Optimal Shape Design for Elliptic Equations via Bie{methods

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Multigrid Methods for PDE Optimization

Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.

Optimal Control Approaches for Some Geometric Optimization Problems

This work is a survey on optimal control methods applied to shape optimization problems. The unknown character of the domain where the state system is defined creates major difficulties both for the theoretical analysis and for the implementation of the numerical approximation methods. The optimal control and the controllability methods for elliptic equations allow the development of approximat...

Optimal Shape Design for a Cooling Pin Fin Connection Profil

A shape optimization problem of cooling fins for computer parts and integrated circuits is modeled and solved in this paper. The main purpose is to determine the shape of a two-dimensional pin fin, which leads to the maximum amount of removed heat. To do this, the shape optimization problem is defined as maximizing the norm of the Nusselt number distribution at the boundary of the pin fin's con...

Boundary Shape Control of Navier-stokes Equations and Geometrical Design Method for Blade’s Surface in the Impeller∗

In this paper A Geometrical Design Method for Blade’s surface I in the impeller is provided here I is a solution to a coupling system consisting of the well-known Navier-Stokes equations and a four order elliptic boundary value problem . The coupling system is used to describe the relations between solutions of Navier-Stokes equations and the geometry of the domain occupied by fluids, and also ...