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Equilibrium on line method (ELM) for imposition of Neumann boundary conditions in the finite point method (FPM)
Author(s) -
Sadeghirad A.,
Mohammadi S.
Publication year - 2006
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.1755
Subject(s) - neumann boundary condition , von neumann stability analysis , boundary value problem , mathematics , mathematical analysis , mixed boundary condition , singular boundary method , boundary (topology) , von neumann architecture , finite element method , boundary element method , pure mathematics , structural engineering , engineering
Equilibrium on line method (ELM) for imposition of Neumann boundary conditions in the finite point method (FPM) is presented. In contrary to weak‐form‐based methods, strong‐form‐based methods such as the FPM are often unstable and less accurate, especially for problems governed by partial differential equations with Neumann (derivative) boundary conditions. In this paper, a truly meshless approach for imposition of Neumann boundary conditions in the FPM is proposed and adopted for 2D elasticity analyses. In the proposed method, equilibrium on lines on the Neumann boundary conditions is satisfied as Neumann boundary condition equations. Numerical studies show that this method for imposition of Neumann boundary is simple to implement and computationally efficient and also leads to more stable and accurate results. Copyright © 2006 John Wiley & Sons, Ltd.