On dual dynamic programming in shape optimization of coupled models

Lipnicka, Marta; Nowakowski, Andrzej

doi:10.1007/s00158-018-2057-5

Cited by 1 publication

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We quote also the recent work [13], where the authors consider a topology optimization of a weakly coupled steady state Navier–Stokes problem for the fluid domain, and treat in the same paper the coupled problem governed by a convection diffusion equation for the whole domain and the linear thermo‐elasticity system in the solid domain. Recently, a shape optimization analysis for coupled models by introducing the framework of the dual dynamic programming was also proposed in Reference [17].…”

Section: Introductionmentioning

confidence: 99%

On numerical study of constrained coupled shape optimization problems based on a new shape derivative method

Boulkhemair

Chakib

Sadik

2022

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach.

show abstract

Section: Introductionmentioning

confidence: 99%