A variational level set method for the topology optimization of steady-state Navier–Stokes flow

Modelling and shape optimization of an actuator

“…Here, at each optimization step, replacing Stokes equations by steady Navier-Stokes equations as the perturbation occurs in the vicinity of the unstable steady solution, the Lagrangian functional becomes (Mohammadi and Pironneau 2010;Zhou and Li 2008):…”

“…Among all these methods in topology optimization it is important to quote the solid isotropic material with penalization (SIMP) approach (Bendsøe and Sigmund 2003;Brackett et al 2010) and the coupling of level-set method with topological derivation (Allaire and Jouve 2006;Duan et al 2008;Osher and Santosa 2001). Besides there are many applications to shape optimization for fluids (Amstutz 2005;Borrvall and Petersson 2003;Gersborg-Hansen et al 2005;Guillaume and Sid 2004;Mohammadi and Pironneau 2010;Zhou and Li 2008).…”

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

“…Topology optimization is currently regarded to be the most robust methodology for the inverse determination of material distribution in structures that meet given structural performance criteria. It was first developed for elastic material response by Bendsøe & Kikuchi [35], and then was extended to a variety of application areas, including acoustic, electromagnetic, fluidic and thermal problems [16,[20][21][22][24][25][26][27][28][29][30][31][32][33][36][37][38][39][40][41][42][43][44][45], to list the most prominent. Most of the reports on topology optimization in electromagnetics have focused on applications, including beamsplitters [18,19], photonic crystals [16,17], cloaks [20][21][22], sensors and resonators [44,45], metamaterials [23][24][25], excitation of surface plasmons [26], and electromagnetic and optical antennas [27][28][29]34], without presenting the systemical topology optimization methodology for electromagnetic waves in three-dimensional space.…”

Adjoint-based shape optimization of fin geometry for heat transfer enhancement in solidification problem

“…More recently, the topology optimization techniques have been also extended to various problems with heat conduction (Gersborg-Hansen et al, 2006;Zhuang et al, 2007;Iga et al, 2009) and Navier-Stokes flows (Zhou & Li, 2008;Deng et al, 2011). In shape optimization methods, the geometrical shape of the boundary surface, which is represented by geometrical parameters, is to be optimized.…”