Analysis of the inherent instability of the interpolating moving least squares method when using improper polynomial bases

This paper first discusses the inherent instability of the interpolating moving least squares (IMLS) method. In the original IMLS method, non-scaled polynomial bases are used. Theoretical and numerical results indicate that the stability of the original IMLS method decreases as the separation distan...

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Bibliographic Details
Published in:Engineering analysis with boundary elements Vol. 73; pp. 21 - 34
Main Authors: Li, Xiaolin, Wang, Qingqing
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.12.2016
Subjects:
Algorithms
Boundaries
Condition number
Galerkin boundary node method
Instability
Interpolating moving least squares method
Least squares method
Mathematical analysis
Mathematical models
Meshless method
Polynomials
Stability
Interpolating moving least squares method
Condition number
Galerkin boundary node method
Stability
Meshless method
ISSN:0955-7997, 1873-197X
Online Access:Get full text
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Summary:This paper first discusses the inherent instability of the interpolating moving least squares (IMLS) method. In the original IMLS method, non-scaled polynomial bases are used. Theoretical and numerical results indicate that the stability of the original IMLS method decreases as the separation distance decreases. Then, using shifted and scaled polynomial bases, a stabilized algorithm of the IMLS method is proposed and analyzed. As an application, the stabilized IMLS method is finally introduced into the meshless Galerkin boundary node method (GBNM) to produce a stabilized GBNM for potential problems and Stokes problems. Numerical examples are given to demonstrate the stability and convergence of the presented stabilized algorithms.
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ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2016.08.012