicative preconditioner (CMP). CMP is a very successful preconditioner for stabilizing EFIE and easy to embed in conventional MoM codes. However, because of the complicated nature of this preconditioner, it gives rise to enormous computational cost additionally, which exceeds any other traditional one. Even with some fast algorithm, the computational efficiency is not satisfactory when the number of unknowns increases obviously in some cases. Here we employ the ACA algorithm with a multi-grade fashion to accelerate CMP for overcoming the CPU time and memory additional cost difficulty. Both complexity analysis and numerical experiments are given to demonstrate the performance of this strategy.