A quasi-linear technique applied to the method of fundamental solution

作者：Shanazari Kamal^*; Fallahi Mahmood

来源：Engineering Analysis with Boundary Elements, 2010, 34(4): 388-392.

DOI：10.1016/j.enganabound.2009.11.002

• Method of fundamental solution
• Meshless method
• Quasi-linear technique
• Non-linear Poisson's equations

This paper proposes the use of a quasi-linear technique for the method of fundamental solution (MFS) to treat the non-linear Poisson-type equations. The MFS, which is a fully meshless method, often deals with the linear and non-linear poisson equations by approximating a particular Solution via employing radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. The current work suggests a linearization scheme for the nonhomogeneous term in terms of the dependent variable resulting in Helmholtz-type equations whose fundamental solutions are available. Consequently, the MFS can be directly applied to the new linearized equation.

• 出版日期2010-4