Velocity extension for the level-set method and multiple eigenvalues in shape optimization

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.