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
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
Dual Stochastic Dominance and Related Mean-Risk Models
SIAM Journal on Optimization
Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions
SIAM Journal on Optimization
Applying the Minimum Risk Criterion in Stochastic Recourse Programs
Computational Optimization and Applications
Free-form airfoil shape optimization under uncertainty using maximum expected value and second-order second-moment strategies
Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse
SIAM Journal on Optimization
Optimality Conditions for Simultaneous Topology and Shape Optimization
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
Polyhedral Risk Measures in Stochastic Programming
SIAM Journal on Optimization
A new algorithm for topology optimization using a level-set method
Journal of Computational Physics
Optimization of Convex Risk Functions
Mathematics of Operations Research
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
Composite finite elements for 3D image based computing
Computing and Visualization in Science
Shape Optimization Under Uncertainty—A Stochastic Programming Perspective
SIAM Journal on Optimization
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Risk averse optimization has attracted much attention in finite dimensional stochastic programming. In this paper, we propose a risk averse approach in the infinite dimensional context of shape optimization. We consider elastic materials under stochastic loading. As measures of risk awareness we investigate the expected excess and the excess probability. The developed numerical algorithm is based on a regularized gradient flow acting on an implicit description of the shapes based on level sets. We incorporate topological derivatives to allow for topological changes in the shape optimization procedure. Numerical results in two dimensions demonstrate the impact of the risk averse modeling on the optimal shapes and on the cost distribution over the set of scenarios.