Scalable Computational Algorithms for Geo-spatial Covid-19 Spread in High Performance Computing

TL;DR

This paper presents a scalable high-performance computing approach using advanced solvers for large-scale PDE-based COVID-19 spread models, enabling rapid predictions over extensive geographical areas.

Contribution

It introduces a parallel scalable solver combining domain decomposition and multigrid preconditioners for high-fidelity COVID-19 models with millions of unknowns.

Findings

Achieved strong and weak scalability in simulations.

Predicted infections for 92 million system size within 7 hours.

Demonstrated effectiveness on a large geographical domain.

Abstract

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.