RapidMoM

2.5D Method-of-Moments for planar RF passives on layered substrates.

RapidMoM is a 2.5D Method-of-Moments solver for planar RF passives on layered substrates: PCB and RFIC, from single inductors and transformers to full metal layouts on a real process stack. The formulation is a mixed-potential surface integral equation with an RWG basis, an A-EFIE saddle-point system against the low-frequency breakdown (stable down to DC), layered-media Green's functions in the Michalski-Mosig formulation, and a kernel-independent ACA / H-matrix fast solver with block-GMRES in O(N log N).

Converging the network, not the residual

A GMRES residual bounds the algebraic error, but a port observable can be a small difference of large quantities (that is exactly what a quality factor is) or live in a different block of the saddle system entirely. RapidMoM therefore continues the solve down a tolerance ladder, warm-started, until the port-space network itself stops moving, including a dedicated criterion for the real part. Every port configuration lands on the dense-operator answer instead of drifting with the iterative tolerance.

Ports are one primitive: a current driven between two contacts, each an oriented segment on a metal layer. The excitation is a voltage source across the gap, never an imposed current profile, so edge singularity and skin crowding come out of the solve. Ambiguous port placements are rejected in a preflight instead of guessed.

Conductor models and outputs

Two production conductor models are available per layer. The sheet model is the classical 2.5D treatment: one RWG current sheet per metal with the two-sided skin-effect surface impedance, the right default for thin metals. The boxed model treats each conductor as a closed thick box with the conductor interior entering through the slab internal-impedance two-port. Output is standard Touchstone (S, Y, Z) plus the extracted device metrics engineers actually design against: L, Q, coupling.

Validation runs against closed-form analytics, physical invariants (Lorentz reciprocity, mutual-sign checks, skin-effect rise), and an independent reference solver on controlled cases before any device claim is made. The evaluation report is fully auto-generated from the same pipeline, so every number is reproducible.

Built for sweeps

Zero-external-dependency pure Rust with a Python API: lightweight, installs in seconds, built for massive cloud parameter sweeps. Solver controls are first-class API (tolerances, warm-started sweeps, feed de-embedding), so embedding needs no environment variables. Broadband S-parameters of an SG13G2 spiral come out of a ROM sweep in about 5 seconds within roughly 600 MB, validated on the real IHP SG13G2 stack.

History

RapidMoM development started in June 2026, in the same push that produced RapidMesh and RSLAB : the planar solver, its mesher, and its linear algebra grew together as one vertically integrated unit. The solver is in early access for evaluation.