Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Computational techniques for materials, composites and composite structures
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
A level set method for structural topology optimization and its applications
Advances in Engineering Software
A multilevel, level-set method for optimizing eigenvalues in shape design problems
Journal of Computational Physics
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
SIAM Journal on Control and Optimization
A new algorithm for topology optimization using a level-set method
Journal of Computational Physics
An extended level set method for shape and topology optimization
Journal of Computational Physics
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
A conservative level set method for two phase flow II
Journal of Computational Physics
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
Shape feature control in structural topology optimization
Computer-Aided Design
Level set method with topological derivatives in shape optimization
International Journal of Computer Mathematics - INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
Shape-topology optimization for Navier-Stokes problem using variational level set method
Journal of Computational and Applied Mathematics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
Journal of Computational Physics
Topological shape optimization of geometrically nonlinear structures using level set method
Computers and Structures
The constrained reinitialization equation for level set methods
Journal of Computational Physics
Shape optimized design of microwave dielectric resonators by level-set and topology gradient methods
International Journal of RF and Microwave Computer-Aided Engineering
Shape and topology optimization based on the phase field method and sensitivity analysis
Journal of Computational Physics
A Level Set Method in Shape and Topology Optimization for Variational Inequalities
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
A study on X-FEM in continuum structural optimization using a level set model
Computer-Aided Design
On the usefulness of non-gradient approaches in topology optimization
Structural and Multidisciplinary Optimization
On projection methods, convergence and robust formulations in topology optimization
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Heaviside projection based topology optimization by a PDE-filtered scalar function
Structural and Multidisciplinary Optimization
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
Parametric structural optimization with radial basis functions and partition of unity method
Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
Sensitivity filtering from a continuum mechanics perspective
Structural and Multidisciplinary Optimization
Parametric structural optimization with dynamic knot RBFs and partition of unity method
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Numerical instabilities in level set topology optimization with the extended finite element method
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
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This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.