Metadata-Version: 2.1
Name: monotonescheme
Version: 0.0.19
Summary: Python wrapper for C++ codes for the monotone scheme for curvature-driven PDEs
Home-page: https://github.com/wonjunee/monotone-scheme
Author: Wonjun Lee
Author-email: wlee@ucla.edu
License: UNKNOWN
Description: # Monotone schemes for curvature-driven PDEs
        
        ## by Jeff Calder (UMN)  and Wonjun Lee (UMN)
        
        - Paper: [arXiv](https://arxiv.org/abs/2310.08450)
        - Jeff Calder, School of Mathematics, University of Minnesota: [website](https://www-users.cse.umn.edu/~jwcalder/)
        - Wonjun Lee, Institute for Mathematics and Its Applications, Uniersity of Minnesota: [website](https://wonjunee.github.io)
        
        ---
        # Introduction
        This repository contains C++ and python codes for running the monotone algorithm to solve curvature-driven PDEs. Here are list of PDEs that can be solved using this algorithm. Let $\Omega = [0,1]^d$ be a domain in $\mathbb{R}^d$ and $\partial \Omega$ be a boundary of $\Omega$.
        
        ### Eikonal equation
        $$ |\nabla u(x)| = f(x),\quad  x \in \Omega $$
        
        $$ u(x) = 0,\quad  x \in \partial \Omega $$
        
        ### Mean curvature PDE
        $$|\nabla u(x)|\kappa(x) = f(x),\quad  x \in \Omega $$
        
        $$ u(x) = 0,\quad  x \in \partial \Omega $$
        
        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 $x$.
        
        ### Affine flows PDE
        
        $$|\nabla u(x)|\kappa(x)_+^{\alpha} = f(x),\quad  x \in \Omega $$
        
        $$u(x) = 0,\quad  x \in \partial \Omega $$
        
        where $\alpha \in (0,1]$ is a constant depending on the dimension $d$ and $(t)_+ := \max(0,t)$.
        
        ### Tukey Depth
        
        $$ |\nabla u(x)| = \int_{(y-x)\cdot \nabla u(x) = 0} \rho(y) dS(y),\quad  x \in \Omega $$
        
        $$ u(x) = 0,\quad  x \in \partial \Omega $$
        
        
        
        ---
        # Tutorial
        
        ## Prerequisites
        
        - `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
        
        Install the package by running the following command:
        ```
            pip install monotonescheme
        ```
        
        ## Running the codes
        
        You can find the example python script files and notebook files in ``tests`` folder. The notebook files in the folder solve the following problems:
        
        1. Affine flows in 2D Cartesian grid. 
        
        - [affine_PDE_2D.ipynb](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/affine_PDE_2D.ipynb)
        - [affine_PDE_2D.py](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/affine_PDE_2D.py)
        
        <!-- ![Alt text](https://github.com/wonjunee/monotone-scheme/blob/v1/figures/affine2d.png) -->
        
        2. Tukey depth eikonal equation in 2D Cartesian grid.
        
        - [tukey_PDE_2D.ipynb](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/tukey_PDE_2D.ipynb)
        - [tukey_PDE_2D.py](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/tukey_PDE_2D.py)
        
        <!-- ![Alt text](https://github.com/wonjunee/monotone-scheme/blob/v1/figures/tukey2d.png) -->
        
        3. Motion by curvature PDE in 3D Cartesian grid.
        
        - [curvature_PDE_3D.ipynb](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/curvature_PDE_3D.ipynb)
        - [curvature_PDE_3D.py](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/curvature_PDE_3D.py)
        
        <!-- ![Alt text](https://github.com/wonjunee/monotone-scheme/blob/v1/figures/square-3d.png) -->
        
        4. Eikonal equation and Tukey depth eikonal equation in unstructured grids
        
        - Eikonal equations
            - [Eikonal_PDE_graph.ipynb](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/Eikonal_PDE_graph.ipynb)
            - [Eikonal_PDE_graph.py](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/Eikonal_PDE_graph.py)
        - Tukey depth eikonal equations
            - [tukey_PDE_graph.ipynb](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/tukey_PDE_graph.ipynb)
            - [tukey_PDE_graph.py](https://github.com/wonjunee/monotone-scheme/blob/v1/tests/tukey_PDE_graph.py)
        
        <!-- ![Alt text](https://github.com/wonjunee/monotone-scheme/blob/v1/figures/point_cloud.png) -->
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
