Abstract: The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier–Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equat...

─ Although many numerical methods have been developed to calculate photonic bandgap structure properties, but always improvement in numerical methods is necessary to have more efficient, accurate and flexible techniques. In the present work, novel periodic meshless shape functions including so-called direct and radial shape functions are presented. The meshless approaches, based on these period...