A new reduced order model of linear parabolic PDEs

TL;DR

This paper introduces a novel reduced order model for linear parabolic PDEs that significantly improves computational speed and memory efficiency while maintaining comparable convergence rates to traditional methods.

Contribution

The paper presents a new ROM for linear parabolic PDEs that is faster, less memory-intensive, and theoretically comparable in convergence to standard solvers.

Findings

Orders of magnitude faster than standard solvers

Much less memory usage

Convergence rates similar to standard methods

Abstract

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.