Domain-type RBF Collocation Methods for Biharmonic Problems

Abstract

In this paper some meshless, domain-type discretization techniques are investigated in the context of problems modeled by biharmonic equations. These numerical methods use interpolant composed of radial basis functions (RBFs) as well as collocation technique to discretize a continuous mathematical model. To overcome a problem that appears for biharmonic equations, where two boundary conditions are associated with a boundary node, at which typically only one degree of freedom exists, some modifications of the methods are proposed. They are validated by a benchmark problem of bending and free vibration of Kirchhoff plates. Special attention is paid to estimate proper value of the shape parameter included in radial functions to ensure stability of the solution process and high accuracy. The results obtained show the usefulness of the proposed approaches.