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
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
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
On numerical simulation of flow through oil filters
Computing and Visualization in Science
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
Shape-topology optimization for Navier-Stokes problem using variational level set method
Journal of Computational and Applied Mathematics
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
Solving the Chan-Vese model by a multiphase level set algorithm based on the topological derivative
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Optimality Conditions for Shape and Topology Optimization Subject to a Cone Constraint
SIAM Journal on Control and Optimization
A new method for inverse electromagnetic casting problems based on the topological derivative
Journal of Computational Physics
Augmented Lagrangian for cone constrained topology optimization
Computational Optimization and Applications
Structural and Multidisciplinary Optimization
Risk Averse Shape Optimization
SIAM Journal on Control and Optimization
Topology optimization considering static failure theories for ductile and brittle materials
Computers and Structures
Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems
Journal of Scientific Computing
Development of a novel phase-field method for local stress-based shape and topology optimization
Computers and Structures
Structural and Multidisciplinary Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
Hi-index | 31.46 |
The level-set method has been recently introduced in the field of shape optimization, enabling a smooth representation of the boundaries on a fixed mesh and therefore leading to fast numerical algorithms. However, most of these algorithms use a Hamilton-Jacobi equation to connect the evolution of the level-set function with the deformation of the contours, and consequently they can hardly create new holes in the domain (at least in 2D). In this work, we propose an evolution equation for the level-set function based on a generalization of the concept of topological gradient. This results in a new algorithm allowing for all kinds of topology changes.