Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization

Frédéric de Gournay (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In the context of structural optimization by the level-set method, we propose an extension of the velocity of the underlying Hamilton-Jacobi equation. The gradient method is endowed with a Hilbertian structure based on the H 1 Sobolev space. Numerical results for compliance minimization and mechanism design show a strong improvement of the rate of convergence of the level-set method. Another important application is the optimization of multiple eigenvalues

Mots clés: multiple eigenvalues; shape optimization; sensitivity analysis; shape derivative; level-set method; regularization

Domaines: Optimisation et contrôle [math.OC]

Frédéric de Gournay. Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization. SIAM Journal on Control and Optimization, 2006, 45 (1), pp.343 - 367. ⟨10.1137/050624108⟩. ⟨hal-01880854⟩