Resolving Hydro-Mechanical Earthquake Cycles with a GPU-based Accelerated Pseudo-Transient Solver

Modeling earthquake source processes is a multi-physics and multi-scale endeavor that tightly links several disciplines, including seismology, numerical computing, continuum mechanics, materials science, and engineering. In particular, incorporating the full range of coupled mechanisms, including complex fault geometries, off-fault inelastic processes, realistic shear-layer response, and fluid effects, brings significant programming and computational challenges. Furthermore, the development of highly efficient, robust and scalable numerical algorithms lags behind the rapid increase in massive parallelism of modern hardware. To address this challenge, we present a physically motivated derivation of coupled solid-fluid interactions on faults using an innovative accelerated pseudo-transient (PT) iterative method. The general approach involves transforming a time-independent problem into an evolution problem, which allows us to utilize the benefits of the Method-of-Lines (MOL) approach with the accelerated PT method. Additionally, we provide an efficient numerical implementation of PT solvers on graphics processing units (GPUs) using the Julia programming language. Julia solves the “two-language problem”, where developers who write scientific software can achieve desired performance, without sacrificing productivity. As a result, this enables us to develop high-performance code for massively parallel hardware with modern GPU-accelerated supercomputers, without requiring architecture-specific code. We aim to unveil preliminary results on the application of PT solvers to fully compressible poro-visco-elasto-plastic media, wave-mediated fully dynamic effects, rate-and-state dependent friction, and an adaptive time stepping to resolve both long- and short-time scales, ranging from years to milliseconds during the dynamic propagation of dynamic rupture. Our work can contribute to a better understanding of the accelerated PT method and its potential for facilitating the implementation of various numerical models in the field of computational earthquake physics.