A spectral meshless method for PDE constrained optimization problem

In this paper a new method based on radial basis functions and spectral method is presented to solve PDE constrained optimization problems. In this paper, we will present the use of a localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for solving PDE constrained optimization problems. The basic idea of this approach is to apply collocation separately on each overlapping sub-domain of the whole domain. This localized method keeps the meshlessness and high accuracy of the RBF method. We employ a test problem to show the accuracy of the proposed technique. Illustrative example shows the reliability and efficiency of the new scheme