Preprint No. MPIMD/11-04

Title: One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem

Author(s): Martin Stoll


Date: 2011-07-18


In this paper we describe the efficient solution of a PDE-constrained optimization problem subject to the time-periodic heat equation. We propose a space-time formulation for which we develop a monolithic solver. We present preconditioners well suited to approximate the Schur-complement of the saddle point system associated with the first order conditions. This means that in addition to a Richardson iteration based preconditioner we also introduce a preconditioner based on the tensor product structure of the PDE discretization, which allows the use of a FFT based preconditioner. We also consider additional bound constraints that can be treated using a semi-smooth Newton method. Moreover, we introduce robust preconditioners with respect to the regularization parameter. Numerical results will illustrate the competitiveness and flexibility of our approach.


author = {Martin Stoll},
title = {One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem},
number = {MPIMD/11-04},
month = jul,
year = 2011,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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