A Novel Density Based Approach for Topology Optimization of Stokes Flow

DOI10.1137/21M143114XOpenAlexW4360999661MaRDI QIDQ5886862

Michael Ulbrich, Unnamed Author, Johannes Haubner

Publication date: 11 April 2023

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/21m143114x

zbMATH Keywords

Stokes flowtopology optimizationdensity based approachesphase field approaches

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Inverse problems for PDEs (35R30) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical analysis (65-XX)

Uses Software

• FEniCS
• Ipopt
• dolfin-adjoint

Cites Work

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• Shape and topology optimization in Stokes flow with a phase field approach
• Numerical quadrature for high-dimensional singular integrals over parallelotopes
• Shape optimization for surface functionals in Navier-Stokes flow using a phase field approach
• Piecewise constant level set method for structural topology optimization with {MBO} type of projection
• Topology optimization of channel flow problems
• Hitchhiker's guide to the fractional Sobolev spaces
• Automated solution of differential equations by the finite element method. The FEniCS book
• The limits of porous materials in the topology optimization of Stokes flows
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• Generating optimal topologies in structural design using a homogenization method
• A homogenization method for shape and topology optimization
• Regularization by functions of bounded variation and applications to image enhancement
• On an open question about functions of bounded variation.
• Material interpolation schemes in topology optimization
• A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints
• Fractional operators with inhomogeneous boundary conditions: analysis, control, and discretization
• Shape variation and optimization. A geometrical analysis
• Mathematical image processing. Translated from the German
• Learning nonlocal regularization operators
• Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation
• Shape and topology optimization
• Fractional Sobolev norms and BV functions on manifolds
• On the numerical evaluation of fractional Sobolev norms
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• Preconditioners for Saddle Point Systems with Trace Constraints Coupling 2D and 1D Domains
• A Total Variation–Based JPEG Decompression Model
• A convex analysis approach to multi-material topology optimization
• Advanced Numerical Methods for PDE Constrained Optimization with Application to Optimal Design in Navier Stokes Flow
• Shapes and Geometries
• Topology optimization of microfluidic mixers
• Discrete Interpolation Norms with Applications
• The method of moving asymptotes—a new method for structural optimization
• Quasi-Newton Methods and Unconstrained Optimal Control Problems
• Weakly Differentiable Functions
• On NEMYTSKIJ Operators inLp-Spaces of Abstract Functions
• Analysis of bounded variation penalty methods for ill-posed problems
• Structural Properties of Solutions to Total Variation Regularization Problems
• Total variation regularization of multi-material topology optimization
• Topology optimization of fluids in Stokes flow
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• Mixed Finite Element Methods and Applications
• Computing Multiple Solutions of Topology Optimization Problems
• A novel W^1,∞ approach to shape optimisation with Lipschitz domains
• Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids
• Mesh Dependence in PDE-Constrained Optimisation
• Topology optimization of slightly compressible fluids
• S<scp>HAPE</scp> O<scp>PTIMIZATION IN</scp> F<scp>LUID</scp> M<scp>ECHANICS</scp>
• Numerical approximation of fractional powers of elliptic operators

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