Towards automatic finite-element methods for geodynamics via Firedrake

Abstract

Firedrake is an automated system for solving partial differential equations using the finite-element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means of creating accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software that is ideally suited to simulating a wide range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach are confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12 288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex non-linear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming Firedrake's suitability for addressing research problems at the frontiers of global mantle dynamics research.