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  • 1
    Book
    Book
    ¬The¬ control reduced interior point method : a function space oriented algorithmic approach (2006)
    München :Hut,
    Details
    Title: ¬The¬ control reduced interior point method : a function space oriented algorithmic approach
    Author: Schiela, Anton
    Edition: 1. Aufl.
    Publisher: München :Hut,
    Year of publication: 2006
    Pages: 175 S. : , Ill., graph. Darst.
    Series Statement: Mathematik
    Dissertation note: Berlin, Freie Univ., Diss., 2006
    ISBN: 978-3-89963-450-1 , 3-89963-450-0
    Type of Medium: Book
    Language: English
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 2
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    Asymptotic Mesh Independence of Newton's Method Revisited (2003)
    Details
    Publication Date: 2019-01-29
    Description: The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 3
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    Barrier methods for a control problem from hyperthermia treatment planning (2009)
    Details
    Publication Date: 2019-01-29
    Description: We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 4
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    Adaptive Timestep Control for the Contact-Stabilized Newmark Method (2010)
    Details
    Publication Date: 2016-06-09
    Description: The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 5
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    A Perturbation Result for Dynamical Contact Problems (2008)
    Details
    Publication Date: 2016-06-09
    Description: This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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    OPUS
  • 6
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    Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox (2010)
    Details
    Publication Date: 2022-01-07
    Description: This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 7
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    Uniqueness criteria for solutions of the adjoint equation in state-constrained optimal control (2010)
    Details
    Publication Date: 2016-06-09
    Description: The paper considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control problems. By a counter-example of Serrin, it is known that, in the presence of non-smooth data, a standard weak formulation does not ensure uniqueness for such equations. Therefore several notions of solution have been developed that guarantee uniqueness. In this note, we compare different definitions of solutions, namely the ones of Stampacchia and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution in the sense of Stampacchia, and prove the existence and uniqueness of solutions in in case of mixed boundary conditions.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 8
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    An optimal control problem in polyconvex hyperelasticity (2012)
    Details
    Publication Date: 2019-01-29
    Description: We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
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    A cubic regularization algorithm for nonconvex optimization in function space (in preparation) (2012)
    Details
    Publication Date: 2016-06-09
    Description: We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework. Moreover, several variants of step computations are compared. In the context of nonlinear elasticity it turns out the a cg method applied to an augmented Hessian is more robust than truncated cg.
    Language: English
    Type: reportzib , doc-type:preprint
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  • 10
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    A Perturbation Result for Dynamical Contact Problems (2009)
    Details
    Publication Date: 2016-06-09
    Language: English
    Type: article , doc-type:article
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