Computational results and Python files for the work "Generalizing Riemann curvature to Regge metrics"

This repository contains the code and data accompanying the numerical experiments for the paper "Generalizing Riemann Curvature to Regge Metrics". The implementation is based on the open-source Finite Element library NGSolve (www.ngsolve.org). To generate the data, we used NGSolve-version NGSolve-6.2.2506-203-gf6f7fcf3e. Overview of the scripts: - generate_test_mesh.py: generates structured 3D meshes, applies a random interior perturbation, and writes the meshes plus mesh diameters. - example_manifolds.py: defines the exact metrics and curvature tensors used as reference solutions. - compute_error.py: computes the H^{-2} error norm and stores intermediate grid functions. - test_convergence.py: runs the convergence experiments and writes tables to CSV/LaTeX. - prepare_data.py: formats convergence CSV files into LaTeX tables. Data and meshes: - meshes/: pre-generated meshes used in the experiments (published to avoid reliance on random seeds). - data/: raw pickles (.pkl) and generated tables (.csv and .tex). Typical workflow: 1) (Optional) Regenerate meshes with generate_test_mesh.py. 2) Run test_convergence.py to produce convergence data in data/. 3) Run prepare_data.py to format LaTeX tables for the paper.