Comparison between shape optimization and volumic level set approximation for geometrical functionals
arXiv:0806.12881 citationsh-index: 8
Originality Synthesis-oriented
AI Analysis
Provides theoretical equivalence for practitioners in shape optimization and level set methods, but is incremental as it confirms known relationships.
The paper shows that shape optimization and volumic level set approximation yield the same derivative for general curvature functionals, unifying two approaches for geometric functional differentiation.
We propose to differentiate a general curvature functional with two different approaches. In the first one we compute the derivative with the tools of shape optimization and in the second one we compute the derivative of a volumic approximation of the functional with respect to a level set function. We show that the two previous approaches give the same result.