Simulation Convergence Metrics
==============================

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

.. list-table::
   :header-rows: 1

   * - #
     - 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.