Title: An Efficient Algorithm for Shape Optimization on Elliptic Eigenvalue
Problems

Abstract: In this talk,  we will discuss an efficient numerical approach
to find the optimal shape and topology for elliptic eigenvalue problems in
an
inhomogeneous media. The method is based on Rayleigh quotient formulation
of eigenvalue and a monotone iteration process to achieve the optimality.
The common numerical approach for these problems is to start with an
initial guess for the shape and then gradually evolve it, until it morphs
into the optimal shape. One of the difficulties is that the topology of
the optimal shape is unknown. Developing numerical techniques which can
automatically handle topology changes becomes essential for shape and
topology optimization problems. The level set approach based on both shape
derivatives and topological derivatives has been well known for its
ability to handle topology changes. However, CFL constrain significantly
slows down the algorithm when the mesh is further refined. Due to the
efficient binary update, our method not only has the ability of
topological changes but also is exempt from CFL condition. We provide
numerous numerical examples to demonstrate the robustness and efficiency
of our approach.