Perturbation technique and method of fundamental solution to solve nonlinear Poisson problems

作者：Tri A; Zahrouni H^*; Potier Ferry M

来源：Engineering Analysis with Boundary Elements, 2011, 35(3): 273-278.

DOI：10.1016/j.enganabound.2010.10.008

• Perturbation technique
• Method of Fundamental Solution
• Asymptotic Numerical Method
• Pade approximants

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.

• 出版日期2011-3