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Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 161 > pp. 19-33
## FAST LOW-FREQUENCY SURFACE INTEGRAL EQUATION SOLVER BASED ON HIERARCHICAL MATRIX ALGORITHMBy T. Wan, Q. I. Dai, and W. C. Chew
Abstract:
A fast low-frequency surface integral equation solver based on hierarchical matrix algorithm is proposed. First, the augmented electric field integral equation (A-EFIE) formulation is introduced to eliminate the low-frequency breakdown of traditional EFIE. To deal with large-scale problems, the low-frequency multilevel fast multipole algorithm (LF-MLFMA) is employed to construct a hierarchical ( H-) matrix representation of the A-EFIE system matrix. Moreover, a recompression method is developed to further compress the H-matrix generated by LF-MLFMA. The H-matrix-based triangular factorization algorithm can be performed with almost linear computational complexity and memory requirement, which produces a fast direct solver for multiple right-hand-side (RHS) problems, and a good preconditioner to accelerate the convergence rate of an iterative solver. Numerical examples demonstrate the effectiveness of the proposed method for the analysis of various low-frequency problems.
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