What is convergence-study?

A workflow for checking whether numerical simulation results change as the mesh or time step becomes finer. It uses refinement studies to estimate accuracy and convergence.

Computing observed convergence rates, estimating values with Richardson extrapolation, estimating error, and calculating the Grid Convergence Index for spatial or time refinements.

It helps reveal whether an answer is approaching a stable value or is still affected by discretization error.

convergence-study — Skill for Claude Code by HeshamFS

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent

npx skills add HeshamFS/materials-simulation-skills --skill convergence-study

Clone the repo

git clone --depth 1 https://github.com/HeshamFS/materials-simulation-skills

Made for: Claude Code.

Or install verification-and-validation, the plugin that ships this one along with the rest of its 4 skills.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

README.md

[![agentmods](https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/convergence-study/github.svg)](https://agentmods.dev/skills/heshamfs/materials-simulation-skills/convergence-study)

Your own site

<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/convergence-study"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/convergence-study/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

Your own site · 80×15

<a href="https://agentmods.dev/skills/heshamfs/materials-simulation-skills/convergence-study"><img src="https://agentmods.dev/badge/skills/heshamfs/materials-simulation-skills/convergence-study.svg" alt="Reviewed on agentmods" width="80" height="20"></a>

Per session 116 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.

When invoked 3,106 The whole file, excluding the scripts and references it only reads on demand.

Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.

Origin original No closer match found in the catalogue.

Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

Model	Per session	Once invoked
Fable 5.1	$0.00116	$0.03106
Opus 5.5	$0.00046	$0.01242
Sonnet 5.5	$0.00023	$0.00621
Haiku 4.5	$0.00012	$0.00311

Measured 2d ago against content hash 2fb1169ce9a7, method: parsed. Prices are Anthropic first-party input rates as of 2026-10-07, from the pricing page.

Security

Grade A, and why

convergence-study scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 2d ago.

The scan reads SKILL.md. This mod also ships 5 executable files (scripts/_support/refinement_order.py, scripts/dt_refinement.py, scripts/gci_calculator.py, …), listed below but not scanned — reading those needs a real analyzer, not pattern matching.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

skills/core-numerical/convergence-study/SKILL.md · 199 lines

How it starts

The opening of the file, as written. The whole thing — 199 lines — stays where its author put it; the contents beside it link to each section on GitHub.

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 3.10+
No third-party packages — scripts use only the Python standard library (math).

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`, `results.gci_fine`, `results.gci_coarse`, `results.asymptotic_ratio`, `results.in_asymptotic_range`, `results.extrapolated_value`, `results.notes`

Workflow

Run grid/timestep refinement study with at least 3 levels
Compute observed convergence order with h_refinement.py or dt_refinement.py
Compare observed order to expected order of the scheme
Estimate discretization error via Richardson extrapolation
Report GCI for formal solution verification using gci_calculator.py
Document convergence results and any anomalies

Decision Guidance

Do you have 3+ refinement levels?
+-- YES --> Run h_refinement.py or dt_refinement.py
|           +-- Observed order matches expected? --> Order agreement; check persistence and error assumptions
|           +-- Order too low? --> Check: pre-asymptotic, coding error, insufficient resolution
|           +-- Order too high? --> Check: superconvergence or cancellation effects
+-- NO (only 2 levels) --> Use richardson_extrapolation.py with assumed order
                           (less reliable without order verification)

Read the full file on GitHub · 199 lines

Files

What ships with it

9 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

2d ago Changed · +20 lines 2fb1169ce9a7
1mo ago First seen · 179 lines · 116 tokens per session scan A f08864b34236

Subscribe to this mod's changes

convergence-study is a skill published in the GitHub repository HeshamFS/materials-simulation-skills (83 stars, last pushed 2d ago), licensed Apache-2.0. It adds 116 tokens to every session and 3,106 once invoked, about $0.0005 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.

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