| Advection-diffusion PDEs are prevalent in models of many physical applications throughout science and engineering. In this paper, we focus on a scalar-valued advection-diffusion equation of the form 6tu=1˙b u+m1˙D1 u+f, where β is a vector-valued advection coefficient that may depend on the scalar-valued solution u, D is a matrix of diffusion coefficients, and f(x, t) is a forcing term. Within different parameter regimes, there exist optimally scalable solvers for problems of this type, however no single solver yet applies well within all regimes of physical interest.;Domain decomposition methods display nearly optimal parallel scalability within the advection-dominated regime, but typically do not scale well for diffusion-dominated problems. The converse occurs when using multigrid methods. Our goal is to find one method that is scalable in both regimes, through using a hybrid approach that combines restrictive additive Schwarz (domain decomposition) and geometric multigrid.;After presenting the details of our algorithm, we present simulation results using the Hopper supercomputer at the National Energy Research Scientific Computing Center (NERSC). We investigate problems in both the advection- and diffusion-dominated regimes, and examine weak scalability of our solver with respect to both iteration count and wall-clock time. |
