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...

Descripción completa

Detalles Bibliográficos
Autores: Heldring, Alexander|||0000-0003-2011-2096, Úbeda Farré, Eduard|||0000-0001-6759-0445, Rius Casals, Juan Manuel|||0000-0003-0606-5422
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
Descripción
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.