Adaptive grid discretizations

A set of tools for discretizing anisotropic PDEs on cartesian grids

This collection of notebooks presents is part of a reproducible research effort in the numerical analysis of partial differential equations. The emphasis is on non-linear and anisotropic problems, discretized on cartesian grids. We present:

  • The mathematical tools underlying the numerical methods, coming in particular from the field of lattice geometry
  • Reference implementations, designed to be (reasonably) efficient and pedagogical. (Except for fast marching methods, where the implementations are contained in a black-box C++ library.)
  • Test cases. Indeed, these notebooks are also intended as a test suite for the numerical libraries.
  • Application examples.

Disclaimer This series of notebooks is part of an ongoing research project. While we do have a strong focus on research reproducibility, the provided numerical codes should be regarded as experimental and come without any guarantee of any type.

Table of contents

1. Fast Marching Methods

2. Non-divergence form PDEs

3. Divergence form PDEs

4. Algorithmic tools

In [2]:
#import sys; sys.path.append("..") # Allow imports from parent directory
#from Miscellaneous import TocTools; print(TocTools.displayTOCss())