Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a big and computationally expensive problem. In the present work we prove that the functional decomposition of the 3D variational data assimilation (3D Var DA) operator, previously introduced by the authors, is equivalent to apply multiplicative parallel Schwarz (MPS) method, to the Euler–Lagrange equations arising from the minimization of the data assimilation functional. It results that convergence issues as well as mesh refininement techniques and coarse grid correction—issues of the functional decomposition not previously addressed—could be employed to improve performance and scalability of the 3D Var DA functional decomposition in real cases.

中文翻译：

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关于求解3D变分数据同化模型的域分解方法的说明

数据同化（DA）是一种将模拟复杂系统（背景知识）和测量值（现实或观测数据）的数学模型组合在一起的方法，以改进对系统状态（预测）的估计。DA是通常用于处理大量数据的逆问题，这是一个很大且计算量很大的问题。在目前的工作中，我们证明了作者先前引入的3D变异数据同化（3D Var DA）算子的功能分解等效于将乘法并行Schwarz（MPS）方法应用于由以下公式产生的Euler-Lagrange方程最小化数据同化功能。