A meshless method for non-linear Poisson problems with high gradients
Abstract
A meshless method for the solution of linear and non-linear Poisson-type problems involving high gradients is presented. The proposed method is based on collocation with 3rd order polynomial radial basis function coupled with the fundamental solution. The linear problem is solved by satisfying the boundary conditions and the governing differential equations over selected points over the boundary and inside the domain, respectively. In the case of the non-linear case, the resulted equations are highly non-linear and therefore, they are solved using an incremental-iterative procedure. The accuracy and efficiency of the method is verified through several numerical examples.
References
[2] Y.T. Gu, G.R. Liu. A radial basis boundary point interpolation method for stress analysis of solids. Structural Engineering and Mechanics. An International Journal, 15: 535- 550, 2003.
[3] R.L. Hardy. Multiquadric equations of topography and other irregular surfaces. Geophysical Research, 176: 1905- 1915, 1971.
[4] E.J. Kansa. Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics. Part I surface approximations and partial derivative estimates. Computers and Mathematics with Applications, 19(8/ 9):127- 145, 1990.
[5] E.J. Kansa. Multiquadrics- a scattered data approximation scheme with applications to computational fiuid dynamics. Part II solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers and Mathematics with Applications, 19(8/ 9): 147- 161 , 1990.
Published
Issue
Section
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
