A spectral meshless method for PDE constrained optimizationproblem

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 presentthe 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 collocationseparately on each overlapping sub-domain of the whole domain. This localized method keeps the meshlessness and highaccuracy 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

Keywords:

meshless methods , spectral method , radial basis functions , PDE optimization