# chunkie examples

An interactive companion to
[chunkie](https://github.com/fastalgorithms/chunkie) — a MATLAB package for
boundary integral equations in two dimensions. Everything here runs in your
browser through [numbl](https://numbl.org): pick a script on the left and click
**Run**.

Every script begins with

```matlab
mip load --install magland/magland/chunkie
```

which fetches chunkie on first use.

## Geometry

chunkie represents a curve as a `chunker`: a panelization into high-order
Gauss-Legendre chunks.

- [`chunkie_ex01_circle.m`](chunkie_ex01_circle.m) — chunk up a circle; plot
  points and normals.
- [`chunkie_ex02_bymode.m`](chunkie_ex02_bymode.m) — a star-shaped curve from a
  Fourier series for the radius.
- [`chunkie_ex03_starfish.m`](chunkie_ex03_starfish.m) — the classic starfish.
- [`chunkie_ex04_chunkerfit.m`](chunkie_ex04_chunkerfit.m) — fit a smooth curve
  to sample points (`chunkerfit`).
- [`chunkie_ex05_barbell.m`](chunkie_ex05_barbell.m) — a rounded polygon
  (`chunkerpoly`).
- [`chunkie_ex06_combined.m`](chunkie_ex06_combined.m) — transform and merge
  several curves into one multi-component domain.
- [`chunkie_ex07_interior.m`](chunkie_ex07_interior.m) — find which points lie
  inside a domain (`chunkerinterior`).

## Solving integral equations

Each PDE is recast as a boundary integral equation, discretized with
`chunkermat`, solved with GMRES, and evaluated on a grid with
`chunkerkerneval`.

- [`chunkie_ex00_starfish.m`](chunkie_ex00_starfish.m) — Helmholtz scattering
  off a starfish (combined-field representation).
- [`chunkie_ex08_laplace.m`](chunkie_ex08_laplace.m) — a Laplace Neumann
  problem (single-layer with nullspace regularization).
- [`chunkie_ex09_helmholtz.m`](chunkie_ex09_helmholtz.m) — sound-soft Helmholtz
  scattering off a peanut.
- [`chunkie_ex10_stokes.m`](chunkie_ex10_stokes.m) — Stokes flow through a
  multiply-connected pipe.

## How it's deployed

On every push to `main`, the workflow in
[`.github/workflows/deploy.yml`](.github/workflows/deploy.yml) bundles these
files with the numbl browser IDE and publishes the result to GitHub Pages. Edit
`numbl-project.json` to change the title or which file opens first.