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.
Mots clés : difference operators, moving least squares interpolation, order of approximation
@article{M2AN_2005__39_5_883_0,
author = {Sonar, Thomas},
title = {Difference operators from interpolating moving least squares and their deviation from optimality},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {883--908},
publisher = {EDP-Sciences},
volume = {39},
number = {5},
year = {2005},
doi = {10.1051/m2an:2005039},
mrnumber = {2178566},
zbl = {1085.39018},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005039/}
}
TY - JOUR AU - Sonar, Thomas TI - Difference operators from interpolating moving least squares and their deviation from optimality JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 883 EP - 908 VL - 39 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2005039/ DO - 10.1051/m2an:2005039 LA - en ID - M2AN_2005__39_5_883_0 ER -
%0 Journal Article %A Sonar, Thomas %T Difference operators from interpolating moving least squares and their deviation from optimality %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 883-908 %V 39 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2005039/ %R 10.1051/m2an:2005039 %G en %F M2AN_2005__39_5_883_0
Sonar, Thomas. Difference operators from interpolating moving least squares and their deviation from optimality. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 5, pp. 883-908. doi : 10.1051/m2an:2005039. http://www.numdam.org/articles/10.1051/m2an:2005039/
[1] ,,, and, Meshless methods: an overview and recent developments. Comput. Methods Appl. Mech. Engrg. 139 (1996) 3-47. | Zbl
[2] , Chebyshev and Fourier Spectral Methods. Springer Verlag (1989). | Zbl
[3] , Generation of Finite Difference Formulas on Arbitrarily Spaced Grids. Math. Comp. 51 (1988) 699-706. | Zbl
[4] , A Practical Guide to Pseudospectral Methods. Cambridge University Press (1996). | MR | Zbl
[5] and, On meshless collocation approximations of conservation laws: preliminary investigations on positive schemes and dissipation models. ZAMM Z. Angew. Math. Mech. 81 (2001) 403-415. | Zbl
[6] , Entwicklung und Untersuchung von Moving Least Square Verfahren zur numerischen Simulation hydrodynamischer Gleichungen. Doktorarbeit, Fakultät für Physik, Eberhard-Karls-Universität zu Tübingen (2001).
[7] and, Surfaces generated by moving least squares methods. Math. Comp. 37 (1981) 141-158. | Zbl
[8] and, Curve and Surface Fitting: An Introduction. Academic Press (1986). | MR | Zbl
[9] and, The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput. Structures 11 (1980) 83-95. | Zbl
[10] , and, Finite difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004).
[11] and, A general finite difference method for arbitrary meshes. Comput. Structures 5 (1975) 45-58.
[12] , Generation of difference and error formulae of arbitrary consistency order on an unstructured grid. ZAMM Z. Angew. Math. Mech. 78 (1998) S1061-S1062. | Zbl
[13] , Ein gitterfreies differenzenverfahren. Doktorarbeit, Institut für Aerodynamik und Gasdynamik, Universität Stuttgart (1983).
[14] , and, Spatial difference operators from moving least squares interpolation. Manuscript, Institut Computational Mathematics, TU Braunschweig (2004).
Cité par Sources :
