Updatable Closed‐Form Evaluation of Arbitrarily Complex Multiport Network Connections

ABSTRACT The inverse design of electrically large wave devices often leverages reduced‐order multiport models combined with discrete optimization, which requires repeated evaluations of complex interconnections of multiport subsystems that differ only in a few constituent blocks. Rather than reevaluating each configuration from scratch, this work introduces a computationally efficient method that reuses previous evaluations via low‐rank updates based on the Woodbury matrix identity. A closed‐form framework for arbitrarily complex connection schemes of multiport networks is formulated. Unified equivalence principles for interpretations of subsystem connections are presented and leveraged to reduce the computational burden of the closed‐form approach. Moreover, a closed‐form expression for the power waves travelling through connected ports is derived. The method is demonstrated on a meta‐network with serial, parallel, and cyclic connections among multiport subsystems, and validated with physics‐compliant analytic calculations on graph‐based subsystems. Exhaustive statistical analyses quantify the computational benefits arising from reducibility and updatability across problem sizes. Finally, it is shown that working with scattering parameters, rather than impedance or admittance parameters, confers a fundamental numerical advantage for an important class of connection schemes whose closed‐form analysis treats some links as delayless, lossless, reflectionless, reciprocal two‐port scattering systems.