Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox

Götschel, Sebastian; Weiser, Martin; Schiela, Anton

doi:10.1007/978-3-642-28589-9_8

Cited by 21 publications

(19 citation statements)

References 10 publications

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“…The degrees of freedom for the state and the control are 44415 and 5043, respectively. Additionally, for the implementation, the finite element library KASKADE7 [12] was applied. This library has been developed at the Zuse Institute Berlin and is based on the DUNE library [4].…”

Section: Examplesmentioning

confidence: 99%

Optimal control of static contact in finite strain elasticity

Stöcklein

2020

ESAIM: COCV

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We consider the optimal control of elastic contact problems in the regime of finite deformations. We derive a result on existence of optimal solutions and propose a regularization of the contact constraints by a penalty formulation. Subsequential convergence of sequences of solutions of the regularized problem to original solutions is studied. Based on these results, a numerical path-following scheme is constructed and its performance is tested.

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Section: Examplesmentioning

confidence: 99%

Optimal control of static contact in finite strain elasticity

Stöcklein

2020

ESAIM: COCV

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“…The numerical algorithm of the finite element simulation is described in detail elsewhere [10,[18][19]. At this point, merely a brief description is given: For the FE simulation the Kaskade7 toolbox [19], implemented in C++, has been used. Flash heating at the front surface leads to a thin boundary layer in the temperature, which needs to be resolved in the numerical solution.…”

Section: Finite Element Simulationmentioning

confidence: 99%

Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography

Müller¹,

Götschel²,

Maierhofer³

et al. 2017

AIP Conference Proceedings

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Abstract. Flash thermography is a fast and reliable non-destructive testing method for the investigation of defects in carbon fiber reinforced polymer (CFRP) materials. In this paper numerical simulations of transient thermography data are presented, calculated for a quasi-isotropic flat bottom hole sample. They are compared to experimental data. These simulations are one important step towards the quantitative reconstruction of a flaw by assessing thermographic data. The applied numerical model is based on the finite-element method, extended by a semi-analytical treatment of the boundary of the sample, which is heated by the flash light. A crucial part for a reliable numerical model is the prior determination of the material parameters of the specimen as well as of the experimental parameters of the set-up. The material parameters in plane and in depth diffusivity are measured using laser line excitation. In addition, the absorption and heat transfer process of the first layers is investigated using an IR microscopic lens. The performance of the two distinct components of CFRP during heating -epoxy resin and carbon fibers -is examined. Finally, the material parameters are optimized by variation and comparison of the simulation results to the experimental data. The optimized parameters are compared to the measured ones and further methods to ensure precise material parameter measurements are discussed.

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“…Estimate (23) follows directly from the definition (20) of δs, using differentiability of c and continuous invertibility of c (x) on ker c (x) ⊥ . Next, (24) directly follows from comparing the Taylor expansion for f at x with q(δx):…”

Section: Order Of Consistency Of Composite Stepsmentioning

confidence: 99%

“…The sets D y ⊆ Ω and D u ⊆ Ω characterize the observation region as well as the region where the control acts. All examples were implemented with the finite element library Kaskade7 [20] using linear Lagrange elements. For the computation of tangential directions the HCG method was employed.…”

Section: Numerical Examplesmentioning

confidence: 99%

An affine covariant composite step method for optimization with PDEs as equality constraints

Lubkoll

Schiela

Weiser

2016

Optimization Methods and Software

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AMS MSC 2000: 49M37, 90C55, 90C06We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.

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Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox

Cited by 21 publications

References 10 publications

Optimal control of static contact in finite strain elasticity

Optimal control of static contact in finite strain elasticity

Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography

An affine covariant composite step method for optimization with PDEs as equality constraints

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