Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study
Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study
复制标题
反应扩散方程的移动数据点簇的连续数据同化：计算研究
DOI：
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发表时间：
2018
影响因子：
3.7
通讯作者：
Collin Victor
中科院分区：
文献类型：
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作者：
Adam Larios;Collin Victor
数据同化是一种通过将可观测的数据随时间的推移纳入解来提高偏微分方程解的模拟精度的技术。最近，Azouani，Olson和Titi（2014）的开创性工作提出了一种基于PDE水平反馈控制的数据同化新算法。该算法的标准版本是基于空间中固定的数据点的测量。在这项工作中，我们考虑的情况下，数据收集点随时间在空间中移动。我们通过计算证明，至少在1D Allen-Cahn反应扩散方程的设置中，该算法在测量点明显较少的情况下收敛，在某些情况下达到一个数量级或数量级。我们还提供了一个应用程序的算法的反问题的情况下，一个统一的静态网格。
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data assimilation based on feedback-control at the PDE level has been proposed in the pioneering work of Azouani, Olson, and Titi (2014). The standard version of this algorithm is based on measurement from data points that are fixed in space. In this work, we consider the scenario in which the data collection points move in space over time. We demonstrate computationally that, at least in the setting of the 1D Allen-Cahn reaction diffusion equations, the algorithm converges with significantly fewer measurement points, up to an order or magnitude in some cases. We also provide an application of the algorithm to an inverse problem in the case of a uniform static grid.