A nonlinear partial differential equation (PDE) based compartmental model of
COVID-19 provides a continuous trace of infection over space and time. Finer
resolutions in the spatial discretization, the inclusion of additional model
compartments and model stratifications based on clinically relevant categories
contribute to an increase in the number of unknowns to the order of millions.
We adopt a parallel scalable solver allowing faster solutions for these high
fidelity models. The solver combines domain decomposition and algebraic
multigrid preconditioners at multiple levels to achieve the desired strong and
weak scalability. As a numerical illustration of this general methodology, a
five-compartment susceptible-exposed-infected-recovered-deceased (SEIRD) model
of COVID-19 is used to demonstrate the scalability and effectiveness of the
proposed solver for a large geographical domain (Southern Ontario). It is
possible to predict the infections up to three months for a system size of 92
million (using 1780 processes) within 7 hours saving months of computational
effort needed for the conventional solvers