A butterfly-based fast direct integral equation solver for analyzing high-frequency scattering from two-dimensional objects is presented. The solver leverages a randomized butterfly scheme to compress blocks corresponding to near- and far-field interactions in the discretized forward and inverse electric field integral operators. The observed memory requirements and computational cost of the proposed solver scale as O(N log2N and O(N1.5log N) , respectively. The solver is applied to the analysis of scattering from electrically large objects spanning over 10 000 wavelengths and modeled in terms of five million unknowns.
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