In the iterative solution of the matrix equation arising from the multilevel fast multipole algorithm (MLFMA), sparse approximate inverse (SAI) preconditioner is widely employed to improve convergence property. In this paper, based on the geometric information of nearby basis functions pairs and finer octree grouping scheme, a new sparse pattern selecting strategy for SAI is proposed to enhance robustness and efficiency. Compared to the conventional selecting strategies, the proposed strategy has only one variable parameter instructing the constructing time and memory usage, which is more user friendly. Numerical results show that the proposed strategy can make use of the non-zero entries of near-field matrix in MLFMA more effectively and elaborately without compromising the numerical accuracy and the natural parallelization of SAI.
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