Parallel ADI Preconditioners for All-Scale Atmospheric Models

Effective preconditioning lies at the heart of multiscale flow simulation, including a broad range of geoscientific applications that rely on semi-implicit integrations of the governing PDEs. For such problems, conditioning of the resulting sparse linear operator directly responds to the squared ratio of largest and smallest spatial scales represented in the model. For thin-spherical-shell geometry of the Earth atmosphere the condition number is enormous, upon which implicit preconditioning is imperative to eliminate the stiffness resulting from relatively fine vertical resolution. Furthermore, the anisotropy due to the meridians convergence in standard latitude-longitude discretizations becomes equally detrimental as the horizontal resolution increases to capture nonhydrostatic dynamics. Herein, we discuss a class of effective preconditioners based on the parallel ADI approach. The approach has been implemented in the established high-performance all-scale model EULAG with flexible computational domain distribution, including a 3D processor array. The efficacy of the approach is demonstrated in the context of an archetypal simulation of global weather.