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
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 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
Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach
International Journal of Applied Mathematics and Computer Science
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
Applied Numerical Mathematics
SIAM Journal on Control and Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
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A class of shape optimization problems is solved numerically by the level set method combined with the topological derivatives for topology optimization. Actually, the topology variations are introduced on the basis of asymptotic analysis, by an evaluation of extremal points (local maxima for the specific problem) of the so-called topological derivatives introduced by Sokolowski and Zochowski [J. Sokolowski and A. Zochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37(4) (1999), pp. 1251-1272] for elliptic boundary value problems. Topological derivatives are given for energy functionals of linear boundary value problems. We present results, including numerical examples, which confirm that the application of topological derivatives in the framework of the level set method really improves the efficiency of the method. Examples show that the level set method combined with the asymptotic analysis is robust for the shape optimization problems, and it allows us to identify the better solution compared to the pure level set method exclusively based on the boundary variation technique.