Fictitious domains methods with distributed Lagrange multipliers Part II: Application to the solution of shape optimization problems

The distributed Lagrange multipliers based fictitious domain method for the numerical computation of state problems presented in Part I is now used in the frame of shape optimization. Practical aspects of this approach are discussed. In general it is shown that the resulting minimization problem is nonsmooth, due to the locking effect. Two possible regularization techniques are described and the results of one numerical example is shown.