The Peano software - parallel, automaton-based, dynamically adaptive grid traversals

TL;DR

The Peano framework provides a parallel, automaton-based approach for dynamically adaptive Cartesian mesh traversals, emphasizing design decisions, automaton formalization, and high-performance implementation for scalable scientific computing.

Contribution

It introduces a novel automaton-based design for mesh traversal in adaptive grids, unifying traversal and application logic with minimal code modifications.

Findings

Supports shared and distributed memory systems efficiently.

Formalizes traversal and algorithm steps with interacting automata.

Provides insights into programming idioms and design choices for adaptive mesh software.

Abstract

We discuss the design decisions, design alternatives and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata---one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized, before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a "one way to implement things" code description into a generic discussion and summary of some alternatives, rationale and design decisions to be made for any tree-based adaptive mesh refinement software.