Parallel Adaptive Mesh Methods on Petascale Computers, with Applications to Geophysical Problems

We present a class of scalable parallel adaptive mesh methods for solution of PDEs, and illustrate with examples from mantle convection modeling. The focus of the talk will be on the ALPS (Adaptive Large-scale Parallel Simulations) library, which features algorithms for parallel adaptive mesh refinement and coarsening (AMR) and dynamic load-balancing on forest-of-octree meshes that scale to tens of thousands of processor cores. The ALPS library supports continuous and discontinuous Galerkin formulations and arbitrary-order octree-based hexahedral spectral element discretizations on general curvilinear geometries.

Mantle convection is the principal control on the thermal and geological evolution of the Earth. Mantle convection modeling involves solution of the mass, momentum, and energy equations for a viscous, creeping, incompressible non-Newtonian fluid at high Rayleigh and Peclet numbers. Our goal is to conduct global mantle convection simulations that can resolve faulted plate boundaries, down to 1 km scales. However, uniform resolution at these scales would result in meshes with a trillion elements, which would elude even sustained petaflops supercomputers. Thus parallel AMR is essential.

We present results of parallel AMR applied to prototype global mantle convection problems on the Texas Advanced Computing Center's 580 Tflops Ranger supercomputer. We demonstrate that the runtime overhead of parallel dynamic AMR is negligible compared to numerical solution of the PDEs, thus allowing strong and weak scalability of parallel AMR simulations to the full 62K processor cores of the system.