Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
A PDE-based fast local level set method
Journal of Computational Physics
On Numerical Solution of Shape Inverse Problems
Computational Optimization and Applications
Optimality Conditions for Simultaneous Topology and Shape Optimization
SIAM Journal on Control and Optimization
A new algorithm for topology optimization using a level-set method
Journal of Computational Physics
Level set method with topological derivatives in shape optimization
International Journal of Computer Mathematics - INNOVATIVE ALGORITHMS IN SCIENCE AND ENGINEERING
Topological Derivatives for Semilinear Elliptic Equations
International Journal of Applied Mathematics and Computer Science
SIAM Journal on Control and Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
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The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.