ForestClaw: A parallel algorithm for patch-based adaptive mesh refinement on a forest of quadtrees
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2017
- DOI:
- 10.48550/arXiv.1703.03116
- arXiv:
- arXiv:1703.03116
- Bibcode:
- 2017arXiv170303116C
- Keywords:
-
- Computer Science - Mathematical Software;
- 65M08;
- 65M50;
- 68W10;
- 65Y05
- E-Print:
- 26 pages, 12 figures