A moving mesh fictitious domain approach for shape optimization problems

DOI10.1051/m2an:2000129zbMath0948.65064OpenAlexW2144351260WikidataQ109564586 ScholiaQ109564586MaRDI QIDQ4950977

Jari Toivanen, Raino A. E. Mäkinen, Tuomo Rossi

Publication date: 27 July 2000

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/197532

zbMATH Keywords

Lagrange multipliersnumerical experimentspreconditioningshape optimizationPoisson equationsaddle-point problemsfictitious domain methodsboundary variation technique

Mathematics Subject Classification ID

Numerical methods involving duality (49M29) Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

Efficient finite element methodology based on Cartesian grids: application to structural shape optimization, Fictitious domain approach via Lagrange multipliers with least squares spectral element method, \(\mathrm{E(FG)}^2\): a new fixed-grid shape optimization method based on the element-free Galerkin mesh-free analysis: taking large steps in shape optimization, Numerical Study of Two Sparse AMG-methods, Fictitious domain approach with \(hp\)-finite element approximation for incompressible fluid flow

Uses Software

• NAG
• nag

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Shape optimal design using B-splines
• A fictitious domain method for Dirichlet problem and applications
• Numerical realization of a fictitious domain approach used in shape optimization. I: Distributed controls
• The finite element method with Lagrangian multipliers
• Analysis of Preconditioners for Domain Decomposition
• A Triangulation Algorithm for Fast Elliptic Solvers Based on Domain Imbedding
• Finite-element design sensitivity analysis for non-linear potential problems
• On Finite Element Domain Imbedding Methods
• Geometric sensitivity analysis with isoparametric finite elements
• The Lagrange Multiplier Method for Dirichlet's Problem
• Fictitious domains with separable preconditioners versus unstructured adapted meshes
• Control/fictitious domain method for solving optimal shape design problems
• Solution of Sparse Indefinite Systems of Linear Equations
• The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
• Method of fictitious domains for a second-order elliptic equation with natural boundary conditions
• On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrande multiplier method
• A Parallel Fast Direct Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension
• Preconditioning Capacitance Matrix Problems in Domain Imbedding
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Fictitious domain/mixed finite element approach for a class of optimal shape design problems
• Efficient iterative solvers for elliptic finite element problems on nonmatching grids
• Numerical simulation and optimal shape for viscous flow by a fictitious domain method