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arXiv · 1807.07103

A remark on Domain Decomposition approaches solving Three Dimensional Variational Data Assimilation models

Luisa D'Amore·Rosalba Cacciapuoti
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Abstract

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. This is a large scale ill posed in- verse problem then in this note we consider the Tikhonov-regularized variational formulation of 3D- DA problem, namely the so-called 3D- Var DA problem. We review two Domain Decomposition (DD) approaches, namely the functional DD and the discrete Multiplicative Parallel Schwarz, and as the 3D-Var DA problem is a least square problem, we prove the equivalence between these approaches.

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Luisa D'Amore, Rosalba Cacciapuoti. 2018-07-18. A remark on Domain Decomposition approaches solving Three Dimensional Variational Data Assimilation models. https://doi.org/10.1007/s11587-019-00432-4

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