Highly scalable geodynamic simulations with HyTeG

High-resolution geodynamic simulations of mantle convection are essential to quantitatively assess the complex physical mechanisms driving the large-scale tectonic processes that shape Earth's surface. Accurately capturing small-scale features such as unstable thermal boundary layers requires global resolution on the order of 1 km. This renders traditional sparse matrix methods impractical due to their prohibitively high memory demands and low arithmetic intensity. Matrix-free methods offer a scalable alternative, enabling the solution of large-scale linear systems efficiently. In this work, we leverage the matrix-free Finite Element framework HyTeG to conduct large-scale geodynamic simulations that incorporate realistic physical models. We validate the framework through a combination of convergence studies of the Finite Element approximations against analytical solutions and through geophysical community benchmarks. The latter include test cases with temperature-dependent and nonlinear rheologies. Our scalability studies demonstrate excellent performance, scaling up to problems with about 100 billion (1011) unknowns in the Stokes system.