Automatic tuning of iterative pseudo-transient solvers for geodynamic modelling

Geodynamic modeling has become a crucial tool for investigating the dynamics of Earth deformation across various scales. This approach involves solving mechanical problems characterized by significant property variations (e.g., viscosity, shear modulus, conductivity) under nearly incompressible conditions. Recent advancements in technology have facilitated the development of iterative pseudo-transient solvers, which require minimal global communication and enable near-optimal parallel scaling on supercomputers. However, selecting numerical parameters that ensure both robust and rapid convergence remains a challenging task. In this contribution, we explore potential strategies to address these challenges and provide application examples using both finite difference and face-centered finite volume methods.