Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 5, page 883-908
  • ISSN: 0764-583X

Abstract

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We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

How to cite

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Sonar, Thomas. "Difference operators from interpolating moving least squares and their deviation from optimality." ESAIM: Mathematical Modelling and Numerical Analysis 39.5 (2010): 883-908. <http://eudml.org/doc/194292>.

@article{Sonar2010,
abstract = { We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality. },
author = {Sonar, Thomas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Difference operators; moving least squares interpolation; order of approximation.; order of approximation; Shepard interpolant},
language = {eng},
month = {3},
number = {5},
pages = {883-908},
publisher = {EDP Sciences},
title = {Difference operators from interpolating moving least squares and their deviation from optimality},
url = {http://eudml.org/doc/194292},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Sonar, Thomas
TI - Difference operators from interpolating moving least squares and their deviation from optimality
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 5
SP - 883
EP - 908
AB - We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.
LA - eng
KW - Difference operators; moving least squares interpolation; order of approximation.; order of approximation; Shepard interpolant
UR - http://eudml.org/doc/194292
ER -

References

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  10. H. Netuzylov, Th. Sonar and W. Yomsatieankul, Finite difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004).  
  11. N. Perrone and R. Kao, A general finite difference method for arbitrary meshes. Comput. Structures5 (1975) 45–58.  
  12. W. Schönauer, Generation of difference and error formulae of arbitrary consistency order on an unstructured grid. ZAMM Z. Angew. Math. Mech.78 (1998) S1061–S1062.  
  13. L. Theilemann, Ein gitterfreies differenzenverfahren. Doktorarbeit, Institut für Aerodynamik und Gasdynamik, Universität Stuttgart (1983).  
  14. W. Yomsatieankul, Th. Sonar and H. Netuzhylov, Spatial difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004).  

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