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

Thomas Sonar

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • 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 - Modélisation Mathématique et Analyse Numérique 39.5 (2005): 883-908. <http://eudml.org/doc/245225>.

@article{Sonar2005,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {difference operators; moving least squares interpolation; order of approximation; Difference operators; Shepard interpolant},
language = {eng},
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/245225},
volume = {39},
year = {2005},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2005
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; Difference operators; Shepard interpolant
UR - http://eudml.org/doc/245225
ER -

References

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  10. [10] H. Netuzylov, Th. Sonar and W. Yomsatieankul, Finite difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004). 
  11. [11] N. Perrone and R. Kao, A general finite difference method for arbitrary meshes. Comput. Structures 5 (1975) 45–58. 
  12. [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. Zbl0925.65175
  13. [13] L. Theilemann, Ein gitterfreies differenzenverfahren. Doktorarbeit, Institut für Aerodynamik und Gasdynamik, Universität Stuttgart (1983). 
  14. [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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