A New Preconditioning Scheme for MLFMA Based on Null-Field Generation Technique

The multilevel fast multipole algorithm (MLFMA) has been widely used in computational electromagnetics (CEM) to efficiently handle the large-scale problems. However, MLFMA belongs to the integral methods that always require strong preconditioners to achieve the final solution, especially for the ill-conditioned electric-field integral equation (EFIE). In this letter, we develop a new efficient preconditioning scheme based on the null-field generation technique that combines subdomain-entire domain basis functions to eliminate the interactions between the near-field lowest-level groups. The impedance matrix generated by the new defined basis functions is more diagonal dominant, and fewer iterations are needed compared to the conventional matrix when equipped with the block diagonal preconditioner. Several representative numerical examples are given to illustrate the validity and efficiency of the proposed preconditioning scheme.