Metadata-Version: 2.1
Name: MonotoneScheme
Version: 0.0.4
Summary: Python wrapper for the monotone discretization problem in 2D and 3D Cartesian grids (join work with Jeff Calder (UMN))
Home-page: https://github.com/wonjunee/monotone-scheme
Author: Wonjun Lee
Author-email: wlee@ucla.edu
License: UNKNOWN
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Requires-Python: >=3.6
Description-Content-Type: text/markdown
Requires-Dist: numpy
Requires-Dist: scipy
Requires-Dist: scikit-learn
Requires-Dist: matplotlib

# monotone schemes for solving curvature motion PDEs

## by Jeff Calder (UMN) and Wonjun Lee (UMN)

---
## Outline
This repository contains c++ and python codes for running the monotone algorithm to solve curvature motion PDEs. Here are list of PDEs that can be solved using this algorithm.

### Eikonal equation
$$ |\nabla u(x)| = f(x), \quad x \in \Omega $$
$$ x = 0, \quad x \in \partial \Omega $$

### Mean curvature PDE
$$ |\nabla u(x)|\kappa(x) = f(x), \quad x \in \Omega $$
$$ x = 0, \quad x \in \partial \Omega $$
where $\kappa(x) = - \text{div}\left( \frac{\nabla u}{|\nabla u|} \right)$ is the mean curvature of the level set surface of $u$ passing through $x$.

### Tukey Depth
$$ |\nabla u(x)| = \int_{(y-x)\cdot \nabla u(x) = 0} \rho(y) dS(y), \quad x \in \Omega.$$



---
## Tutorial

### Prerequisite

- `pip`
- `python >= 3.6`

Follow this link to see the instruction for the installation of `pip`: [https://pip.pypa.io/en/stable/installation/](https://pip.pypa.io/en/stable/installation/).


### Installing the package

First install the package by running the following command:
```
    pip install MonotoneScheme
```

(TO BE CONTINUED)

