Shape Optimization and Fictitious Domain Approach for Solving Free Boundary Problems of Bernoulli Type

Authors:
J. Haslinger;T. Kozubek;K. Kunisch;G. Peichl
Affiliations:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Praha 2, Czech Republic. haslin@apollo.karlov.mff.cuni.cz;Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic. tomas.kozubek@vsb.cz;Department for Mathematics, University Graz, Heinrichstrasse 36, A-8010 Graz, Austria. karl.kunisch@uni-graz.at;Department for Mathematics, University Graz, Heinrichstrasse 36, A-8010 Graz, Austria. gunther.peichl@uni-graz.at
Venue:
Computational Optimization and Applications
Year:
2003

Citing 5
Cited 7

Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
The controlled random search algorithm in optimizing regression models

Computational Statistics & Data Analysis
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis

Journal of the ACM (JACM)
Convex analysis and variational problems

Convex analysis and variational problems
Shapes and geometries: analysis, differential calculus, and optimization

Shapes and geometries: analysis, differential calculus, and optimization

Efficient treatment of stationary free boundary problems

Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Shape-topology optimization for Navier-Stokes problem using variational level set method

Journal of Computational and Applied Mathematics
An inverse model for a free-boundary problem with a contact line: Steady case

Journal of Computational Physics
Tracking Neumann Data for Stationary Free Boundary Problems

SIAM Journal on Control and Optimization
Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Domain-Map Linearization Approach

SIAM Journal on Scientific Computing
On a Kohn-Vogelius like formulation of free boundary problems

Computational Optimization and Applications
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method

Computational Mechanics

Quantified Score

Hi-index	0.01

Visualization

Abstract

This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems. It is based on a shape optimization approach. The state problems are solved by a fictitious domain solver using boundary Lagrange multipliers.