Two Algorithms for a Class of Elliptic Problems in Shape Optimization

Abstract EN

We propose two algorithms for elliptic boundary value problems in shape optimization.

With the finite element method, the optimization problem is replaced by a discrete variational problem.

We give rules and use them to decide which elements are to be reserved.

Those rules are determined by the optimization; as a result, we get the optimal design in shape.

Numerical examples are provided to show the effectiveness of our algorithms.