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A method for calculating meshless finite difference weights
Author(s) -
Roberts J. L.
Publication year - 2007
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.2169
Subject(s) - mathematics , taylor series , function (biology) , finite difference , finite difference method , gaussian elimination , matrix (chemical analysis) , gaussian , mathematical analysis , series (stratigraphy) , variable (mathematics) , scale (ratio) , limiting , physics , mechanical engineering , paleontology , materials science , quantum mechanics , evolutionary biology , biology , engineering , composite material
An exact method for calculating the finite difference weights for arbitrary distributed points in multiple dimensions is presented. The method avoids the numerical ill conditioning associated with a small‐scale factor (ε) by delaying the limiting of ε → 0. The Gaussian Radial Basis function is approximated by a Taylor's series expansion in the variable ε, and the resultant matrix equation is solved using the Fraction Free LU decomposition method. Copyright © 2007 John Wiley & Sons, Ltd.