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Biharmonic and bi-Helmholtz Type Scattered Data Interpolation Using Quadtrees and Multigrid Technique

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Book cover Multigrid Methods VI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 14))

Abstract

The interpolation problem over unstructured point sets is considered. The problem is converted to the solution of certain higher order differential equations. The method is constructed and analysed in Sobolev spaces using variational formulations. To solve the associated differential equation, multigrid methods based on quadtree-generated (unstructured) cell systems can be used, thus avoiding large, full and ill-conditioned algebraic systems. The resulting interpolation method is stable, the computational cost as well as the memory requirement are typically O (N log N) where N is the number of the scattered points. An application to the Dual Reciprocity Method (DRM) of the Boundary Element Method is also presented.

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Authors and Affiliations

  1. Department of Mathematics, Széclicnyi István College, P.O.Box 701, H-9007, Györ, Hungary

    Csaba Gáspár

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  1. Csaba Gáspár
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Editor information

Editors and Affiliations

  1. Department of Flow, Heat and Combustion Mechanics, University of Gent, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Erik Dick , Kris Riemslagh  & Jan Vierendeels ,  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Gáspár, C. (2000). Biharmonic and bi-Helmholtz Type Scattered Data Interpolation Using Quadtrees and Multigrid Technique. In: Dick, E., Riemslagh, K., Vierendeels, J. (eds) Multigrid Methods VI. Lecture Notes in Computational Science and Engineering, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58312-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-58312-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67157-2

  • Online ISBN: 978-3-642-58312-4

  • eBook Packages: Springer Book Archive

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