Some working examples

In the following pages, you will find some notebooks showcasing the Dxtr library in action.

• The Poisson problem. This is the well-known "Hello world!" boundary value problem. In this notebook we show how to instanciate it in DEC and checks the accuracy of the solutions.
• Accuracy of the exterior derivatve. The exterior derivative is the founding operator of DEC. It is therefore crutial to estimate its accuracy to better understand the limitations of our framework. This is the goal of this notebook.
• Hodge-Laplacian Spectral analysis on spheres. The Laplacian might be the most famous differential operator ever. In this notebook, we check that its spectrum matches the expected spherical harmonics eigenvalues when computed on unit spheres; for differential forms of various degrees.

Experimenting directly with these examples:

All the presented notebooks can be downloaded from a link within their first cell.