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An incomplete LU (ILU) preconditioner using the near-field matrix of the fast multipole method (FMM) is investigated to increase the efficiency of the iterative conjugate gradient squared (CGS) solver. Unlike the conventional LU, ILU requires no fill ins, and hence no extra memory and CPU time in computing the LU decomposed preconditioner. It is shown that, due to the nature of the near-field matrix, ILU preconditioning decreases the number of iterations dramatically.
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Sertel et al. (2000) studied this question.
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