Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

Abstract

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within the Community Atmospheric Model (CAM-SE). In this paper, we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.