@misc{Sali2016, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60508}, year = {2016}, abstract = {The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model.}, language = {en} } @misc{Sali2016, type = {Master Thesis}, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, pages = {63}, year = {2016}, abstract = {The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model.}, language = {en} } @article{WeiserGhosh2018, author = {Weiser, Martin and Ghosh, Sunayana}, title = {Theoretically optimal inexact SDC methods}, journal = {Communications in Applied Mathematics and Computational Science}, number = {13-1}, doi = {10.2140/camcos.2018.13.53}, pages = {53 -- 86}, year = {2018}, abstract = {In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples.}, language = {en} } @misc{GoetschelWeiserMaierhoferetal.2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15243}, year = {2012}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @article{HochmuthDeuflhard2004, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {Multiscale Analysis for the Bio-Heat-Transfer Equation - The Nonisolated Case}, volume = {14}, journal = {Mathematical Models and Methods in Applied Sciences (M\$^3\$AS)}, number = {11}, pages = {1621 -- 1634}, year = {2004}, language = {en} } @article{HellerDudaEhrigetal.2005, author = {Heller, Markus O. and Duda, Georg and Ehrig, Rainald and Schell, H. and Seebeck, P. and Taylor, William R.}, title = {Muskuloskeletale Belastungen im Schafshinterlauf}, journal = {Materialwissenschaft und Werkstofftechnik}, number = {36}, pages = {775 -- 780}, year = {2005}, language = {en} } @inproceedings{HellerDudaKoenigetal.2005, author = {Heller, Markus O. and Duda, G. and K{\"o}nig, Christian and Taylor, William R. and Ehrig, Rainald and Hinterwimmer, S. and Graichen, H.}, title = {Validation of a New Model of Human Knee Kinematics against in Vivo Data under Physiologic Neuromuscular Activation Patterns}, booktitle = {Proceedings of the 51th Annual Meeting of the Orthopedic Society}, address = {Washington}, year = {2005}, language = {en} } @article{HellmichKoberErdmann2008, author = {Hellmich, Christian and Kober, Cornelia and Erdmann, Bodo}, title = {Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible}, volume = {36}, journal = {Annals of Biomedical Engineering}, number = {1}, doi = {10.1007/s10439-007-9393-8}, pages = {108 -- 122}, year = {2008}, language = {en} } @article{HellerKratzensteinEhrigetal.2011, author = {Heller, Markus O. and Kratzenstein, Stefan and Ehrig, Rainald and Wassilew, Georgi and Duda, Georg and Taylor, William R.}, title = {The weighted optimal common shape technique improves identification of the hip joint centre of rotation in vivo}, volume = {29}, journal = {Journal of Orthopedic Research}, pages = {1470 -- 5}, year = {2011}, language = {en} } @article{GellermannWeihrauchChoetal.2006, author = {Gellermann, Johanna and Weihrauch, Mirko and Cho, C. and Wlodarczyk, Waldemar and F{\"a}hling, Horst and Felix, Roland and Budach, Volker and Weiser, Martin and Nadobny, Johanna and Wust, Peter}, title = {Comparison of MR-thermography and planning calculations in phantoms}, volume = {33}, journal = {Medical Physics}, pages = {3912 -- 3920}, year = {2006}, language = {en} } @article{HellerKoenigGraichenetal.2007, author = {Heller, Markus O. and K{\"o}nig, Christian and Graichen, F. and Hinterwimmer, S. and Ehrig, Rainald and Duda, G. and Taylor, William R.}, title = {A new model to predict in vivo human knee kinematics under physiological-like muscle activation}, journal = {Journal of Biomechanics}, pages = {45 -- 53}, year = {2007}, language = {en} } @techreport{GladilinPeckarRohretal.1999, author = {Gladilin, Evgeny and Peckar, W. and Rohr, K. and Stiehl, H.}, title = {A Comparsion Between BEM and FEM for Elastic Registration of Medical Images}, number = {FBI-HH-M-287/99}, publisher = {FB Informatik}, address = {Hamburg, Germany}, year = {1999}, language = {en} } @article{GaenzlerVolkweinWeiser2006, author = {G{\"a}nzler, Tobias and Volkwein, S. and Weiser, Martin}, title = {SQP methods for parameter identification problems arising in hyperthermia}, volume = {21}, journal = {Optim. Methods Softw.}, number = {6}, pages = {869 -- 887}, year = {2006}, language = {en} } @article{EhrigHellerKratzensteinetal.2011, author = {Ehrig, Rainald and Heller, Markus O. and Kratzenstein, Stefan and Duda, Georg and Trepczynski, Adam and Taylor, William R.}, title = {The SCoRE residual: A quality index to assess the accuracy of joint estimations}, volume = {44}, journal = {Journal of Biomechanics}, number = {7}, doi = {10.1016/j.jbiomech.2010.12.009}, pages = {1400 -- 1404}, year = {2011}, language = {en} } @inproceedings{ErdmannKoberLangetal.2002, author = {Erdmann, Bodo and Kober, C. and Lang, Jens and Deuflhard, Peter and Zeilhofer, J. and Sader, Robert}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, booktitle = {proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2002}, language = {en} } @article{ErdmannLjubijankicNytschGeusen2007, author = {Erdmann, Bodo and Ljubijankic, M. and Nytsch-Geusen, C.}, title = {Entwicklung einer Toolbox zur zwei- und dreidimensionalen instation{\"a}ren thermischen Bauteilsimulation mit KARDOS}, volume = {29}, journal = {Bauphsik}, number = {1}, pages = {33 -- 39}, year = {2007}, language = {en} } @inproceedings{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments}, booktitle = {CHT'97}, editor = {de Vahl Davis, G. and Leonardi, E.}, address = {Cesme, Turkey}, pages = {103 -- 110}, year = {1997}, language = {en} } @inproceedings{ErdmannLangSeebass1998, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Optimization of Temperature Distributions for Regional Hyperthermia based on a Nonlinear Heat Transfer Model}, volume = {858}, booktitle = {Biotransport}, editor = {Diller, K.}, pages = {36 -- 46}, year = {1998}, language = {en} } @article{ErdmannLangSeebass1999, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {The Impact of a Nonlinear Heat Transfer Model for Temperature Control in Regional Hyperthermia}, volume = {49}, journal = {IEEE Transactions on Biomedical Engineering}, number = {9}, pages = {1129 -- 1138}, year = {1999}, language = {en} } @article{EhrigTaylorDudaetal.2006, author = {Ehrig, Rainald and Taylor, William R. and Duda, G. and Heller, Markus O.}, title = {A Survey for Formal Methods for Determining the Centre of Ball Joints}, journal = {Journal of Biomechanics}, number = {39}, pages = {2798 -- 2809}, year = {2006}, language = {en} } @inproceedings{EhrigTaylorDudaetal.2006, author = {Ehrig, Rainald and Taylor, William R. and Duda, G. and Heller, Markus O.}, title = {A New Approach for the Determination of Joint Axes}, booktitle = {Proceedings of the 52th Annual Meeting of the Orthopedic Society}, address = {Chicago}, year = {2006}, language = {en} } @article{EhrigTaylorDudaetal.2007, author = {Ehrig, Rainald and Taylor, William R. and Duda, Georg and Heller, Markus O.}, title = {A Survey for Formal Methods for Determining Functional Joint Axes}, journal = {Journal of Biomechanics}, pages = {2150 -- 2157}, year = {2007}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {A nonlinear soft tissue model for craniofacial surgery simulations}, booktitle = {Proc. of Modeling and Simulation for Computer-aided Medicine and Surgery (MS4CMS}, publisher = {INRIA}, address = {Paris, France}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Biomechanical modeling of individual facial emotion expressions}, booktitle = {Proc. of Visualization, Imaging, and Image Processing (VIIP)}, address = {Malaga, Spain}, pages = {7 -- 11}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Biomechanisches Modell zur Absch{\"a}tzung der individuellen Gesichtsmimik}, booktitle = {Proc.of Workshop Bildverarbeitung f{\"u}r die Medizin (BVM)}, editor = {Meiler, M. and Saupe, D. and Krugel, F. and Handels, H. and Lehmann, T.}, address = {Leipzig, Germany}, pages = {25 -- 28}, year = {2002}, language = {en} } @phdthesis{Gladilin2003, author = {Gladilin, Evgeny}, title = {Biomechanical Modeling of Soft Tissue and Facial Expressions for Craniofacial Surgery Planning}, address = {Germany}, year = {2003}, language = {en} } @inproceedings{Gladilin2004, author = {Gladilin, Evgeny}, title = {A contour based approach for invariant shape description}, volume = {5370}, booktitle = {SPIE Medical Imaging Conference}, address = {San Diego, USA}, pages = {1282 -- 1291}, year = {2004}, language = {en} } @incollection{LangErdmannKoberetal.2003, author = {Lang, Jens and Erdmann, Bodo and Kober, Cornelia and Deuflhard, Peter and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Effiziente und zuverl{\"a}ssige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers}, volume = {1}, booktitle = {Berichte des IZWR - Interdisziplin{\"a}res Zentrum f{\"u}r Wissenschaftliches Rechnen}, editor = {Alt, Walter and Hermann, Martin}, publisher = {Universit{\"a}t Jena}, address = {Germany}, pages = {49 -- 57}, year = {2003}, language = {en} } @inproceedings{KornaropoulosTaylorDudaetal.2009, author = {Kornaropoulos, Evgenios I. and Taylor, William R. and Duda, Georg and Ehrig, Rainald and Matziolis, Georg and M{\"u}ller, Michael and Wassilew, Georgi and Asbach, Patrick and Perka, Carsten and Heller, Markus O.}, title = {An imageless method to quantify the mechanical femoral-tibial angle based on the functional determination of joint centers and axes}, booktitle = {Annual meeting of the ESMAC 2009}, address = {London}, year = {2009}, language = {en} } @article{KornaropoulosTaylorDudaetal.2010, author = {Kornaropoulos, Evgenios I. and Taylor, William R. and Duda, Georg and Ehrig, Rainald and Matziolis, Georg and M{\"u}ller, Michael and Wassilew, Georgi and Asbach, Patrick and Perka, Carsten and Heller, Markus O.}, title = {Frontal plane alignment: An imageless method to predict the mechanical femoral-tibial angle (mFTA) based on functional determination of joint centres and axes}, volume = {31}, journal = {Gait \& Posture}, number = {2}, doi = {10.1016/j.gaitpost.2009.10.006}, pages = {204 -- 208}, year = {2010}, language = {en} } @inproceedings{KratzensteinTaylorEhrigetal.2009, author = {Kratzenstein, Stefan and Taylor, William R. and Ehrig, Rainald and Heller, Markus O.}, title = {Reduction of the influence of skin marker artefacts using the optimal common shape technique}, booktitle = {Annual meeting of the ESMAC 2009}, address = {London}, year = {2009}, language = {en} } @inproceedings{KassiTaylorSchwarzkopfetal.2004, author = {Kassi, J.-P. and Taylor, William R. and Schwarzkopf, J. and Schell, H. and Duda, G. and Ehrig, Rainald}, title = {Wie sind Osteosynthesesysteme und Defektzonen in vivo belastet?}, booktitle = {68. Jahrestagung der Deutschen Gesellschaft f{\"u}r Unfallchirurgie in Verbindung mit dem Deutschen Orthop{\"a}denkongress}, address = {Berlin}, year = {2004}, language = {en} } @inproceedings{KratzensteinEhrigHelleretal.2010, author = {Kratzenstein, Stefan and Ehrig, Rainald and Heller, Markus O. and Duda, Georg and Taylor, William R.}, title = {A Quantification of Accuracy in Estimating Joint Centers}, booktitle = {17th Congress of the European Society of Biomechanics}, address = {Edinburgh}, year = {2010}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Geiger, M. and Sader, Robert and Zeilhofer, Hans-Florian}, title = {How does the periodontal ligament influence overall stress/strain profiles of a partially edentulous mandible?}, booktitle = {Proc. of 8th Int. Conference on Biological Mechanisms of Tooth Eruption, Resorption and Movement, Phuket, Thailand}, editor = {Davidovitch, Z. and Mah, J. and Suthanarak, S.}, address = {Harvard Society of the Advancement of Orthodontics, Boston, Massachusetts, USA}, year = {2005}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2004, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Anisotropic Simulation of the Human Mandible}, booktitle = {Proc. of 17th ASCE Engineering Mechanics Conference}, publisher = {Univ. of Delaware}, year = {2004}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Consideration of Bone Inhomogeneity and Anisotropy in Deformation Analysis of a Human Mandible}, volume = {1}, booktitle = {Proc. of BMT2005, 39th Annual Congress of the German Society of Biomedical Engineering, Nuremberg, Germany}, editor = {Boenick, U. and Bolz, A.}, publisher = {VDE}, address = {Nuremberg, Germany}, pages = {814 -- 815}, year = {2005}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {The Influence of the Periodontal Ligament on Overall Stress/Strain Profiles of a Human Mandible}, booktitle = {Proc. of 23rd CADFEM Users' Meeting, Int. Congress on FEM Technology, Biomechanics}, editor = {CADFEM GmbH, Grafing}, address = {Bonn, Germany}, pages = {1 -- 10}, year = {2005}, language = {en} } @inproceedings{KoberErdmannLangetal.2004, author = {Kober, C. and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Sensitivity of the Temporomandibular Joint Capsule for the Structural Behaviour of the Human Mandible}, volume = {49-2}, booktitle = {Proc. BMT 2004}, address = {Ilmenau, Deutschland}, pages = {372 -- 373}, year = {2004}, language = {en} } @article{KlapprothDeuflhardSchiela2009, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, volume = {2}, journal = {Numer. Math}, pages = {237 -- 257}, year = {2009}, language = {en} } @phdthesis{Klapproth2012, author = {Klapproth, Corinna}, title = {Adaptive numerical integration for dynamical contact problems}, year = {2012}, language = {en} } @inproceedings{KoberSaderZeilhoferetal.2003, author = {Kober, C. and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {An Individual Anisotropic and Inhomogeneous Material Description of the Human Mandible}, booktitle = {Mathematical Modelling and Computing in Biology and Medicine}, editor = {Capasso, Vincenzo}, publisher = {ESTMB}, pages = {103 -- 109}, year = {2003}, language = {en} } @article{DeuflhardErdmannRoitzschetal.2009, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Dynamics}, volume = {12}, journal = {J. Computing and Visualization in Science}, pages = {201 -- 205}, year = {2009}, language = {en} } @inproceedings{KoberErdmannLangetal.2004, author = {Kober, C. and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Adaptive Finite Element Simulation of the Human Mandible Using a New Physiological Model of the Masticatory Muscles}, volume = {4}, booktitle = {Proc. of 75th Annual Meeting of the GAMM}, number = {1}, pages = {332 -- 333}, year = {2004}, language = {en} } @inproceedings{KoberErdmannSaderetal.2003, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Simulation of the Human Mandible}, booktitle = {Proceedings of 10th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2003}, language = {en} } @article{KoberErdmannSaderetal.2003, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Belastungssimulation beim menschlichen Biss im Vergleich mit der Dichtestruktur im Unterkieferknochen}, volume = {48}, journal = {Biomedizinische Technik}, number = {Erg{\"a}nzungsband 1}, pages = {268 -- 269}, year = {2003}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2009, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Schr{\"o}der, J{\"o}rg H. and Taylor, William R.}, title = {Die Bestimmung der Genauigkeit nicht-invasiver Techniken zur Ermittlung der H{\"u}ftgelenksposition in-vivo}, booktitle = {6th annual meeting of the German Society for Biomechanics (DGfB)}, address = {M{\"u}nster}, year = {2009}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2009, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Schr{\"o}der, J{\"o}rg H. and Taylor, William R.}, title = {Der Vergleich von nicht-invasiven Techniken zur Bestimmung der H{\"u}ftgelenksposition}, booktitle = {Annual meeting of the German Society of Orthopaedics and Trauma Surgery}, address = {Berlin}, year = {2009}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2010, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Taylor, William R.}, title = {The Residual: A Reliable Measure of Accuracy in the Determination of Joint Centers}, booktitle = {Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society}, address = {New Orleans}, year = {2010}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2010, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Taylor, William R.}, title = {The Hip Joint Centre can be determined to within 3 mm}, booktitle = {17th Congress of the European Society of Biomechanics}, address = {Edinburgh}, year = {2010}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2010, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Wassilew, Georgi and Duda, Georg and Taylor, William R.}, title = {A new approach for optimally reducing skin marker artifact allows determination of the hip joint center within 3mm}, booktitle = {Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society}, address = {New Orleans}, year = {2010}, language = {en} } @article{SchielaGuenther2011, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {An Interior Point Algorithm with Inexact Step Computation in Function Space for State Constrained Optimal Control}, volume = {119}, journal = {Numer. Math.}, number = {2}, publisher = {Springer Berlin / Heidelberg}, doi = {10.1007/s00211-011-0381-4}, pages = {373 -- 407}, year = {2011}, language = {en} } @article{SchielaWeiser2008, author = {Schiela, Anton and Weiser, Martin}, title = {Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization}, volume = {39}, journal = {Computational Optimization and Applications}, number = {3}, pages = {369 -- 393}, year = {2008}, language = {en} } @article{SreenivasaGellermannNadobnyetal.2003, author = {Sreenivasa, G. and Gellermann, Johanna and Nadobny, Johanna and Schlag, P. and Deuflhard, Peter and Felix, Roland and Wust, Peter}, title = {Clinical Use of the Hyperthermia Treatment Planning System Hyperplan to Predict Effectiveness and Toxicity}, volume = {55}, journal = {Int. J. Oncology Biol. Phys.}, number = {2}, pages = {407 -- 419}, year = {2003}, language = {en} } @inproceedings{TaylorEhrigDudaetal.2006, author = {Taylor, William R. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {The determination of joint axes}, booktitle = {5. World Congress of Biomechanics, Munich, Journal of Biomechanics}, number = {39, Suppl. 1}, pages = {S571 -- S572}, year = {2006}, language = {en} } @incollection{ZachowWeiserHegeetal.2005, author = {Zachow, Stefan and Weiser, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {Soft Tissue Prediction in Computer Assisted Maxillofacial Surgery Planning}, booktitle = {Biomechanics Applied to Computer Assisted Surgery}, editor = {Payan, Y.}, publisher = {Research Signpost}, pages = {277 -- 298}, year = {2005}, language = {en} } @incollection{ZachowWeiserDeuflhard2008, author = {Zachow, Stefan and Weiser, Martin and Deuflhard, Peter}, title = {Modellgest{\"u}tzte Operationsplanung in der Kopfchirurgie}, booktitle = {Modellgest{\"u}tzte Therapie}, editor = {Niederlag, Wolfgang and Lemke, Heinz and Meixensberger, J{\"u}rgen and Baumann, Michael}, publisher = {Health Academy}, pages = {140 -- 156}, year = {2008}, language = {en} } @article{HinzeSchiela2011, author = {Hinze, Michael and Schiela, Anton}, title = {Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: optimal error estimates and parameter adjustment}, volume = {48}, journal = {Comp. Opt. and Appl.}, number = {3}, publisher = {Springer}, doi = {10.1007/s10589-009-9278-x}, pages = {581 -- 600}, year = {2011}, language = {en} } @article{Weiser2009, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion Equations}, volume = {59}, journal = {Appl. Num. Math.}, number = {8}, pages = {1858 -- 1869}, year = {2009}, language = {en} } @article{WeihrauchWustWeiseretal.2007, author = {Weihrauch, Mirko and Wust, Peter and Weiser, Martin and Nadobny, Johanna and Eisenhardt, Steffen and Budach, Volker and Gellermann, Johanna}, title = {Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system}, volume = {34}, journal = {Medical Physics}, number = {12}, pages = {4717 -- 4725}, year = {2007}, language = {en} } @article{Weiser2005, author = {Weiser, Martin}, title = {Interior point methods in function space}, volume = {44}, journal = {SIAM J. Control Optimization}, number = {5}, pages = {1766 -- 1786}, year = {2005}, language = {en} } @inproceedings{TaylorKassiSchwarzkopfetal.2005, author = {Taylor, William R. and Kassi, J.-P. and Schwarzkopf, J. and Ehrig, Rainald and Schell, H. and Duda, G.}, title = {The Profile of Mechanical Loading is Independent of Fracture Fixation Principle}, booktitle = {Proceedings of the 51th Annual Meeting of the Orthopedic Society}, address = {Washington}, year = {2005}, language = {en} } @article{TaylorPoepplauKoenigetal.2011, author = {Taylor, William R. and P{\"o}pplau, Berry M. and K{\"o}nig, Christian and Ehrig, Rainald and Zachow, Stefan and Duda, Georg and Heller, Markus O.}, title = {The medial-lateral force distribution in the ovine stifle joint during walking}, volume = {29}, journal = {Journal of Orthopaedic Research}, number = {4}, doi = {10.1002/jor.21254}, pages = {567 -- 571}, year = {2011}, language = {en} } @article{BoethDudaHelleretal.2013, author = {Boeth, Heide and Duda, Georg and Heller, Markus O. and Ehrig, Rainald and Doyscher, Ralf and Jung, Tobias and Moewis, Philippe and Scheffler, Sven and Taylor, William R.}, title = {Anterior cruciate ligament-deficient patients with passive knee joint laxity have a decreased range of anterior-posterior motion during active movements}, volume = {41}, journal = {The American Journal of Sports Medicine}, number = {5}, doi = {10.1177/0363546513480465}, pages = {1051 -- 7}, year = {2013}, language = {en} } @inproceedings{TaylorEhrigDudaetal.2006, author = {Taylor, William R. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {The Symmetrical Axis of Rotation Approach (SARA) for Determination of Joint Axes in Clinical Gait Analysis}, booktitle = {1st Joint ESMAC-GCMAS Meeting, Amsterdam}, year = {2006}, language = {en} } @inproceedings{TaylorEhrigHelleretal.2004, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Duda, G.}, title = {Can Skin Markers Determine the Kinematics of Underlying Bones?}, booktitle = {Proceedings of the 50th Annual Meeting of the Orthopedic Society}, address = {San Francisco}, year = {2004}, language = {en} } @article{TaylorEhrigHelleretal.2005, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Klein, P. and Duda, G.}, title = {On the Influence of Soft Tissue Coverage in the Determination of Bone Kinematics using Bone Markers}, journal = {Journal of Orthopedic Research}, number = {23}, pages = {726 -- 734}, year = {2005}, language = {en} } @inproceedings{TaylorEhrigHelleretal.2005, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Seebeck, P. and Duda, G.}, title = {Animal Models for Knee Injury Frequently Underestimate the Mechanical Conditions of the Clinical Situation}, booktitle = {Proceedings of the 51th Annual Meeting of the Orthopedic Society}, address = {Washington}, year = {2005}, language = {en} } @article{TaylorEhrigHelleretal.2006, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Seebeck, P. and Duda, G.}, title = {Tibio-femoral Joint Contact Forces in Sheep}, journal = {Journal of Biomechanics}, number = {39}, pages = {791 -- 798}, year = {2006}, language = {en} } @inproceedings{TaylorKornaropoulosEhrigetal.2009, author = {Taylor, William R. and Kornaropoulos, Evgenios I. and Ehrig, Rainald and Heller, Markus O. and Duda, Georg}, title = {Reproducibility of a functional approach to gait analysis}, booktitle = {Annual meeting of the ESMAC 2009}, address = {London}, year = {2009}, language = {en} } @inproceedings{TaylorKratzensteinKornaropoulosetal.2009, author = {Taylor, William R. and Kratzenstein, Stefan and Kornaropoulos, Evgenios I. and Ehrig, Rainald and Moewis, Philippe and Heller, Markus O.}, title = {Non-invasive Assessment of Skeletal Kinematics}, booktitle = {Measurement and Sensing in Medicine and Health}, address = {London}, year = {2009}, language = {en} } @inproceedings{TaylorKornaropoulosKratzensteinetal.2011, author = {Taylor, William R. and Kornaropoulos, Evgenios I. and Kratzenstein, Stefan and Ehrig, Rainald and Plank, F. and Heller, Markus O.}, title = {Targeted Marker Placement for the Functional Identification of the Hip Joint Centre}, booktitle = {Transactions Vol. 36, 2011 Annual Meeting of the Orthopedic Society}, address = {Long Beach}, year = {2011}, language = {en} } @inproceedings{TaylorKoenigSpeirsetal.2006, author = {Taylor, William R. and K{\"o}nig, Christian and Speirs, A. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {The medio-lateral force distribution in the sheep knee during walking}, booktitle = {5. World Congress of Biomechanics, Munich, Journal of Biomechanics}, number = {39, Suppl. 1}, pages = {S491}, year = {2006}, language = {en} } @inproceedings{TaylorKoenigSpeirsetal.2006, author = {Taylor, William R. and K{\"o}nig, Christian and Speirs, A. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {Die medio-laterale Kraftverteilung im Schafsknie}, booktitle = {Deutscher Kongress f{\"u}r Orthp{\"a}die und Unfallchirurgie, Berlin}, year = {2006}, language = {en} } @article{VolkweinWeiser2002, author = {Volkwein, S. and Weiser, Martin}, title = {Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian SQP Methods}, volume = {41}, journal = {SIAM J. Control Optim.}, number = {3}, pages = {875 -- 899}, year = {2002}, language = {en} } @techreport{VolkweinWeiser2004, author = {Volkwein, S. and Weiser, Martin}, title = {Optimality Conditions for a Constrained Parameter Identification Problem in Hyperthermia}, number = {305}, publisher = {University of Graz, SFB F003}, address = {Graz, Austria}, year = {2004}, language = {en} } @article{WeiserGaenzlerSchiela2008, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A control reduced primal interior point method for a class of control constrained optimal control problems}, volume = {41}, journal = {Comput. Optim. Appl.}, number = {1}, pages = {127 -- 145}, year = {2008}, language = {en} } @article{WeiserSchiela2004, author = {Weiser, Martin and Schiela, Anton}, title = {Function space interior point methods for PDE constrained optimization}, volume = {4}, journal = {PAMM}, number = {1}, pages = {43 -- 46}, year = {2004}, language = {en} } @article{WeiserSchielaDeuflhard2005, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, volume = {42}, journal = {SIAM J. Num. Anal.}, number = {5}, pages = {1830 -- 1845}, year = {2005}, language = {en} } @article{Weiser2009, author = {Weiser, Martin}, title = {Optimization and Identification in Regional Hyperthermia}, volume = {30}, journal = {Int. J. Appl. Electromagn. and Mech.}, pages = {265 -- 275}, year = {2009}, language = {en} } @misc{Massing2007, type = {Master Thesis}, author = {Massing, Andre}, title = {1D-Reduktion thermal signifikanter Aderstr{\"a}nge in der Hyperthermie-Modellierung}, address = {Fachbereich Mathematik}, year = {2007}, language = {en} } @article{MeyerPruefertTroeltzsch2007, author = {Meyer, Christian and Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi}, title = {On two numerical methods for state-constrained elliptic control problems}, volume = {22}, journal = {Optimization Methods and Software}, number = {6}, pages = {871 -- 899}, year = {2007}, language = {en} } @article{PruefertSchiela2009, author = {Pr{\"u}fert, Uwe and Schiela, Anton}, title = {The Minimization of a maximum-norm functional subject to an elliptic PDE and state constraints}, volume = {89}, journal = {Z. angew. Math. Mech.}, number = {7}, pages = {536 -- 551}, year = {2009}, language = {en} } @article{Schiela2008, author = {Schiela, Anton}, title = {A Simplified Approach to Semismooth Newton Methods in Function Space}, volume = {19}, journal = {SIAM J. on Optimization}, number = {3}, pages = {369 -- 393}, year = {2008}, language = {en} } @phdthesis{Schiela2006, author = {Schiela, Anton}, title = {The Control Reduced Interior Point Method. A Function Space Oriented Algorithmic Approach}, address = {Fachbereich Mathematik}, year = {2006}, language = {en} } @inproceedings{Schiela2009, author = {Schiela, Anton}, title = {An Extended Mathematical Framework for Barrier Methods in Function Space}, volume = {70}, booktitle = {Domain Decomposition Methods in Science and Engineering XVIII}, year = {2009}, language = {en} } @article{Schiela2009, author = {Schiela, Anton}, title = {Barrier Methods for Optimal Control Problems with State Constraints}, volume = {20}, journal = {SIAM J. on Optimization}, number = {2}, pages = {1002 -- 1031}, year = {2009}, language = {en} } @article{Schiela2009, author = {Schiela, Anton}, title = {State constrained optimal control problems with states of low regularity}, volume = {48}, journal = {SIAM J. on Control and Optimization}, number = {4}, pages = {2407 -- 2432}, year = {2009}, language = {en} } @misc{Schraeer2008, type = {Master Thesis}, author = {Schr{\"a}er, Ingo}, title = {Modellreduktion in der Hyperthermie mittels POD}, address = {Fachbereich Mathematik}, year = {2008}, language = {en} } @article{PruefertTroeltzschWeiser2008, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, volume = {39}, journal = {Comput. Optim. Appl.}, number = {2}, pages = {183 -- 218}, year = {2008}, language = {en} } @inproceedings{GoetschelTycowiczPolthieretal.2015, author = {G{\"o}tschel, Sebastian and Tycowicz, Christoph von and Polthier, Konrad and Weiser, Martin}, title = {Reducing Memory Requirements in Scientific Computing and Optimal Control}, booktitle = {Multiple Shooting and Time Domain Decomposition Methods}, editor = {Carraro, T. and Geiger, M. and Koerkel, S. and Rannacher, R.}, publisher = {Springer}, pages = {263 -- 287}, year = {2015}, language = {en} } @article{GoetschelNagaiahKunischetal.2014, author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, volume = {60}, journal = {J. Sci. Comput.}, number = {1}, doi = {10.1007/s10915-013-9785-x}, pages = {35 -- 59}, year = {2014}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @article{GoetschelWeiserMaierhoferetal.2013, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina and R{\"o}llig, Mathias}, title = {Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography}, volume = {6}, journal = {Nondestructive Testing of Materials and Structures}, pages = {83 -- 89}, year = {2013}, language = {en} } @misc{Lubkoll2011, type = {Master Thesis}, author = {Lubkoll, Lars}, title = {Optimal Control in Implant Shape Design}, pages = {67}, year = {2011}, language = {en} } @misc{Lehmann2013, type = {Master Thesis}, author = {Lehmann, Felix}, title = {Inexaktheit in Newton-Lagrange-Verfahren f{\"u}r Optimierungsprobleme mit Elliptischen PDGL-Nebenbedingungen}, pages = {73}, year = {2013}, abstract = {Bei der numerischen L{\"o}sung von Optimalsteuerungsproblemen mit elliptischen partiellen Differentialgleichungen als Nebenbedingung treten unvermeidlich Diskretisierungs- und Iterationsfehler auf. Man ist aus Aufwandsgr{\"u}nden daran interessiert die dabei entstehenden Fehler nicht sehr klein w{\"a}hlen zu m{\"u}ssen. In der Folge werden die linearisierten Nebenbedingungen in einem Composite-Step-Verfahren nicht exakt erf{\"u}llt. In dieser Arbeit wird der Einfluss dieser Ungenauigkeit auf das Konvergenzverhalten von Newton-Lagrange-Verfahren untersucht. Dabei sollen mehrere einschl{\"a}gige lokale Konvergenzresultate diskutiert werden. Anschließend wird ein konkretes Composite-Step-Verfahren formuliert, in dem die Genauigkeit der inneren Iterationsverfahren adaptiv gesteuert werden kann. Am Ende der Arbeit wird an zwei Musterproblemen die hohe {\"U}bereinstimmung der analytischen Voraussagen und der tats{\"a}chlichen Performanz der dargestellten Methoden demonstriert.}, language = {de} } @article{GoetschelWeiser2015, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy Compression for PDE-constrained Optimization: Adaptive Error Control}, volume = {62}, journal = {Comput. Optim. Appl.}, number = {1}, publisher = {Springer}, pages = {131 -- 155}, year = {2015}, abstract = {For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.}, language = {en} } @inproceedings{KornaropoulosTaylorDudaetal.2009, author = {Kornaropoulos, Evgenios I. and Taylor, William R. and Duda, Georg and Ehrig, Rainald and Heller, Markus O.}, title = {Frontal plane lower limb alignment using functionally determined joint centers and axes}, booktitle = {International Conference on Computational Bioengineering}, year = {2009}, language = {en} } @article{SchenklMuggenthalerHubigetal.2017, author = {Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Erdmann, Bodo and Weiser, Martin and Zachow, Stefan and Heinrich, Andreas and G{\"u}ttler, Felix Victor and Teichgr{\"a}ber, Ulf and Mall, Gita}, title = {Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis}, volume = {131}, journal = {International Journal of Legal Medicine}, number = {3}, doi = {doi:10.1007/s00414-016-1523-0}, pages = {699 -- 712}, year = {2017}, abstract = {Temperature based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex, but allow a higher accuracy of death time estimation as in principle all relevant cooling mechanisms can be taken into account. Here, a complete work flow for finite element based cooling simulation models is presented. The following steps are demonstrated on CT-phantoms: • CT-scan • Segmentation of the CT images for thermodynamically relevant features of individual geometries • Conversion of the segmentation result into a Finite Element (FE) simulation model • Computation of the model cooling curve • Calculation of the cooling time For the first time in FE-based cooling time estimation the steps from the CT image over segmentation to FE model generation are semi-automatically performed. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using different CTphantoms. Some of the CT phantoms thermodynamic material parameters had to be experimentally determined via independent experiments. Moreover the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis.}, language = {en} } @article{WeiserFreytagErdmannetal.2018, author = {Weiser, Martin and Freytag, Yvonne and Erdmann, Bodo and Hubig, Michael and Mall, Gita}, title = {Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine}, volume = {34}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/aae7a5}, pages = {125005}, year = {2018}, abstract = {Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements.}, language = {en} } @misc{Binkowski2017, author = {Binkowski, Felix}, title = {On the convergence behavior of spectral deferred correction methods for convection-diffusion equations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66016}, pages = {64}, year = {2017}, abstract = {Spectral deferred correction (SDC) Methoden, vorgestellt von Dutt, Greengard und Rokhlin in [1], sind iterative Verfahren zur numerischen L{\"o}sung von Anfangswertproblemen f{\"u}r gew{\"o}hnliche Differentialgleichungen. Wenn diese Methoden konvergieren, dann wird unter Verwendung von Zeitschrittverfahren niedriger Ordnung eine Kollokationsl{\"o}sung berechnet. Die L{\"o}sung von steifen Anfangswertproblemen ist eine relevante Problemstellung in der numerischen Mathematik. SDC-Methoden, speziell f{\"u}r steife Probleme, werden von Martin Weiser in [2] konstruiert. Die Theorie und die Experimente beziehen sich dabei auf Probleme, die aus r{\"a}umlich semidiskretisierten Reaktions-Diffusions-Gleichungen entstehen. In dieser Arbeit werden die Ans{\"a}tze aus [2] auf Konvektions-Diffusions-Gleichungen angewendet und das resultierende Konvergenzverhalten von SDC-Methoden untersucht. Basierend auf einem einfachen Konvektions-Diffusions-Operator, dessen spektrale Eigenschaften umfassend studiert werden, wird ein Schema zur Verbesserung dieses Verhaltens entwickelt. Numerische Experimente zeigen, dass eine Verbesserung der in [1] eingef{\"u}hrten SDC-Methoden m{\"o}glich ist. Die Untersuchungen ergeben weiterhin, dass das auch f{\"u}r komplexere Konvektions-Diffusions-Probleme gilt. [1] Alok Dutt, Leslie Greengard, und Vladimir Rokhlin. "Spectral deferred correction methods for ordinary differential equations." In: BIT 40.2 (2000), pp. 241-266. [2] Martin Weiser. "Faster SDC convergence on non-equidistant grids by DIRK sweeps." In: BIT 55.4 (2015), pp. 1219-1241.}, 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} }