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 ideally suited to simulating wide range problems in geophysical fluid dynamics. Here, we demonstrate applicability geodynamical simulation, with focus on mantle The accuracy efficiency approach are confirmed via comparisons against suite analytical benchmark cases systematically increasing complexity, whilst parallel scalability demonstrated up 12 288 compute cores, where problem size number processing cores simultaneously increased. In addition, Firedrake's flexibility highlighted straightforward application different physical (e.g. complex non-linear rheologies, compressibility) geometrical (2-D 3-D Cartesian spherical domains) scenarios. Finally, representative simulation global convection examined, which incorporates 230 Myr plate motion history as kinematic surface boundary condition, confirming suitability addressing at frontiers dynamics research.