kerautret / adaptivegriddiscretizations

Adaptive schemes for anisotropic PDEs on cartesian grids

Adaptive Grid Discretizations using Lattice Basis Reduction (AGD-LBR)

A set of tools for discretizing anisotropic PDEs on cartesian grids

This repository contains

• the agd library (Adaptive Grid Discretizations)
• a series of jupyter notebooks in the Python® language, reproducing my research in Anisotropic PDE discretizations and their applications.

The AGD library

The recommended way to install is

conda install agd -c agd-lbr --force

The notebooks

The notebooks are intended as documentation and testing for the adg library. They encompass:

• Anisotropic fast marching methods, for shortest path computation.
• Non-divergence form PDEs, including non-linear PDEs such as Monge-Ampere.
• Divergence form anisotropic PDEs, often encountered in image processing.
• Algorithmic tools, related with lattice basis reduction methods, and automatic differentiation.

The notebooks can be visualized online, view summary online, or executed and/or modified offline. For offline consultation, please download and install anaconda or miniconda.
Optionally, you may create a dedicated conda environnement by typing the following in a terminal:

conda env create --file agd-hfm.yaml
conda activate agd-hfm

In order to open the book summary, type in a terminal:

jupyter notebook Summary.ipynb

Then use the hyperlinks to navigate within the notebooks.