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

The Integral equation (IE) based computational electromagnetic methods generally lead to a dense system of linear equations, the solution of which could be very expensive. Recently, fast solvers [1–3] such as FMM-based methods, fast low-rank compression methods, FFT-based methods, and H2-matrix based methods have been developed, which dramatically reduce the memory and CPU time of iterative IE solvers for electrodynamic problems. Fast direct solvers have also been developed. LU factorization of O(N2) time complexity and O(N1.5) memory complexity was reported [4]. Compared to iterative solvers, direct solvers have advantages when the number of iterations or the number of right hand sides is large.

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