warp-convergence-analysis

Performs a convergence analysis of your warp-solver by running validation tests at multiple grid spacings (Δr), computing observed convergence orders, and emitting a NDJSON convergence report.

Dependencies

• run_validation.py
  Copied from warp-solver-validation repository
  Validation script that accepts --h parameter for grid spacing

• solver.py
  Copied from warp-solver-validation repository
  Solver implementation with integrate_step() function

• solver_update.tex
  Copied from warp-solver-equations repository
  Contains solver equation definitions and stencil information

• Python 3.7+

• numpy

Inputs

• run_validation.py
  Validation script that runs warp solver with specified grid spacing (copied from warp-solver-validation)

• solver.py
  Solver implementation (copied from warp-solver-validation)

• solver_update.tex
  Contains solver equations and finite difference stencils (copied from warp-solver-equations)

Outputs

• convergence.ndjson
  Newline-delimited JSON file containing:
  • Header record with study metadata
  • Test records with error data at each grid spacing
  • Order records with computed convergence rates between successive grid refinements

Repository Structure

warp-convergence-analysis/  
├── convergence_analysis.py ← main analysis script  
├── run_validation.py ← validation script from warp-solver-validation
├── solver.py ← solver implementation from warp-solver-validation
├── solver_update.tex ← solver equations and stencils
└── convergence.ndjson ← generated NDJSON convergence report

Usage

1. Make sure input files are available
   Ensure run_validation.py, solver.py, and solver_update.tex exist in the repository.

2. Run convergence analysis

python convergence_analysis.py

This:

• Calls run_validation.py --h=<h> for each grid spacing in the study
• Parses the stdout output to extract L₂ and L∞ errors
• Computes observed convergence orders between successive grid refinements
• Produces convergence.ndjson with newline-delimited JSON records containing convergence data

3. View the report
   Parse convergence.ndjson with any NDJSON-compatible tool, or process it line by line as JSON objects.

How It Works

The script:

1. Runs run_validation.py --h=<h> for each grid spacing in hs = [0.1, 0.05, 0.025, 0.0125]
2. Parses the stdout output using regex to extract L₂ and L∞ errors for each test case
3. Computes observed convergence orders between successive grid refinements
4. Outputs structured convergence data in NDJSON format

Customization

• Adjust hs = [ … ] in convergence_analysis.py to change grid spacings Δr
• Extend tests = [ … ] to add new test cases; the script will parse their errors from run_validation.py output

Scope, Validation & Limitations

• Scope: The materials and numeric outputs in this repository are research-stage examples and depend on implementation choices, parameter settings, and numerical tolerances.
• Validation: Reproducibility artifacts (scripts, raw outputs, seeds, and environment details) are provided in docs/ or examples/ where available; reproduce analyses with parameter sweeps and independent environments to assess robustness.
• Limitations: Results are sensitive to modeling choices and discretization. Independent verification, sensitivity analyses, and peer review are recommended before using these results for engineering or policy decisions.