Numerical solution for biharmonic equation using multilevel radial basis functions and domain decomposition methods

Biharmonic equation has significant applications in physics and engineering, but is difficult to solve due to the existing fourth order derivatives. One of the domain-type mashless methods is obtained by simply applying the radial basis functions (RBFs) as a direct collocation, which has shown to be effective in solving complicated physical problems with irregular domains. In this paper, we utilize overlapping domain decomposition and multilevel RBF methods for solving biharmonic equation. Numerical results indicate that these two methods circumvent the ill-conditioning problem resulted from using the radial basis function as a global interpolant.