Geometric aspects of shape optimization (Q6100448)

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scientific article; zbMATH DE number 7685090

Language	Label	Description	Also known as
English	Geometric aspects of shape optimization	scientific article; zbMATH DE number 7685090

Statements

scholarly article

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Geometric aspects of shape optimization (English)

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P. I. Plotnikov

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The Journal of Geometric Analysis

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publication date

12 May 2023

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zbMATH Keywords

shape optimization

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gradient flow

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boundary value problem

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s12220-023-01252-7

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The fast construction of extension velocities in level set methods

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Shape Methods for the Transmission Problem with a Single Measurement

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Shape optimization by the homogenization method

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Structural optimization using sensitivity analysis and a level-set method.

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Shape and topology optimization

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An optimal design problem with perimeter penalization

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A consistent approximation of the total perimeter functional for topology optimization algorithms

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Shape optimization problems

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The Differentiability of the Drag with Respect to the Variations of a Lipschitz Domain in a Navier--Stokes Flow

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Material interpolation schemes in topology optimization

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Characterization of optimal shapes and masses through Monge-Kantorovich equation

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Design-dependent loads in topology optimization

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Phase-field approximations of the Willmore functional and flow

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Variational methods in shape optimization problems

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Free Energy of a Nonuniform System. I. Interfacial Free Energy

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Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

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A Phase-Field Approximation of the Willmore Flow with Volume and Area Constraints

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User’s guide to viscosity solutions of second order partial differential equations

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An introduction to \(\Gamma\)-convergence

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A Willmore-Helfrich \(L^2\)-flow of curves with natural boundary conditions

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Numerical Solution of the Poisson Equation on Domains with a Thin Layer of Random Thickness

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Incorporating knowledge on the measurement noise in electrical impedance tomography

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Topological Derivative of State-Constrained Objective Functions: A Direct Method

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One-Sided Derivative of Parametrized Minima for Shape and Topological Derivatives

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Oriented Distance Function and Its Evolution Equation for Initial Sets with Thin Boundary

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Evolution equations for shapes and geometries

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Shapes and Geometries

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A phase field formulation of the Willmore problem

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Evolution of Elastic Curves in $\Rn$: Existence and Computation

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On a Kohn-Vogelius like formulation of free boundary problems

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Motion of level sets by mean curvature. I

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Phase-field approximation of the Willmore flow

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Axially symmetric cavitational flow

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A phase field approach to shape optimization in Navier-Stokes flow with integral state constraints

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The second order perturbation approach for elliptic partial differential equations on random domains

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Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM

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Analysis of the domain mapping method for elliptic diffusion problems on random domains

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Variation and optimization of formes. A geometric analysis

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On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions

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Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature

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Implicit time discretization for the mean curvature flow equation

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Determining conductivity by boundary measurements

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Drag minimization and lift maximization in laminar flows via topology optimization employing simple objective function expressions based on body force integration

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Robust shape and topology optimization of nanophotonic devices using the level set method

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A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

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\(L^2\)-flow of elastic curves with clamped boundary conditions

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Propagation of fronts in a nonlinear fourth order equation

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The Łojasiewicz-Simon inequality for the elastic flow

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The gradient theory of phase transitions and the minimal interface criterion

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S<scp>HAPE</scp> O<scp>PTIMIZATION IN</scp> F<scp>LUID</scp> M<scp>ECHANICS</scp>

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A Li-Yau inequality for the 1-dimensional Willmore energy

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Optimal approximations by piecewise smooth functions and associated variational problems

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Contre-exemples pour divers problèmes ou le contrôle intervient dans les coefficients

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Asymptotic analysis of shape functionals

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Topological derivatives in shape optimization

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An Introduction to the Topological Derivative Method

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Applications of the topological derivative method

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Structure of shape derivatives

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Michell truss type theories as a \(\Gamma\)-limit of optimal design in linear elasticity

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Level set methods: An overview and some recent results

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Geometric Level Set Methods in Imaging, Vision, and Graphics

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Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

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On optimum design in fluid mechanics

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Compressible Navier-Stokes Equations

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On a modified conjecture of De Giorgi

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Structural boundary design via level set and immersed interface methods

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On the Topological Derivative in Shape Optimization

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Distortion compensation as a shape optimisation problem for a sharp interface model

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Shape and topology optimization based on the phase field method and sensitivity analysis

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Level set methods and their applications in image science

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The Shapes of Things

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A level set method for structural topology optimization.

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Curve straightening flow deforms closed plane curves with nonzero rotation number to circles

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Global analysis of the generalised Helfrich flow of closed curves immersed in ℝⁿ

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Identifiers

zbMATH Open document ID

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10.1007/s12220-023-01252-7

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6100448

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