Invited Session Tue.1.MA 415

Tuesday, 10:30 - 12:00 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Adaptive methods in PDE constrained optimization

 

Chair: Stefan Ulbrich

 

 

Tuesday, 10:30 - 10:55 h, Room: MA 415, Talk 1

Winnifried Wollner
Adaptive finite element discretizations in structural optimization

 

Abstract:
In this talk we will consider a prototypical example from structural optimization.
Namely the well known compliance minimization of a variable thickness sheet, i.e.,
given a domain Ω ⊂ R2, we consider


minq ∈ L2, u ∈ H1D l(u)


subject to the constraints


(q ,σ(∇ u),∇ φ) = l(φ)   ∀, φ ∈ H1D(Ω;R2),



0 < qmin ≤ q ≤ qmax,



Ω q ≤ Vmax,


where H1D(Ω;R2) denotes the usual H1-Sobolev space with certain Dirichlet boundary conditions,
and σ(∇ u) denotes the usual (linear) Lam{é}-Navier stress tensor.
As it is well known that the effort for the optimization is directly linked to the number of unknowns
present in the discretization we will derive an a posteriori error estimator in order to drive local mesh
refinement with respect to a given target quantity.
Finally we will give an outlook to possible extensions.

 

 

Tuesday, 11:00 - 11:25 h, Room: MA 415, Talk 2

Ronald H. Hoppe
Adaptive space-time finite element approximations of parabolic optimal control problems

 

Abstract:
We consider adaptive space-time finite element approximations of parabolic
optimal control problems with distributed controls based on an approach
where the optimality system is stated as a fourth order elliptic boundary
value
problem. The numerical solution relies on the formulation of the fourth
order
equation as a system of two second order ones which enables the
discretization
by P1 conforming finite elements with respect to simplicial triangulations
of
the space-time domain. The resulting algebraic saddle point problem is
solved
by preconditioned Richardson iterations featuring preconditioners
constructed
by means of appropriately chosen left and right transforms. The space-time
adaptivity is realized by a reliable residual-type a posteriori error
estimator
which is derived by the evaluation of the two residuals associated with
the
underlying second order system. Numerical results are given that
illustrate
the performance of the adaptive space-time finite element approximation.
% The results are based on joint work with F. Ibrahim, M. Hintermüller, M.
% Hinze, and Y. Iliash.

 

  Getting California Loans Online should be thought of many times. The new drug with unique properties was developed to help men to get rid of all sexual disorders, and its name is Cialis Super Force. Now you do not have to buy two different medications to solve sexual problems.