NDLI: Radial point interpolation collocation method (RPICM) for the solution of nonlinear poisson problems

Content Provider	Springer Nature Link
Author	Liu, Xin Liu, G. R. Tai, Kang Lam, K. Y.
Copyright Year	2005
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.
Starting Page	298
Ending Page	306
Page Count	9
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	36
Issue Number	4
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-04-14
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	RPICM Hermite-type interpolation Meshfree Nonlinear poisson equation Thin plate spline Thermodynamics Condensed Matter Numerical and Computational Methods in Engineering Systems and Information Theory in Engineering Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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