Adaptive mesh refinement for solving PDEs on logically Cartesian mapped, multiblock quadtree domains.
Dept. of Mathematics, Colorado State University, Fort Collins, CO (USA) (Invited)
Dynamically adaptive Cartesian grid methods have been used for over 30 years as a means of making Cartesian grid calculations practical and scalable. In this talk, I will describe an approach to adaptive mesh refinement (AMR) in which the refinement patches are leaves in a quadtree or octree. The chief advantages of this approach is that fast scalable tree-based codes can be used to handle the neighbor searches and dynamic regridding, and that nearest neighbor connections occur in one of only three regular patterns. These features provide a path towards high performance adaptive mesh calculations as well as greatly facilitating the development of numerical algorithms for AMR. In our software platform, ForestClaw, we separate numerics and grid management by building our Cartesian grid solvers on top of the highly scalable grid management library p4est (C. Burstedde, Univ. of Bonn). Solvers in ForestClaw include hyperbolic solvers based on Clawpack and GeoClaw (University of Washington). I will show results of simulations using ForestClaw to solve problems in gas dynamics, and geophysical flow problems, as well as scaling results on the BlueGene/Q on up to 65K processors.`