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), written in Python® and cuda®
• a series of jupyter notebooks in the Python® language (online static and interactive view), reproducing my research in Anisotropic PDE discretizations and their applications.
• a basic documentation, generated with pdoc.

The AGD library

The recommended way to install is

pip install agd

Deprecated conda package (this version does not include the GPU codes, and is not maintained)

conda install agd -c agd-lbr

Reboot of the git history (february 8th 2024)

The whole notebooks, including images and videos, were previously saved in the git history, which as a result had grown to approx 750MB. After some unsuccessful attempts with BFG, I eventually had to delete and recreate the repository.

The notebooks

You may :

• Visualize the notebooks online using nbviewer. Note : prefer to use this link to view the notebooks, rather than the present repository, which contains some notebooks in a partially evaluated state.
• Run and modify the notebooks online using GoogleColab. Note : some notebooks require turning on the GPU acceleration in GoogleColab (typical error: cannot import cupy) : Modify->Notebook parameters->GPU.

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.

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.

Matlab users

Recent versions of Matlab are able to call the Python interpreter, and thus to use the agd library. See Notebooks_FMM/Matlab for examples featuring the CPU and GPU eikonal solvers.