Numerical Experiments and Reproducible Code for the QBMAX Paper

This project contains numerical experiments and reproducible code for the QBMAX paper.

Dependencies

This project depends on pytential. We strongly recommend following the official install guide: https://documen.tician.de/pytential/misc.html

Examples Structure

Below are the code examples included in the repo. For other numerical test results, code is available upon request.

QBMAX Paper Examples
├── 2D Problems
│   ├── Circle Domain
│   │   └── Close evaluations of single and double layer potentials
│   └── Starfish Domain
│       ├── Close evaluation of double layer potentials
│       ├── Jump relations of double layer potentials
│       ├── Oscillatory Helmholtz
│       └── Interior Neumann BVP
├── 3D Problems
│   └── Cruller
│       └── Jump relations of double layer potentials
└── Cost Analysis
    └── Weighted operation counts of QBX and QBMAX expansions (SymPy)

The interior Neumann example runs both QBX and QBMAX, stores the relative error of each evaluation, and reproduces the convergence figure of the paper from the saved Neumann.pkl. The cost-analysis scripts regenerate flop_count_2d.pkl and flop_count_3d.pkl (symbolic differentiation up to order 8, which takes a while) and plot_flop_count.py draws the figure from them.