Efficient Algorithm Based on the Woodbury Formula for Modeling Multi-port Antenna Systems

Rufina M. Tretiakova; Alexey V. Setukha; Ilya A. Mass

doi:10.14529/jsfi250404

Authors

Rufina M. Tretiakova Research Computing Center, Lomonosov Moscow State University, Moscow, Russian Federation; Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation https://orcid.org/0000-0002-1814-9140
Alexey V. Setukha Research Computing Center, Lomonosov Moscow State University, Moscow, Russian Federation; Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation https://orcid.org/0000-0003-1173-0976
Ilya A. Mass Research Computing Center, Lomonosov Moscow State University, Moscow, Russian Federation; Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation

DOI:

https://doi.org/10.14529/jsfi250404

Keywords:

matrix methods, numerical algorithms, computational electrodynamics, antenna radiation, boundary integral equations, Woodbury formula

Abstract

This work presents an efficient computational approach for modeling antenna systems with multiple ports using boundary integral equations. The method employs the RWG basis functions within the Galerkin scheme to evaluate for surface currents. A key challenge addressed is the repeated solution of linear systems when calculating mutual coupling characteristics (impedance matrix, S-parameters, VSWR) for various port loading conditions. To overcome this, an algorithm based on the Woodbury formula is developed, significantly reducing computational costs by leveraging the low-rank nature of port-related matrix modifications. The method's effectiveness is demonstrated for both wire and patch antenna arrays, showing substantial speedups—approximately proportional to the number of ports for direct solvers and significant gains for iterative solvers using mosaic-skeleton approximations while maintaining solution accuracy.

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