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For the electrically large problems, the discrete unknowns of surface integral equation are very large, resulting in the matrix condition is relatively poor. The high order hierarchical basis functions are utilized to reduce the discrete unknowns, thereby reducing the memory consumption and computation time. Meanwhile, modified multilevel compressed block decomposition (MMLCBD) is applied to accelerate the matrix-vector multiplication operations, which utilizes novel technique to improve the solving efficiency by combining a less accurate truncating threshold in MLCBD with a rapid and cheap iterative refinement process. Combining the high order hierarchical basis functions with MMLCBD can make good use of their respective advantages to analyze the large-scale electromagnetic problems efficiently. The numerical results demonstrate that the proposed method is much more efficient than conventional MLCBD for analyzing the large-scale electromagnetic problems. [ABSTRACT FROM AUTHOR]