Computational and Applied Mathematics

, Volume 37, Issue 3, pp 2519–2532 | Cite as

A line search algorithm for wind field adjustment with incomplete data and RBF approximation

  • Daniel A. Cervantes
  • Pedro González Casanova
  • Christian Gout
  • Miguel Ángel MorelesEmail author


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.


Wind adjustment RBF methods Line search 

Mathematics Subject Classification

65K10 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.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • Daniel A. Cervantes
    • 1
  • Pedro González Casanova
    • 1
  • Christian Gout
    • 2
  • Miguel Ángel Moreles
    • 3
    Email author
  1. 1.Instituto de MatemáticasUNAM, Ciudad UniversitariaMexicoMexico
  2. 2.INSA Rouen, LMISt Etienne du Rouvray CedexFrance
  3. 3.CIMATValencianaMexico

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