论文标题
线性抛物线PDE的新降低订单模型
A new reduced order model of linear parabolic PDEs
论文作者
论文摘要
如何为多维时间依赖性偏微分方程（PDE）构建准确的减少订单模型（ROM）是非常开放的。在本文中，我们为线性抛物线PDE提出了一个新的ROM。我们证明，我们的新方法比标准求解器要快的数量级，而且内存密集也要少得多。在问题数据的一些假设下，我们证明新方法的收敛速率与标准求解器相同。提出数值实验以确认我们的理论结果。
How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for linear parabolic PDEs. We prove that our new method can be orders of magnitude faster than standard solvers, and is also much less memory intensive. Under some assumptions on the problem data, we prove that the convergence rates of the new method is the same with standard solvers. Numerical experiments are presented to confirm our theoretical result.
