Login
Guest
Search for:
Browse:
Resources:
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Online from: 1991
Subject Area: Mechanical & Materials Engineering
Content: Latest Issue | 
Latest Issue RSS | Previous Issues
Options: To add Favourites and Table of Contents Alerts please take a Emerald profile
A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs
| Title: | A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs |
|---|---|
| Author(s): | N. Mai-Duy, (School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, Australia), R.I. Tanner, (School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, Australia) |
| Citation: | N. Mai-Duy, R.I. Tanner, (2007) "A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 Iss: 2, pp.165 - 186 |
| Keywords: | Boundary-elements methods, Differential equations, Numerical analysis |
| Article type: | Research paper |
| DOI: | 10.1108/09615530710723948 (Permanent URL) |
| Publisher: | Emerald Group Publishing Limited |
| Abstract: | Purpose – To present a new collocation method for numerically solving partial differential equations (PDEs) in rectangular domains. Design/methodology/approach – The proposed method is based on a Cartesian grid and a 1D integrated-radial-basis-function scheme. The employment of integration to construct the RBF approximations representing the field variables facilitates a fast convergence rate, while the use of a 1D interpolation scheme leads to considerable economy in forming the system matrix and improvement in the condition number of RBF matrices over a 2D interpolation scheme. Findings – The proposed method is verified by considering several test problems governed by second- and fourth-order PDEs; very accurate solutions are achieved using relatively coarse grids. Research limitations/implications – Only 1D and 2D formulations are presented, but we believe that extension to 3D problems can be carried out straightforwardly. Further, development is needed for the case of non-rectangular domains. Originality/value – The contribution of this paper is a new effective collocation formulation based on RBFs for solving PDEs. |
Fulltext Options:
Purchase
Downloadable; Printable; Owned
HTML, PDF (223kb)
To purchase this item please login or register.
Order
Fill in an Order form to request this document from your librarian
|
|
