Shengfeng Zhu, East China Normal University
Room 306, No.5 Science Building
Shape and topology optimization have many applications in science and engineering fields. In engineering, boundary type Eulerian derivative is widely used in shape gradient algorithms. The distributed Eulerian derivative is seldom noticed. For the model problems of eigenvalue optimization and shape design in flows, we present two kinds of finite element discretization schemes for shape gradients corresponding to the distributed and boundary Eulerian derivatives. Our a prior error estimates show that the discrete shape gradient associated with the distributed Eulerian derivative has higher convergence rate. We find that the distributed Eulerian derivative can have better numerical performance during deformations. In addition, we will report a level set method for shape and topology optimization of a class of semilinear elliptic problems. Numerical algorithm and results will be reported.