convergence-study
Spatial and temporal convergence analysis with Richardson extrapolation and Grid Convergence Index (GCI) for solution verification
npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill convergence-study --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Convergence Study ## Goal Provide script-driven convergence analysis for verifying that numerical solutions converge at the expected rate as the mesh or timestep is refined. ## Requirements - Python 3.8+ - NumPy (not required; scripts use only math stdlib) ## Inputs to Gather | Input | Description | Example | |-------|-------------|---------| | Grid spacings | Sequence of mesh sizes (coarse to fine) | `0.4,0.2,0.1,0.05` | | Timestep sizes | Sequence of dt values | `0.04,0.02,0.01` | | Solution values | QoI at each refinement level | `1.16,1.04,1.01,1.0025` | | Expected order | Formal order of the numerical scheme | `2.0` | | Safety factor | GCI safety factor (1.25 default) | `1.25` | ## Script Outputs (JSON Fields) | Script | Key Outputs | |--------|-------------| | `scripts/h_refinement.py` | `results.observed_orders`, `results.mean_order`, `results.richardson_extrapolated_value`, `results.convergence_assessment` | | `scripts/dt_refinement.py` | Same as h_refinement but for temporal convergence | | `scripts/richardson_extrapolation.py` | `results.extrapolated_value`, `results.error_estimate`, `results.observed_order` | | `scripts/gci_calculator.py` | `results.observed_order`, `r
- Goal
- Requirements
- Inputs to Gather
- Script Outputs (JSON Fields)
- Workflow
- Decision Guidance
- CLI Examples
- Error Handling
- Interpretation Guidance
- References
Spatial convergence with 4 grid levels python3 scripts/h_refinement.py --spacings 0.4,0.2,0.1,0.05 --values 1.16,1.04,1.01,1.0025 --expected-order 2.0 --json Temporal convergence with 3 timestep levels python3 scripts/dt_refinement.py --timesteps 0.04,0.02,0.01 --values 2.12,2.03,2.0075 --expected-order 2.0 --json Richardson extrapolation with assumed 2nd-order python3 scripts/richardson_extrapolation.py --spacings 0.02,0.01 --values 1.0032,1.0008 --order 2.0 --json GCI for 3-mesh verification python3 scripts/gci_calculator.py --spacings 0.04,0.02,0.01 --values 1.0128,1.0032,1.0008 --json
What does the convergence-study skill do?
Spatial and temporal convergence analysis with Richardson extrapolation and Grid Convergence Index (GCI) for solution verification
How do I install it?
Run `npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill convergence-study --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From FreedomIntelligence/OpenClaw-Medical-Skills, a repository with 2,909 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.