An Adaptive Level Set Method For Solving Shape Design Problems

In this thesis,a level set method based on finite element discretization and adaptive moving grid is proposed.We use this method to solve the problem of nonuniform acoustic drum and the problem of optimal design of photonic crystal band gap structure.The method proposed in this thesis will automatically adjust the mesh density during the iteration process,optimize the smoothness of the interface of the level-set method and reduce computational costs.Numerical results show effectiveness of the method.