Two Algorithms for a Class of Elliptic Problems in Shape Optimization

Algorithm 1

(1) = 0.

(2) Compute the solution of (8) with domain ∖, .

  For = 1 : Nelement

   Find no marked elements, and compute their shape functional

    , and the sum of shape functional

   ;

  end

  Find the minimum of and mark the element.

(3) = + 1, Go to Step  2.