Near field preconditioner for the fast multipole method

Efficient solutions of integral numerical methods usually require the use of effective preconditioning techniques. Preconditioners involving the near-field information are available for the Fast Multipole Method (FMM), enabling fast convergence up to certain problems sizes. Nevertheless, for large electromagnetic problems, the near-field matrix containing the near-coupling blocks of the impedance matrix becomes insufficient to approximate the whole dense matrix. We present here an extension of the near-filed matrix iterative preconditioner applied in the context of the Nested-FMM-FFT algorithm, which is a bi-level variation of the original FMM-FFT. The new preconditioner extends the information of the near-field matrix allowing a closer approximation to the complete problem.