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Perturbation technique and method of fundamental solution to solve nonlinear Poisson problems |
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| Authors: | A Tri H Zahrouni M Potier-Ferry |
| Affiliation: | 1. Laboratoire de Mécanique, Faculté des Sciences Aïn Chok, Université Hassan II Casablanca, Casablanca, Maroc;2. Laboratoire d’Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Université Paul Verlaine – Metz, Ile du Saulcy, 57045 Metz, France |
| Abstract: | We show in this work that the Asymptotic Numerical Method (ANM) combined with the Method of Fundamental Solution (MFS) can be a robust algorithm to solve the nonlinear Poisson problem. The ANM transforms the nonlinear problem into a sequence of linear ones which can be solved by MFS. This last method consists of approximating the solution of the linear Poisson problem by a linear combination of fundamental solutions. Some examples are presented to show the efficiency of the proposed method. |
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