ForestClaw: A parallel algorithm for patch-based adaptive mesh refinement on a forest of quadtrees

TL;DR

ForestClaw introduces a scalable parallel algorithm for adaptive mesh refinement on quadtree-based grids, enabling efficient PDE solutions on complex geometries with minimal regridding overhead.

Contribution

It presents a novel parallel, multi-block algorithm using quadtree structures for adaptive mesh refinement applicable to various geometries.

Findings

Achieves high scalability on up to 64Ki MPI processes.

Demonstrates negligible regridding overhead.

Successfully solves scalar advection problems on complex domains.

Abstract

We describe a parallel, adaptive, multi-block algorithm for explicit integration of time dependent partial differential equations on two-dimensional Cartesian grids. The grid layout we consider consists of a nested hierarchy of fixed size, non-overlapping, logically Cartesian grids stored as leaves in a quadtree. Dynamic grid refinement and parallel partitioning of the grids is done through the use of the highly scalable quadtree/octree library p4est. Because our concept is multi-block, we are able to easily solve on a variety of geometries including the cubed sphere. In this paper, we pay special attention to providing details of the parallel ghost-filling algorithm needed to ensure that both corner and edge ghost regions around each grid hold valid values. We have implemented this algorithm in the ForestClaw code using single-grid solvers from ClawPack, a software package for solving hyperbolic PDEs using finite volumes methods. We show weak and strong scalability results for scalar advection problems on two-dimensional manifold domains on 1 to 64Ki MPI processes, demonstrating neglible regridding overhead.