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A novel preconditioner for the finite-element boundary integral analysis of electromagnetic scattering

The finite-element boundary integral method (FEBI) combining with the multilevel fast multipole algorithm (MLFMA) is well known as a powerful tool to solve the complex scattering problems. Unfortunately, because the coefficient matrix arising from the FEBI is badly conditioned, this hybrid method suffers from a very slow convergence rate with iterative solvers, and even disconverges for a very complex media. Therefore, it is necessary to use preconditioning techniques to improve the conditioning number of the system matrix and then accelerate the convergence rate. Some preconditioners have been proposed. In this paper, a more effective preconditioner is proposed, which is constructed by the finite-element part and the near-field value terms of the boundary integral, both of which can be easily obtained from the matrix of the FEBI-MLFMA with no additional computing time and store requirement. The basic idea is based on the fact that the greatest construction to the boundary integral is given by the near-field part. The numerical results of several scattering problems in the free space are presented to show the high effectiveness of the proposed preconditioner and the fast convergence of the iterative solution.