NDLI: A second generation wavelet based finite elements on triangulations

Content Provider	Springer Nature Link
Author	Quraishi, S. M. Sandeep, K.
Copyright Year	2011
Abstract	In this paper we have developed a second generation wavelet based finite element method for solving elliptic PDEs on two dimensional triangulations using customized operator dependent wavelets. The wavelets derived from a Courant element are tailored in the second generation framework to decouple some elliptic PDE operators. Starting from a primitive hierarchical basis the wavelets are lifted (enhanced) to achieve local scale-orthogonality with respect to the operator of the PDE. The lifted wavelets are used in a Galerkin type discretization of the PDE which result in a block diagonal, sparse multiscale stiffness matrix. The blocks corresponding to different resolutions are completely decoupled, which makes the implementation of new wavelet finite element very simple and efficient. The solution is enriched adaptively and incrementally using finer scale wavelets. The new procedure completely eliminates wastage of resources associated with classical finite element refinement. Finally some numerical experiments are conducted to analyze the performance of this method.
Starting Page	163
Ending Page	174
Page Count	12
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	48
Issue Number	2
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-03-16
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Second generation wavelets Wavelet customization Courant triangles Local orthogonalization Wavelet Galerkin Classical Continuum Physics Computational Science and Engineering Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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