A novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving 3D electromagnetic scattering by integral equation. This multilevel formatted preconditioning is derived from the hierarchical data structure of hierarchical (H-) matrix, which overcomes the construction restrict of conventional SAI preconditioner combined with popular fast algorithms like multilevel fast multipole algorithm (MLFMA). Numerical experiments have demonstrated that this proposed preconditioner has a good property, can achieve fast convergence even for very complex structures.
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