Simulation Convergence Metrics

Numerical-quality checks for adaptive passes, mesh size, energy error, S-parameter convergence, and RAM use.

#	VER ID	Parameter	Severity	Design Rule / Constraint	Ideal / Optimal Value	Acceptable Range	Good	Bad	Why It Matters
48	HFSS-V-001	Delta S Convergence (ΔS)	Critical	ΔS < 0.002 (max |S-matrix change| between passes)	< 0.001	0.001 – 0.005	< 0.001: S-parameters converged to 3rd decimal place; Q-factor reliable to ±1%	> 0.01: S-parameters still shifting; Q and coupling coefficients unreliable	Primary HFSS convergence criterion. Maximum change in S-parameter matrix between successive adaptive mesh refinement passes.
49	HFSS-V-002	Adaptive Pass Count	Medium	Converge within 6 – 15 adaptive passes	6 – 12 passes	6 – 25 passes	6–12 passes: efficient meshing; geometry well-suited to HFSS basis functions	> 40 passes without convergence: poorly conditioned geometry or material error; abort and review	Number of mesh refinement iterations to reach ΔS criterion. Many passes indicates difficult geometry or incorrect material setup.
50	HFSS-V-003	Mesh Element Count	Medium	10,000 – 500,000 tetrahedra for typical qubit geometry	20k – 100k	10k – 500k	20k–100k: sufficient resolution for junction, pad, and resonator without excessive RAM	> 1,000,000: direct solver RAM > 256 GB; iterative solver with lower accuracy required	Total finite-element mesh size. Under-meshed → inaccurate fields; over-meshed → excessive compute cost and RAM.
51	HFSS-V-004	Energy Error Δε/ε	High	Energy error < 0.5% (relative stored energy error)	< 0.2 %	0.2 – 1 %	< 0.2%: field solution accurate; participation ratios and Q-factors reliable to < 1%	> 2%: field solution inaccurate; EPR and loss calculations may be off by > 10%	Relative error in total stored electromagnetic energy. Low energy error confirms accurate field solutions and Q-factor extraction.
52	HFSS-V-005	Simulation RAM Usage	Low	Peak RAM < 64 GB for standard qubit simulation	< 16 GB	16 – 64 GB	< 16 GB: fits standard workstation; direct solver; fastest and most accurate	> 128 GB: requires HPC cluster; iterative solver fallback; convergence harder	RAM required for direct matrix solver. Excess forces iterative solver with lower accuracy and convergence risk.