Total generalized variation regularization in data assimilation for Burgers' equation
| Autor: | Estefanía Loayza-Romero, Juan Carlos De los Reyes |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Conservation law
Control and Optimization Bayesian probability Regularization (mathematics) Stationary point Burgers' equation Data assimilation Inviscid flow Modeling and Simulation Discrete Mathematics and Combinatorics Applied mathematics Initial value problem Pharmacology (medical) Analysis Mathematics |
| Zdroj: | Inverse Problems & Imaging. 13:755-786 |
| ISSN: | 1930-8345 |
| DOI: | 10.3934/ipi.2019035 |
| Popis: | We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and a Bayesian MAP estimator, we focus on the detailed study of the inviscid Burgers' data assimilation problem. Due to the difficult structure of the governing hyperbolic conservation law, we consider a discretize–then–optimize approach and rigorously derive a first-order optimality condition for the problem. For the numerical solution, we propose a globalized reduced Newton-type method together with a polynomial line-search strategy, and prove convergence of the algorithm to stationary points. The paper finishes with some numerical experiments where, among others, the performance of TGV–regularization compared to TV–regularization is tested. |
| Databáze: | OpenAIRE |
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