A Cartesian‐grid collocation method based on radial‐basis‐function networks for solving PDEs in irregular domains | Zendy

MaiDuy N. | Zendy; TranCong T. | Zendy

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A Cartesian‐grid collocation method based on radial‐basis‐function networks for solving PDEs in irregular domains

Author(s) -

MaiDuy N.,

TranCong T.

Publication year - 2007

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.20217

Subject(s) - cartesian coordinate system , partial differential equation , collocation (remote sensing) , mathematics , radial basis function , discretization , collocation method , orthogonal collocation , grid , partial derivative , dirichlet boundary condition , basis function , boundary value problem , interpolation (computer graphics) , convergence (economics) , elliptic partial differential equation , boundary (topology) , mathematical analysis , ordinary differential equation , differential equation , computer science , geometry , artificial neural network , animation , computer graphics (images) , machine learning , economic growth , economics

This paper reports a new Cartesian‐grid collocation method based on radial‐basis‐function networks (RBFNs) for numerically solving elliptic partial differential equations in irregular domains. The domain of interest is embedded in a Cartesian grid, and the governing equation is discretized by using a collocation approach. The new features here are (a) one‐dimensional integrated RBFNs are employed to represent the variable along each line of the grid, resulting in a significant improvement of computational efficiency, (b) the present method does not require complicated interpolation techniques for the treatment of Dirichlet boundary conditions in order to achieve a high level of accuracy, and (c) normal derivative boundary conditions are imposed by means of integration constants. The method is verified through the solution of second‐ and fourth‐order PDEs; accurate results and fast convergence rates are obtained. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

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