A line search algorithm for wind field adjustment with incomplete data and RBF approximation
The problem of concern in this work is the construction of free divergence fields given scattered horizontal components. As customary, the problem is formulated as a PDE constrained least squares problem. The novelty of our approach is to construct the so-called adjusted field, as the unique solution along an appropriately chosen descent direction. The latter is obtained by the adjoint equation technique. It is shown that the classical adjusted field of Sasaki’s is a particular case. On choosing descent directions, the underlying mass consistent model leads to the solution of an elliptic problem which is solved by means of a radial basis functions method. Finally, some numerical results for wind field adjustment are presented.
KeywordsWind adjustment RBF methods Line search
Mathematics Subject Classification65K10 65N35 35Q86
The authors would like to acknowledge ECOS-NORD project number 000000000263116/M15M01 for financial support during this research. C. Gout thanks the M2NUM project which is co-financed by the European Union with the European Regional Development Fund (ERDF, HN0002137) and by the Normandie Regional Council. Funding was provided by PAPIIT UNAM (Grant No. IN102116). The authors thank the anonymous referees for their very constructive comments and suggestions, leading to a much improved manuscript.
- Gonzlez-Casanova P, Muoz-Gmez JA, Rodrguez-Gmez G (2009) Node adaptive domain decomposition method by radial basis functions. Numer Methods Partial Differ Equ 25(6):1482–1501Google Scholar
- Kansa EJ (1990) Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19(8):147–161Google Scholar
- Sarra A (2008) A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs. Numer Methods Partial Differ Equ 24(2) 670–686Google Scholar
- Zeidler E (2013) Nonlinear functional analysis and its applications: III: variational methods and optimization. Springer-Verlag, New YorkGoogle Scholar