Title: 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.