Journal ArticleDOI
Shape Optimization and Fictitious Domain Approach for Solving Free Boundary Problems of Bernoulli Type
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This contribution deals with an efficient method for the numerical realization of the exterior and interior Bernoulli free boundary problems based on a shape optimization approach.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.read more
Citations
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Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method
TL;DR: Numerical experiments show that this intervention allows for stable nonlinear FCM analysis, preserving the full range of advantages of linear elastic FCM, in particular exponential rates of convergence.
Journal ArticleDOI
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics
TL;DR: The hp-d-adaptive finite cell method (hp-d) as discussed by the authors combines the FA with the p-version of the finite element method and adaptive integration to achieve high convergence rate and simple mesh generation, irrespective of the geometric complexity involved.
Journal ArticleDOI
A fictitious domain approach to the numerical solution of PDEs in stochastic domains
Claudio Canuto,Tomáš Kozubek +1 more
TL;DR: An efficient method for the numerical realization of elliptic PDEs in domains depending on random variables, using the combination of a fictitious domain approach and a polynomial chaos expansion is presented.
Journal ArticleDOI
Shape-topology optimization for Navier-Stokes problem using variational level set method
TL;DR: This work considers the shape-topology optimization of the Navier-Stokes problem and proposes a new algorithm based on the variational level set method, which can be maintained without re-initialization and drastic topology change can be handled easily.
Journal ArticleDOI
On Convergence in Elliptic Shape Optimization
TL;DR: Existence and convergence of approximate solutions are proved, provided that the infinite dimensional shape problem admits a stable second order optimizer.
References
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Journal ArticleDOI
A simplex method for function minimization
John A. Nelder,R. Mead +1 more
TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Book
Mixed and Hybrid Finite Element Methods
Franco Brezzi,Michel Fortin +1 more
TL;DR: Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.
Book
Convex analysis and variational problems
Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.