A complexity-reduced H-matrix based direct integral equation solver with prescribed accuracy for large-scale electrodynamic analysis

In this work, by further developing the ℌ-matrix based mathematical framework, we achieved an efficient LU-factorization based direct IE solver of k²_aveC²_spO(N log² N) time complexity and k_aveC_spO(N log N) memory complexity, with the two parameters k_ave and C_sp minimized, with the prescribed accuracy satisfied, to solve large-scale electrodynamic problems. The k_ave is a weighted average rank we introduce to derive the complexity bounds for the ℌ-matrix-based computation of electrodynamic problems. It is introduced based on the fact that the rank required by an electrodynamic system for a given accuracy is a variable with respect to tree levels and admissible blocks, and hence existing constant-rank based complexity analysis does not apply.