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Compact local integrated-RBF approximations for second-order elliptic differential problems
- Source :
-
Journal of Computational Physics . Jun2011, Vol. 230 Issue 12, p4772-4794. 23p. - Publication Year :
- 2011
-
Abstract
- Abstract: This paper presents a new compact approximation method for the discretisation of second-order elliptic equations in one and two dimensions. The problem domain, which can be rectangular or non-rectangular, is represented by a Cartesian grid. On stencils, which are three nodal points for one-dimensional problems and nine nodal points for two-dimensional problems, the approximations for the field variable and its derivatives are constructed using integrated radial basis functions (IRBFs). Several pieces of information about the governing differential equation on the stencil are incorporated into the IRBF approximations by means of the constants of integration. Numerical examples indicate that the proposed technique yields a very high rate of convergence with grid refinement. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 230
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 60223659
- Full Text :
- https://doi.org/10.1016/j.jcp.2011.03.002