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Toward a computational multiresolution analysis for radial point interpolation meshless method
Author(s) -
Afsari Arman,
Chehrazi Akram,
Movahhedi Masoud
Publication year - 2014
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1977
Subject(s) - interpolation (computer graphics) , scaling , point (geometry) , meshfree methods , regularized meshless method , computer science , computational science , algorithm , mathematics , mathematical optimization , mathematical analysis , geometry , finite element method , structural engineering , engineering , image (mathematics) , artificial intelligence , singular boundary method , boundary element method
SUMMARY In this work, the application of Daubechies' scaling functions (DSFs) in computational engineering, particulary radial point interpolation meshless method (RPIM) in electromagnetic engineering, is studied. This analysis indicates some shortcomings of DSFs in computational engineering. In fact, the DSFs take the role of shape functions in RPIM, but they do not hold some general properties of shape functions. Modifying these shortcomings according to engineering requirements as time consumption rate, new scaling (shape) functions are derived, and testing them into two important classes of electromagnetic problems, that is, incident wave on dielectrics and scatterers, gives good agreement with exact solutions. Copyright © 2014 John Wiley & Sons, Ltd.