Many problems in computational science and engineering, and in particular in solid earth geophysics, are characterized by dynamics occurring on a wide range of length and time scales. One approach to overcoming the tyranny of scales is adaptive mesh refinement (AMR), which locally and dynamically coarsens and refines the mesh to resolve spatio-temporal scales and features of interest. For example, we are interested in modeling global mantle convection with nonlinear rheology and kilometer-scale resolution at faulted plate boundaries. Another problem of interest is modeling the dynamics of polar ice sheets with fine resolution in the vicinity of transition regions. Geophysical inverse problems characterized by a wide range of medium properties can also benefit from AMR as the earth model is updated.
While AMR promises to help overcome the challenges inherent in modeling multiscale problems, the benefits are difficult to achieve in practice on the highly parallel computers that are essential for the most difficult problems. Due to the complex dynamic data structures and frequent load balancing, scaling dynamic AMR to hundreds of thousands of processors has long been considered a challenge. Another difficulty is extending parallel AMR techniques to high-order-accurate, complex-geometry-respecting finite element methods that are favored for many classes of solid earth geophysical problems.
Here we present ALPS, which incorporates new parallel algorithms and data structures for dynamic mesh refinement/coarsening on forest-of-octree-based geometries with arbitrary-order continuous and discontinuous spectral element discretizations. ALPS exhibits excellent weak and strong scaling to over 224,000 Cray XT5 cores. We describe applications to several solid earth geophysics problems: global mantle convection with nonlinear rheology, full Stokes models of ice sheet dynamics, and global seismic wave propagation.
This work is joint with Tan Bui-Thanh, Carsten Burstedde, Tobin Isaac, George Stadler, and Lucas Wilcox from UT-Austin, and Laura Alisic and Mike Gurnis from Caltech.