## 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.

### 1. Fast Marching Methods¶

• A. Isotropic and anisotropic metrics

• B. Non holonomic metrics and curvature penalization

• C. Algorithmic enhancements to the fast marching method

• D. Application examples

• E. Seismology and crystallography

• F. Applications

### 2. Non-divergence form PDEs¶

• A. One space dimension

• B. Monotone numerical schemes

• C. Eikonal equation and variants

• D. Time dependent optimal control

### 3. Divergence form PDEs¶

• A. One space dimension

• B. Static problems

• C. Linear elasticity

• D. Applications

### 4. Algorithmic tools¶

• A. Tensor decomposition techniques

• B. Generalized acuteness

• C. Automatic differentiation

• D. Domain representation

• E. Convex functions and convex bodies

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