# An HSS-Matrix-Based Fast Direct Solver with Randomized Algorithm

## Keywords:

Electric field integral equation, HSS matrix, randomized algorithm## Abstract

Discretization of the electric field integral equation (EFIE) generally leads to dense impedance matrix. The resulting matrix, however, can be compressed in sparsity based on hierarchical structure and low rank approximation. In this paper, we propose an HSS-matrix-based fast direct solver for surface integral equation (SIE) that has a compression complexity of O(rN2) to analysis the large-scale electromagnetic problems, where r is a modest integer. The proposed solver efficiently compresses the dense matrices using a randomized algorithm and requires modest memory. Efficiency and accuracy is validated by numerical simulations. In addition, being an algebraic method, the HSS-matrix-based fast solver employs Green’s kernels and hence is suitable for other integral equations in electromagnetism.

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*The Applied Computational Electromagnetics Society Journal (ACES)*,

*33*(07), 814–817. Retrieved from https://journals.riverpublishers.com/index.php/ACES/article/view/9091