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
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Journal of Computational Physics
The Topological Asymptotic Expansion for the Dirichlet Problem
SIAM Journal on Control and Optimization
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
Journal of Mathematical Imaging and Vision
A level set method for structural topology optimization and its applications
Advances in Engineering Software
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
A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
Journal of Computational Physics
Incorporating topological derivatives into shape derivatives based level set methods
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
Domain reconstruction using photothermal techniques
Journal of Computational Physics
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
A level set method for structural shape and topology optimization using radial basis functions
Computers and Structures
Journal of Computational Physics
Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design
Journal of Computational Physics
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
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
A 199-line Matlab code for Pareto-optimal tracing in topology optimization
Structural and Multidisciplinary Optimization
Journal of Computational Physics
Applied Numerical Mathematics
A new method for inverse electromagnetic casting problems based on the topological derivative
Journal of Computational Physics
Structural and Multidisciplinary Optimization
Augmented Lagrangian for cone constrained topology optimization
Computational Optimization and Applications
Structural and Multidisciplinary Optimization
Piecewise constant level set method for structural topology optimization with MBO type of projection
Structural and Multidisciplinary Optimization
A level set solution to the stress-based structural shape and topology optimization
Computers and Structures
Risk Averse Shape Optimization
SIAM Journal on Control and Optimization
Simultaneous optimization of cast part and parting direction using level set method
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Stress-based topology optimization using an isoparametric level set method
Finite Elements in Analysis and Design
Fixed-mesh curvature-parameterized shape optimization of an acoustic horn
Structural and Multidisciplinary Optimization
Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems
Journal of Scientific Computing
Structural and Multidisciplinary Optimization
Combination of topology optimization and optimal control method
Journal of Computational Physics
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 | 31.51 |
The aim of this paper is to investigate the use of topological derivatives in combination with the level set method for shape reconstruction and optimization problems. We propose a new approach generalizing the standard speed method, which is obtained by using a source term in the level set equation that depends on the topological derivative of the objective functional. The resulting approach can be interpreted as a generalized fixed-point iteration for the optimality system (with respect to topological and shape variations). Moreover, we apply the new approach for a simple model problem in shape reconstruction, where the topological derivative can be computed without additional effort. Finally, we present numerical tests related to this model problem, which demonstrate that the new method based on shape and topological derivative successfully reconstructs obstacles in situations where the standard level set approach fails.