Numerical and Scalability Studies with TerraNeo: Matrix-Free Mantle Convection Framework
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Convective processes in the Earth’s mantle drive plate tectonics and, thus, govern geological activity such as major earthquakes and mountain building. On geological timescales the rocks in the mantle behave like a highly viscous fluid and can be modelled with a coupled Stokes-transport system of PDEs. To capture small-scale thermal structures (rising plumes and sinking slabs) that develop at realistic convective vigour (Ra ≃ 1e7), such models require fine resolution (≃ 1 km), but also need to remain scalable on modern supercomputing systems. High efficiency, however, is not only needed for forward simulations, but also to allow solving the inverse problem with adjoint techniques. To achieve this, we make use of the matrix-free finite element package HyTeG (Kohl et al. 2018) as the backend for our TerraNeo mantle convection framework. We first present numerical studies to assess the framework in terms of geodynamic relevance (Ilangovan et al. 2025). One of these is verifying order of convergence of velocity and pressure against analytical solutions for isoviscous cases and against highly accurate solutions provided by the propagator matrix method (Zhong 1996) for radially varying viscosity and density cases. We then turn to standard geophysical benchmark setups that are used for comparison of quantities of interest, such as e.g. temperature and velocity profiles or the Nusselt number, against other community codes. Finally, we present scalability studies performed with the framework on the supercomputer Hawk at HLRS (66th in TOP500, Nov’ 24) and SuperMUC-NG Phase 1 at LRZ (91st in TOP500, Nov’ 25). In these experiments we scaled the framework to handle up to 1e11 DoFs for the Stokes system on Hawk and up to 300,000 MPI processes on SuperMUC-NG Phase 1. These results clearly show that the TerraNeo framework based on the HyTeG finite element package is well suited for extreme scale geodynamic modelling.
