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RBF collocation path-following approach: optimal choice for shape parameter based on genetic algorithm

This paper presents a new method to solve a challenging problem and a topic of current research namely the selection of optimal shape parameters for the Radial Basis Function (RBF) collocation methods in  both interpolation and nonlinear Partial Differential Equations (PDEs) problems.  To this intent, a compromise must be made to achieve the conflict between accuracy and stability referred to as the trade-off  or uncertainty principle.  The use of genetic algorithm and path-following continuation allows us on the one hand to avoid the local optimum issue associated with RBF interpolation ma

Optimal variable support size for mesh-free approaches using genetic algorithm

The main difficulty of the meshless methods is related to the support of shape functions.  These methods become stable when sufficiently large support is used.  Rather larger support size leads to higher calculation costs and greatly degraded quality.  The continuous adjustment of the support size to approximate the shape functions during the simulation can avoid this problem, but the choice of the support size relative to the local density is not a trivial problem.  In the present work, we deal with finding a reasonable size of influence domain by using a genetic algorithm coupled with hig