Robust preconditioning techniques for electromagnetic wave scattering problems

We investigate preconditioned iterative solutions of large dense complex valued matrices arising from discretizing the integral equation of electromagnetic scattering. The main purpose of this study is to evaluate the efficiency of preconditioning techniques based on incomplete LU (ILU) factorization and sparse approximate inverse (SAI) for solving this class of dense matrices. We solve the electromagnetic wave equations using the BiCG method with the preconditioners in the context of a multilevel fast multipole algorithm (MLFMA). The novelty of this work is that the preconditioners are constructed using the near part block diagonal submatrix generated from the MLFMA. Experimental results show that the ILU and SAI preconditioners reduce the number of BiCG iterations substantially.