A meshless method for non-linear Poisson problems with high gradients

Husain J. Algahtani

Husain J. Algahtani King Fahd University of Petroleum & Minerals

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.

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References

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