On sequential multiscale inversion and data assimilation

Nadeem, A., Potthast, R. ORCID: https://orcid.org/0000-0001-6794-2500 and Rhodin, A. (2018) On sequential multiscale inversion and data assimilation. Journal of Computational and Applied Mathematics, 336. pp. 338-352. ISSN 0377-0427 doi: 10.1016/j.cam.2017.08.013

Abstract/Summary

Multiscale approaches are very popular for example for solving partial differential equations and in many applied fields dealing with phenomena which take place on different levels of detail. The broad idea of a multiscale approach is to decompose your problem into different scales or levels and to use these decompositions either for constructing appropriate approximations or to solve smaller problems on each of these levels, leading to increased stability or increased efficiency. The idea of sequential multiscale is to first solve the problem in a large-scale subspace and then successively move to finer scale spaces. Our goal is to analyse the sequential multiscale approach applied to an inversion or state estimation problem. We work in a generic setup given by a Hilbert space environment. We work out the analysis both for an unregularized and a regularized sequential multiscale inversion. In general the sequential multiscale approach is not equivalent to a full solution, but we show that under appropriate assumptions we obtain convergence of an iterative sequential multiscale version of the method. For the regularized case we develop a strategy to appropriately adapt the regularization when an iterative approach is taken. We demonstrate the validity of the iterative sequential multiscale approach by testing the method on an integral equation as it appears for atmospheric temperature retrieval from infrared satellite radiances.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/74326
Identification Number/DOI	10.1016/j.cam.2017.08.013
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
Download/View statistics	View download statistics for this item