Dynamic programming approach to structural optimization problem – numerical algorithm

In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed

Dynamic programming approach to structural optimization problem - numerical algorithm

Tyt. z nagłówka.Bibliogr. s. 722-723.In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.Dostępny również w formie drukowanej.KEYWORDS: sufficient optimality condition, elliptic equations, optimal shape control, structural optimization, stationary Navier-Stokes equations, dynamic programming, numerical approximation

Note on Level Set Functions

Part 6: Shape and Structural OptimizationInternational audienceIn this note a concept of ε-level set function is introduced, i.e. a function which approximates a level set function satisfying the Hamilton-Jacobi inequality. We prove that each Lipschitz continuous solution of the Hamilton-Jacobi inequality is an ε-level set function. Next, a numerical approximation of the level set function is presented, i.e. method for the construction of an ε-level set function