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A local multilevel fast multipole algorithm (LMLFMA) is proposed to further speed up the efficiency of the multilevel fast multipole algorithm (MLFMA), which is used to expedite the computation of matrix-vector multiplication in conjugate gradient iteration. In the present method, the coarsest level is determined by the iterative error. And at the coarsest level, the interaction between far regions is omitted. When the iterative error is less than the critical iteration error, only the interaction between nearby regions is considered. Numerical results show that the LMLFMA has a reasonable accuracy, and higher efficiency, compared with the MLFMA combined with the partly approximation iteration (PAI) technique. So it is very efficient for solution of scattering from 3D targets with electrically large sizes.