The 1-D Hermite Shepard and MLS method

Document Type : Original Article

Authors

1 Department of mathematics, Qom University of Technology, Qom, Iran

2 Department of Applied Mathematics, Iran University of Science and Technology, Tehan, Iran

Abstract

In many applications, one encounters the problem of approximating 1-D curve and 2-D surfaces from data given on a set of scattered points. Meshless methods strategy is based on some facts: (1) deleting mesh generation and re-meshing, (2) raising smooth degree of solution, (3) localization by using compact support weights. This research presented three generalizations for ancient pseudo interpolation, localization, appending a complete polynomial to the Shepard average weighted approximation and Hermite form of Shepard and MLS method. The new bases for relevant space of approximants are developed and, when evaluated directly, improves the accuracy of evaluation of the fitted method, especially the Hermite type. In this work, we develop some efficient schemes for computing global or local approximation curves and surfaces interpolating a given smooth data. Then we raise the smooth degree of approximation and use of derivatives data. The Hermite Shepard (HSH) is straightforward and efficient.

Keywords

References

[1] G.E. Backus and J.F. Gilbert, Numerical application of a formalism for geophysical inverse problems, Geophysical Journal of the Royal Astronomical Society, 13 (1-3) 1967, 247-276.
[2] T. Belytschko, Y.Y. Lu , L. Gu, Element‐Free Galerkin methods, International Numerical Methods in Engineering, 37(2) 1994.
[3] F. Cao, M. Li, Spherical Data Fitting by Multiscale Moving Least Squares, Applied Mathematical Modelling, 39(12) 2015, 3448-3458. [4] M. Ghorbani, Diffuse Element Kansa Method, Applied Mathematical Sciences, 4(12) 2010, 583-594.
[5] Z. Komargodski, D. Levin, Hermite Type Moving Least Squares Approximations, Computers and Mathematics with Applications, 51(8) 2006, 1223-1232.
[6] P. Lancaster and K. Salkauskas, Surfaces Generated by Moving Least Squares Methods, mathematics of computation, 37(155) 1981.
[7] D.H. McLain, Drawing contours from arbitrary data points, The Computer Journal, 17(4) 1974, 318-324.
[8] A.R. Mitchell and R. Wait, Finite Element Analysis and Applications, John Wiley, 1985.
[9] Th. Most, Ch. Bucher, New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares, Engineering Analysis with Boundary Elements 32(6) 2008, 461-470.
[10] B. Nayroles, G. Touzot, P. Villon, Generalizing the finite element method: Diffuse approximation and diffuse elements, Computational Mechanics, 10(5) 1992, 307-318.
[11] D. Shepard, A Two-Dimensional Interpolation Function for Irregularly Spaced Points, Proceedings of the 1968 23rd ACM national conference, 1968.
Mathematics and Computational Sciences
Volume 2, Issue 3
September 2021
Pages 33-42

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History

  • Receive Date: 12 June 2021
  • Revise Date: 23 July 2021
  • Accept Date: 21 August 2021
  • First Publish Date: 21 August 2021

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