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Multiscale Galerkin method using interpolation wavelets for two‐dimensional elliptic problems in general domains
Author(s) -
Jang GangWon,
Kim Jae Eun,
Kim Yoon Young
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.872
Subject(s) - quadrilateral , wavelet , mathematics , lagrange multiplier , interpolation (computer graphics) , boundary value problem , multiresolution analysis , galerkin method , lagrange polynomial , mathematical optimization , mathematical analysis , algorithm , computer science , finite element method , wavelet transform , image (mathematics) , artificial intelligence , wavelet packet decomposition , structural engineering , polynomial , engineering
Abstract One major hurdle in developing an efficient wavelet‐based numerical method is the difficulty in the treatment of general boundaries bounding two‐ or three‐dimensional domains. The objective of this investigation is to develop an adaptive multiscale wavelet‐based numerical method which can handle general boundary conditions along curved boundaries. The multiscale analysis is achieved in a multi‐resolution setting by employing hat interpolation wavelets in the frame of a fictitious domain method. No penalty term or the Lagrange multiplier need to be used in the present formulation. The validity of the proposed method and the effectiveness of the multiscale adaptive scheme are demonstrated by numerical examples dealing with the Dirichlet and Neumann boundary‐value problems in quadrilateral and quarter circular domains. Copyright © 2003 John Wiley & Sons, Ltd.