Fast direct high frequency MoM solver using Butterfly algebra
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, achieving N log2 N, or “pseudo-linear” complexity per iteration. For direct solvers, pseudo-linear complexity has remai...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/448597 |
| Acceso en línea: | https://hdl.handle.net/2117/448597 https://dx.doi.org/10.1109/TAP.2025.3627867 |
| Access Level: | acceso abierto |
| Palabra clave: | Computational electromagnetics Method of Moments Direct solvers Butterfly decomposition Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal |
| Sumario: | 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, achieving N log2 N, 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 be N3/2 logN, 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 yield N log4 N complexity. |
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