Multilevel Rbf-Fd Method for Steady Navier-Stokes Equations

This book contributes towards the development of two new meshfree local radial basis function (RBF-FD) methods for the numerical solution of initial and/or boundary value problems in physical science and engineering through partial differential equations. Meshfree methods are currently undergoing tremendous research. The efficiency of any numerical scheme is measured on its accuracy and computation time. Meshfree methods like radial basis function methods are not computationally efficient because it requires calculation of weights and square roots. So, in order to improve computational efficiency, some researchers combined meshfree method with mesh based method. However, this adjustment not only adulterates the main essence of meshfree methods but also restricts the original advantage and applicability of meshfree methods. Our attempt is to increase the efficiency of meshfree methods without compromising its meshfree nature thereby preserving its originality and applicability. Two multilevel augmented local radial basis function meshfree methods namely residue based V-cycle and bootstrap local refinement multilevel methods are developed.