Fast Direct High-Frequency MoM Solver Using Butterfly Algebra
Year: 2025
Type: article
Abstract: Butterfly decomposition is a powerful method for compressing the Method of Moments impedance matrix at arbitrarily high frequency. It has been used to accelerate iterative solvers, achievingNlog2N, or “pseudo-linear” complexity per iteration. For direct solvers, pseudo-linear complexity has remained elusive. Presently, the lowest complexity achieved for high frequency impedance matrix factorization appears to beN3/2logN, with an algorithm based on Butterfly decomposition. Further improvement requires an efficient Butterfly algebra, itself of pseudo-linear complexity. This paper introduces such an algebra, including summation, multiplication, concatenation and splitting of Butterfly decompositions. It is applied to matrix factorization, which is demonstrated both theoretically and through numerical examples to yieldNlog4Ncomplexity.
Authors: Alex Heldring, Eduard Ubeda, Juan M. Rius
Institution: Universitat Politècnica de Catalunya
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,645
Awards: G1175115578, G1720063283, G2038104832, G2262748287, G24120701, G2601397997, G288263039, G294895050, G300979063, G3080236146, G3461529875, G3480869486, G3577311703, G3681454997, G4042783231, G425668148, G4584320707, G464105488, G5080475149, G5195188938, G5852091828, G586857820, G6917280427, G7000471414, G7084143925, G8389516595
OpenAlex ID: W4415971185
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