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A point collocation method based on reproducing kernel approximations
Author(s) -
Aluru N. R.
Publication year - 2000
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/(sici)1097-0207(20000228)47:6<1083::aid-nme816>3.0.co;2-n
Subject(s) - collocation (remote sensing) , collocation method , kernel (algebra) , galerkin method , mathematics , singular boundary method , orthogonal collocation , regularized meshless method , boundary value problem , meshfree methods , boundary (topology) , mathematical analysis , mathematical optimization , algorithm , computer science , boundary element method , differential equation , finite element method , ordinary differential equation , discrete mathematics , physics , machine learning , thermodynamics
A reproducing kernel particle method with built‐in multiresolution features in a very attractive meshfree method for numerical solution of partial differential equations. The design and implementation of a Galerkin‐based reproducing kernel particle method, however, faces several challenges such as the issue of nodal volumes and accurate and efficient implementation of boundary conditions. In this paper we present a point collocation method based on reproducing kernel approximations. We show that, in a point collocation approach, the assignment of nodal volumes and implementation of boundary conditions are not critical issues and points can be sprinkled randomly making the point collocation method a true meshless approach. The point collocation method based on reproducing kernel approximations, however, requires the calculation of higher‐order derivatives that would typically not be required in a Galerkin method, A correction function and reproducing conditions that enable consistency of the point collocation method are derived. The point collocation method is shown to be accurate for several one and two‐dimensional problems and the convergence rate of the point collocation method is addressed. Copyright © 2000 John Wiley & Sons, Ltd.