gpd-numerical-convergence

Name: gpd-numerical-convergence
Availability: InStock
Author: CharlieGreenman

Validate numerical physics results via convergence testing and Richardson extrapolation.

1|Updated Mar 29, 2026

Search Tags:#validation #stability #benchmarking #convergence #numerical-analysis #richardson-extrapolation #error-estimation

Ready to run

npx skills add https://github.com/CharlieGreenman/roomtemp-superconductor-gpd --skill gpd-numerical-convergence

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: gpd-numerical-convergence
Source: https://github.com/CharlieGreenman/roomtemp-superconductor-gpd/tree/main/.agents/skills/gpd-numerical-convergence
Command: npx skills add https://github.com/CharlieGreenman/roomtemp-superconductor-gpd --skill gpd-numerical-convergence

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Systematically validating numerical results to ensure they are converged and trustworthy, by exposing discretization errors and quantifying uncertainty.

Core Features & Use Cases

Convergence studies across discretization parameters (grid size, time step, basis size, cutoff, Monte Carlo samples)
Richardson extrapolation and error budgeting to estimate true values
Benchmarking against analytical results and conservation-law checks
End-to-end validation workflow with automatic report generation

Quick Start

Run the convergence workflow on your target project to begin structured validation of numerical results.

Frequently Asked Questions about gpd-numerical-convergence

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I verify that my numerical simulation results are truly converged?▼

Numerical convergence validation systematically refines discretization parameters like grid size and time step to expose discretization errors and quantify uncertainty. This process applies Richardson extrapolation to estimate true values and confirm results are trustworthy.

What is Richardson extrapolation and how does it estimate numerical error?▼

Richardson extrapolation is an error estimation technique applied during convergence testing to project the true solution from a series of refined discretization parameters. It builds an error budget to estimate exact values and quantify numerical uncertainty.

How do I perform a convergence study for PDEs and Monte Carlo simulations?▼

Perform convergence testing by systematically refining phase-appropriate computations such as basis size for PDEs or sample count for Monte Carlo simulations. The workflow includes benchmark validation against analytical results and conservation-law checks.

Can I use convergence validation for ODEs, eigenvalue problems, and Monte Carlo simulations?▼

Yes, convergence validation applies to ODEs, PDEs, eigenvalue problems, and Monte Carlo simulations. It targets phase-appropriate computations by refining grid sizes, time steps, basis sizes, and sample counts to ensure stability and accuracy.

What is the best way to check numerical stability and conservation laws?▼

The best way involves a rigorous validation workflow combining stability analysis and conservation checks alongside convergence testing. This approach benchmarks results against analytical data to ensure numerical physics computations remain stable and physically accurate.

Why does my numerical analysis lack a structured validation report?▼

A structured validation report requires running a comprehensive workflow covering error estimation, stability analysis, and benchmarking. Completing this process automatically generates a NUMERICAL-VALIDATION.md report detailing your convergence studies and uncertainty quantification.