A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations (EFIE) solved by method of moments (MoM). The multilevel fast multipole method (MLFMM) is used to accelerate matrix-vector product. An improved sparse approximate inverse (SAI) preconditioner in the higher order hierarchical MLFMM context is constructed based on the nearfield matrix of the EFIE. The quality of the SAI

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... itioner can be greatly improved by use of information from higher order hierarchical MLFMM implementation. Numerical experiments with a few electromagnetic scattering problems for open structures are given to show the validity and efficiency of the proposed SAI preconditioner.