A shape optimization approach to free boundary value problems

نویسندگان

  • J. Haslinger
  • T. Kozubek
چکیده

This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

متن کامل

Shape Optimization Problems with Robin Conditions on the Free Boundary

We provide a free discontinuity approach to a class of shape optimization problems involving Robin conditions on the free boundary. More precisely, we identify a large family of domains on which such problems are well posed in a way that the extended problem can be considered a relaxed version of the corresponding one on regular domains, we prove existence of a solution and obtain some qualitat...

متن کامل

Optimum Shape Design of a Radiant Oven by the Conjugate Gradient Method and a Grid Regularization Approach

This study presents an optimization problem for shape design of a 2-D radiant enclosure with transparent medium and gray-diffuse surfaces. The aim of the design problem is to find the optimum geometry of a radiant enclosure from the knowledge of temperature and heat flux over some parts of boundary surface, namely the design surface. The solution of radiative heat transfer is based on the net r...

متن کامل

A Bilevel Shape Optimization Problem for the Exterior Bernoulli Free Boundary Value Problem

A bilevel shape optimization problem with the exterior Bernoulli free boundary problem as lower-level problem and the control of the free boundary as the upper-level problem is considered. Using the shape of the inner boundary as the control, we aim at reaching a specific shape for the free boundary. A rigorous sensitivity analysis of the bilevel shape optimization in the infinite-dimensional s...

متن کامل

Shape Optimization and Trial Methods for Free Boundary Problems Shape Optimization and Trial Methods for Free Boundary Problems

In this work we consider diierent formulations for a free boundary problem and analyze the related numerical methods. In particular, we formulate various shape optimization problems that are weak forms of a free boundary problem and analyze their properties using the tools of 'shape calculus'. The main result is that it is possible to innuence the conditioning of the shape cost functional and t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003