Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00466-005-0667-4
Title: Radial point interpolation collocation method (RPICM) for the solution of nonlinear poisson problems
Authors: Liu, X.
Liu, G.R. 
Tai, K.
Lam, K.Y.
Keywords: Hermite-type interpolation
Meshfree
Nonlinear poisson equation
RPICM
Thin plate spline
Issue Date: Sep-2005
Source: Liu, X., Liu, G.R., Tai, K., Lam, K.Y. (2005-09). Radial point interpolation collocation method (RPICM) for the solution of nonlinear poisson problems. Computational Mechanics 36 (4) : 298-306. ScholarBank@NUS Repository. https://doi.org/10.1007/s00466-005-0667-4
Abstract: This paper applies radial point interpolation collocation method (RPICM) for solving nonlinear Poisson equations arising in computational chemistry and physics. Thin plate spline (TPS) Radial basis functions are used in the work. A series of test examples are numerically analysed using the present method, including 2D Liouville equation, Bratu problem and Poisson-Boltzmann equation, in order to test the accuracy and efficiency of the proposed schemes. Several aspects have been numerically investigated, namely the enforcement of additional polynomial terms; and the application of the Hermite-type interpolation which makes use of the normal gradient on Neumann boundary for the solution of PDEs with Neumann boundary conditions. Particular emphasis was on an efficient scheme, namely Hermite-type interpolation for dealing with Neumann boundary conditions. The numerical results demonstrate that a good accuracy can be obtained. The h-convergence rates are also studied for RPICM with coarse and fine discretization models. © Springer-Verlag 2005.
Source Title: Computational Mechanics
URI: http://scholarbank.nus.edu.sg/handle/10635/61193
ISSN: 01787675
DOI: 10.1007/s00466-005-0667-4
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