Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario, Canada.
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland.
Math Biosci Eng. 2023 Jul 5;20(8):14634-14674. doi: 10.3934/mbe.2023655.
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 that permits 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 scalabilities. 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 for a period of three months for a system size of 186 million (using 3200 processes) within 12 hours saving months of computational effort needed for the conventional solvers.
基于非线性偏微分方程（PDE）的 COVID-19 房室模型提供了感染在空间和时间上的连续轨迹。在空间离散化中进行更精细的分辨率、包含更多的模型房室以及基于临床相关类别进行的模型分层，都会导致未知数的数量增加到数百万。我们采用了一种并行可扩展的求解器，可以更快地解决这些高保真模型。该求解器结合了域分解和代数多重网格预处理子，可以在多个级别上实现所需的强和弱可扩展性。作为这种通用方法的数值说明，使用 COVID-19 的五房室易感-暴露-感染-恢复-死亡（SEIRD）模型来演示所提出的求解器对于大地理区域（安大略省南部）的可扩展性和有效性。对于 1.86 亿个系统大小（使用 3200 个进程），可以在 12 小时内预测三个月的感染情况，从而节省了传统求解器所需的数月计算工作量。
