Nonlinear continuous data assimilation

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2023-01-01 DOI:10.3934/eect.2023048

Adam Larios, Yuan Pei

引用次数: 15

Abstract

We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models, we computationally investigate these algorithms in the context of the 1D Kuramoto-Sivashinsky equations. We observe that the nonlinear models experience super-exponential convergence in time, and converge to machine precision significantly faster than the linear AOT algorithm in our tests. For both simplicity and completeness, we provide the key analysis of the exponential-in-time convergence in the linear case.

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非线性连续数据同化

介绍了三种新的非线性连续数据同化算法。将这些模型与Azouani, Olson和Titi (AOT)引入的线性连续数据同化算法进行了比较。作为这些模型的概念验证，我们在一维Kuramoto-Sivashinsky方程的背景下计算研究了这些算法。在我们的测试中，我们观察到非线性模型在时间上经历了超指数收敛，并且收敛到机器精度的速度明显快于线性AOT算法。为了简洁性和完整性，我们给出了线性情况下的指数时间收敛性的关键分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology