@misc{GoetschelMinion2019, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71490}, year = {2019}, abstract = {To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE constrained optimization. In order to develop an efficient fully time-parallel algorithm we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a non-linear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.}, language = {en} } @article{GoetschelMinion2019, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs}, volume = {41}, journal = {SIAM J. Sci. Comput.}, number = {6}, doi = {10.1137/19M1239313}, pages = {C603 -- C626}, year = {2019}, abstract = {To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.}, language = {en} } @article{GoetschelSchielaWeiser2021, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 - a Flexible Finite Element Toolbox}, volume = {81}, journal = {Computers and Mathematics with Applications}, doi = {10.1016/j.camwa.2020.02.011}, pages = {444 -- 458}, year = {2021}, abstract = {Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.}, language = {en} } @inproceedings{MuellerGoetschelWeiseretal.2017, author = {M{\"u}ller, Jan and G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane}, title = {Thermografie mit optimierter Anregung f{\"u}r die quantitative Untersuchung von Delaminationen in kohlenstofffaserverst{\"a}rkten Kunststoffen}, booktitle = {NDT.net Proc. DGZfP 2017}, year = {2017}, abstract = {Da kohlenstofffaserverst{\"a}rkte Kunststoffe (CFK) in anspruchsvollen sicherheitsrelevanten Einsatzgebieten wie im Automobilbau und in der Luftfahrt eingesetzt werden, besteht ein zunehmender Bedarf an zerst{\"o}rungsfreien Pr{\"u}fmethoden. Ziel ist die Gew{\"a}hrleistung der Sicherheit und Zuverl{\"a}ssigkeit der eingesetzten Bauteile. Aktive Thermografieverfahren erm{\"o}glichen die effiziente Pr{\"u}fung großer Fl{\"a}chen mit hoher Aufl{\"o}sung in wenigen Arbeitsschritten. Ein wichtiges Teilgebiet der Pr{\"u}fungen ist die Ortung und Charakterisierung von Delaminationen, die sowohl bereits in der Fertigung als auch w{\"a}hrend der Nutzung eines Bauteils auftreten k{\"o}nnen, und dessen strukturelle Integrit{\"a}t schw{\"a}chen. ;In diesem Beitrag werden CFK-Strukturen mit k{\"u}nstlichen und nat{\"u}rlichen Delaminationen mit Hilfe unterschiedlich zeitlich modulierter Strahlungsquellen experimentell untersucht. Verwendet werden dabei Anregungen mit Blitzlampen und mit frequenzmodulierten Halogenlampen. Mittels Filterfunktionen im Zeit- und Frequenzbereich wird das Kontrast-zu-Rausch-Verh{\"a}ltnis (CNR) der detektierten Fehlstellen optimiert. Verglichen werden anschließend die Nachweisempfindlichkeit, das CNR und die Ortsaufl{\"o}sung der zu charakterisierenden Delaminationen f{\"u}r die unterschiedlichen Anregungs- und Auswertungstechniken. Erg{\"a}nzt werden die Experimente durch numerische Simulationen des dreidimensionalen W{\"a}rmetransportes.}, language = {de} } @misc{GoetschelMinion2018, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST}, journal = {Domain Decomposition Methods in Science and Engineering XXIV}, publisher = {Springer}, address = {Cham}, doi = {10.1007/978-3-319-93873-8_34}, pages = {363 -- 371}, year = {2018}, abstract = {In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.}, language = {en} } @misc{GoetschelSchielaWeiser2019, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 -- a Flexible Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74616}, year = {2019}, abstract = {Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the Dune interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.}, language = {en} } @inproceedings{GoetschelMaierhoferMuelleretal.2016, author = {G{\"o}tschel, Sebastian and Maierhofer, Christiane and M{\"u}ller, Jan and Rothbart, Nick and Weiser, Martin}, title = {Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites}, booktitle = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, year = {2016}, language = {en} } @inproceedings{MuellerGoetschelMaierhoferetal.2017, author = {M{\"u}ller, Jan and G{\"o}tschel, Sebastian and Maierhofer, Christiane and Weiser, Martin}, title = {Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography}, volume = {1806}, booktitle = {AIP Conference Proceedings}, doi = {10.1063/1.4974671}, year = {2017}, language = {en} } @misc{FischerGoetschelWeiser2017, author = {Fischer, Lisa and G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy data compression reduces communication time in hybrid time-parallel integrators}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63961}, year = {2017}, abstract = {Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups.}, language = {en} } @misc{GoetschelMinion2017, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64989}, year = {2017}, abstract = {In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.}, language = {en} } @article{FischerGoetschelWeiser2018, author = {Fischer, Lisa and G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy data compression reduces communication time in hybrid time-parallel integrators}, volume = {19}, journal = {Comput. Vis. Sci.}, number = {1}, doi = {10.1007/s00791-018-0293-2}, pages = {19 -- 30}, year = {2018}, abstract = {Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups.}, language = {en} } @misc{GoetschelMaierhoferMuelleretal.2016, author = {G{\"o}tschel, Sebastian and Maierhofer, Christiane and M{\"u}ller, Jan P. and Rothbart, Nick and Weiser, Martin}, title = {Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58374}, year = {2016}, abstract = {Carbon-fiber reinforced composites are becoming more and more important in the production of light-weight structures, e.g., in the automotive and aerospace industry. Thermography is often used for non-destructive testing of these products, especially to detect delaminations between different layers of the composite. In this presentation, we aim at methods for defect reconstruction from thermographic measurements of such carbon-fiber reinforced composites. The reconstruction results shall not only allow to locate defects, but also give a quantitative characterization of the defect properties. We discuss the simulation of the measurement process using finite element methods, as well as the experimental validation on flat bottom holes. Especially in pulse thermography, thin boundary layers with steep temperature gradients occurring at the heated surface need to be resolved. Here we use the combination of a 1D analytical solution combined with numerical solution of the remaining defect equation. We use the simulations to identify material parameters from the measurements. Finally, fast heuristics for reconstructing defect geometries are applied to the acquired data, and compared for their accuracy and utility in detecting different defects like back surface defects or delaminations.}, language = {en} }