Highly Scalable Geodynamic Simulations with HyTeG

Abstract. High-resolution geodynamic simulations of mantle convection are essential to quantitatively assess the complex physical processes driving the large-scale tectonic phenomena 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, which renders traditional sparse matrix methods impractical due to prohibitive 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 and geophysical benchmarks. These include verifying the convergence rates of Finite Element solutions against analytical solutions and through community benchmarks, including test cases with temperature-dependent and nonlinear rheologies. Our scalability studies demonstrate excellent performance, scaling up to problems with about 10¹¹ unknowns in the Stokes system.