A level set method for structural topology optimization and its applications
Advances in Engineering Software
Feature sensitivity: A generalization of topological sensitivity
Finite Elements in Analysis and Design
Level set method with topological derivatives in shape optimization
International Journal of Computer Mathematics - INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
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
Topological Derivatives for Semilinear Elliptic Equations
International Journal of Applied Mathematics and Computer Science
An SL(2) Invariant Shape Median
Journal of Mathematical Imaging and Vision
A 199-line Matlab code for Pareto-optimal tracing in topology optimization
Structural and Multidisciplinary Optimization
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
Topological derivative and training neural networks for inverse problems
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Augmented Lagrangian for cone constrained topology optimization
Computational Optimization and Applications
Risk Averse Shape Optimization
SIAM Journal on Control and Optimization
Structural and Multidisciplinary Optimization
Sensitivity analysis of hyperbolic optimal control problems
Computational Optimization and Applications
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New optimality conditions are derived for a class of shape optimization problems. The conditions are established on the boundary by an application of the boundary variations technique and in the interior of an optimal domain by exploiting the topological derivative method. An example is provided for which the classical second order sufficient optimality conditions are verified for an optimal simply connected domain. However, the value of the cost can be improved by the topology variations, and therefore, the optimal solution can be substantially changed by applying the topology optimization.