Automatic tuning of iterative pseudo-transient solvers for modeling the deformation of heterogeneous media

Abstract

Geodynamic modeling has become a crucial tool for investigating the dynamics of Earth deformation across various scales. Such simulations often involve solving mechanical problems with significant material heterogeneities (e.g. strong viscosity contrasts) under nearly incompressible conditions. Recent advancements have enabled the development of iterative solvers based on Dynamic Relaxation (DR) or Pseudo-Transient schemes, which require minimal global communication and exhibit quasi-linear scaling on GPU and supercomputing architectures. These solvers incorporate automatic tuning of iterative parameters, including pseudo-time steps and damping coefficients, based on spectral estimates of the discrete operators, ensuring both robust and rapid convergence. We demonstrate the effectiveness of this approach on discretized problems with finite-difference and face-centered finite volume methods, including heterogeneous incompressible Stokes flows. Moreover, the relative algorithmic simplicity of DR-based methods allows straightforward extensions to compressible flow, multiphase flow, and nonlinear constitutive laws, opening promising avenues for large-scale, high-resolution simulations of geoscientific problems.