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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 H1 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.

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