A Finite Pointset Method for Biharmonic Equation Based on Mixed Formulation

Abstract

In this paper, a meshless method based on finite point set is presented for solving the biharmonic equation with simply supported boundary condition. The biharmonic equation is split into a coupled system of two Poisson equations by introducing an intermediate function. The system of two Poisson equations is then solved by finite pointset method. This method is a local iterative method based on the weighted least square approximation. The advantage of this method is that two resultant of sizes only [Formula: see text] matrices are solved at each particle for the original and intermediate solution. Numerical results indicate a good accuracy of the finite pointset method.