In this article, a new method called fast directional multilevel algorithm (FDMA) is proposed for three-dimensional electromagnetic problems. Combined with the Caldron identities of Calderon multiplicative preconditioner (CMP), the new algorithm has a fast convergence rate of iterative solvers and is stable at low frequency for the electrical field integral equation solutions. Like the fast multipole method, octree structure is used in our proposed algorithm. However, the new algorithm does not require the implementation of multipole expansions of the Green's function but based only on kernel evaluations. It does not suffer from low-frequency breakdown when the discretization density is high. The numerical results demonstrate that the CMPpreconditioned FDMA leads to significant reduction of both the iteration number and the computer processing use (CPU) time for radar cross section (RCS) calculation.
In this paper, a new method called fast directional multilevel algorithm is preconditioned by an efficient Calderon multiplicative preconditioner (CMP) for three-dimensional (3-D) electromagnetic problems. The new algorithm does not require the implementation of multipole expansions of the Green's function but based only on kernel evaluations. Combined with the Caldron identities of the CMP, the new algorithm has a fast convergence rate of iterative solvers and is stable at low frequency for the electrical field integral equation (EFIE) solutions. The numerical results demonstrate that the CMP preconditioned FDMA leads to significant reduction of both the iteration number and the CPU time for RCS calculation.
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