dyada 0.0.1

A Code for Memory-Saving Dyadic Adaptivity in Optimization and Simulation

DyAda: A Code for Dyadic Adaptivity in Optimization, Simulation, and Machine Learning

Dyadic Adaptivity

Dyadic adaptivity means: A given hypercube of 2 or more dimensions may or may not be subdivided into two parts in any number of dimensions. Of the resulting sub-boxes, each may again be subdivided into two in any dimension, and so forth.

Why Dyadic Adaptivity?

Currently, the most common approach to adaptivity are octrees, which are a special type of dyadic adaptivity: Each box is either refined in every dimension or not at all. For a three-d domain, the tree and the resulting partitioning could look like this:

But maybe you didn't need all this resolution?

Maybe, in the finely-resolved areas, you only needed only some of the dimensions resolved finely:

This is what DyAda provides.

The tree will then look like this:

And you will only have to use 14 degrees of freedom instead of 29! This reduction will be even stronger if you go to higher dimensions.

Contributing

Feel free to request features or voice your intent to work on/with DyAda as an issue. Depending on what you are looking for, exciting features may be in preparation, or they may just be waiting for you to implement them!