Solving parabolic equations with radial basis meshless domain decomposition method

Abstract

The configuration matrix obtained through the global radial basis function collocation method is usually an asymmetry full matrix and highly ill-conditioned for parabolic equations. To overcome the deficiencies, a radial basis meshless domain decomposition algorithm is proposed. It has the advantages of both the radial basis collocation method and the domain decomposition method. The new method can transform the solution to a large-scale problem into the solutions to several small sub-area ones. It effectively reduce the condition numbers of the collocation matrix. It is shown by numerical example that this method improves the stability and accelerates convergence of the numerical solution to parabolic equations.