Mixed order discretization based two-level Schwarz preconditioners for a tracer transport problem on the cubed-sphere

Solving tracer transport problems on the sphere at high resolution is important for atmospheric science. In this paper, we study a fully implicit method that allows larger time step size than explicit methods. The key to the success of the implicit approach is how to solve the discretized linear system at each time step. We investigate a parallel Krylov–Schwarz approach based on two discretizations, and test the proposed algorithm with two benchmark test cases. We show numerically that the solver scales well in terms of both strong and weak scalabilities on a supercomputer with thousands of processors.