A remark on Domain Decomposition approaches solving Three Dimensional Variational Data Assimilation models
Numerical Analysis
2019-01-15 v1
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.
Keywords
Cite
@article{arxiv.1807.07103,
title = {A remark on Domain Decomposition approaches solving Three Dimensional Variational Data Assimilation models},
author = {Luisa D'Amore and Rosalba Cacciapuoti},
journal= {arXiv preprint arXiv:1807.07103},
year = {2019}
}