Adaptive HODBF-Based Direct Surface Integral Equation Solver for Electromagnetic Analysis

An adaptive hierarchically off-diagonal butterfly direct solver (A-HODBF) is proposed for fast and accurate solution of three-dimensional surface integral equations (SIE). The novel generalized admissibility condition (GAC) is put forward to enable refined control of the butterfly rank (BF-rank) during matrix filling and inversion phases. Numerical results show that the proposed method has a reduced complexity compared to hierarchically off-diagonal low-rank-based Matrix solver (HODLR) and has optimized leading coefficients compared to traditional BF methods, providing a scalable solution for large-scale electromagnetic problems.