2D Adaptive Mesh Refinement (AMR) (QuadTree)

A tiny, pure-NumPy/Matplotlib demo of 2D adaptive refinement on a scalar field. It refines a quadtree mesh where the field varies rapidly, so you see more cells clustered around sharp features (e.g., a narrow Gaussian peak or a step).

Features

• Minimal quadtree mesh (amr/mesh.py)
• Field definitions with sharp features (amr/domain.py)
• Simple error indicators: corner range (max−min) and center gradient (amr/error_indicator.py)
• One-step or multi-iteration refinement driver (amr/refine.py)
• Visualization helpers for mesh, points, field contours, and error shading (amr/visualize.py)
• Command-line runner: run_demo.py

Install

python -m venv .venv
source .venv/bin/activate  # Windows: .venv\Scripts\activate
pip install -r requirements.txt

Run examples

Refine a narrow Gaussian peak and show mesh, point distribution, and contours:

python run_demo.py --field gaussian --x0 0.55 --y0 0.55 --sigma 0.03   --seed-splits 2 --iters 3 --plot mesh points contours

Refine using the center-gradient indicator and save a figure:

python run_demo.py --method center_gradient --plot mesh error --save demo.png

Try a discontinuous step in x or a circular disc:

python run_demo.py --field step_x --x0 0.4 --plot mesh error
python run_demo.py --field circle_step --cx 0.6 --cy 0.5 --r 0.2 --plot mesh contours

Repo layout

amr2d/
├─ run_demo.py
├─ requirements.txt
├─ README.md
├─ amr/
│  ├─ __init__.py
│  ├─ domain.py
│  ├─ mesh.py
│  ├─ error_indicator.py
│  ├─ refine.py
│  └─ visualize.py
└─ .gitignore

Notes

• If you omit --threshold, the top --top-fraction (default 0.2) of cells by error are refined each iteration.
• The demo’s 2:1 balancing pass is intentionally simple and O(N²); leave --balance off unless you need it.