ALPS: A framework for parallel adaptive PDE solution

Adaptive mesh refinement and coarsening (AMR) is essential for the numerical solution of partial differential equations (PDEs) that exhibit behavior over a wide range of length and time scales. Because of the complex dynamic data structures and communication patterns and frequent data exchange and redistribution, scaling dynamic AMR to tens of thousands of processors has long been considered a challenge. We are developing ALPS, a library for dynamic mesh adaptation of PDEs that is designed to scale to hundreds of thousands of compute cores. Our approach uses parallel forest-of-octree-based hexahedral finite element meshes and dynamic load balancing based on space-filling curves. ALPS supports arbitrary-order accurate continuous and discontinuous finite element/spectral element discretizations on general geometries. We present scalability and performance results for two applications from geophysics: seismic wave propagation and mantle convection.