Peano 4

Table of Contents

• Traversal

• The typical main.cpp in a Peano code
• Domain decomposition
• Action sets and events
• Localisation of a solver
• Runtime analysis and statistics
• Performance optimisation
• SYCL support
• python api intro
• Adaptive Mesh Refinement (AMR)
• Utilities
• Merging/coupling various applications

Peano is a framework for generating dynamically adaptive grids for a wide range of scientific applications. The original article on Peano can be found here. Peano works with spacetrees, similar to octrees, and runs through these trees top-down, i.e. from coarse to fine. This traversal cannot be changed and is hidden within the Peano code. Users interact with the traversal via listeners of observers, i.e. classes that are notified by the traversal whenever the traversal loads a cell, enters a cell, leaves a cell, and so forth. The present subsection discussed Peano-specific details, and it might be reasonable to study the high level description of the code base first. Most users never interact with the low level C++ routines in Peano as they either use Peano's Python API or they use an extension built on top of Peano (such as ExaHyPE) which hides away most technical details.

Todo

add links to the python and c++ documentation which has already been captured.

tidy this up - just adding this page in to introduce methods which need to be written for multigrid, such as touchVertexFirstTime

Peano allows us to embed the computational domain into a unit hypercube of dimension \( d \). The domain can be refined, where needed, by dividing the unit hypercube \( k^d \) times along each axis, leading to \( k^d \) hypercubes. We call this process refinement. By default, we take \( k \) to be 3, as this allows for traversing the cells using a Peano curve.

Where necessary, some cells in the hypercube may be further refined where greater computational resources are necessary. This leads to a hierarchy called a spacetree, where, loosely speaking, the nodes at a depth \( n \) represent a cell which has been \( n\)-times refined.

Todo

clear up wording here!

Crucially, cells and vertices are made unique through both their level of refinement/resolution and their position in space.

Traversal

The Peano backend chooses the order in which to traverse the spacetree. Each cell at each level of refinement are processed each traversal. The user can define what exactly is to happen in each cell upon each traversal, by writing functionality into each of the functions in the Action Set.

Todo

Specify each of these, and how they can be given extra functionality.

In general, making a new simulation in Peano is about defining the computational domain, informing the software about the number of unknowns per cell, the number of unknowns per vertex and so on.