TY - GEN A1 - Sali, Adrian T1 - Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology N2 - 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. T3 - ZIB-Report - 16-50 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60508 SN - 1438-0064 ER - TY - THES A1 - Sali, Adrian T1 - Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology N2 - 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. Y1 - 2016 ER - TY - JOUR A1 - Weiser, Martin A1 - Ghosh, Sunayana T1 - Theoretically optimal inexact SDC methods JF - Communications in Applied Mathematics and Computational Science N2 - 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. Y1 - 2018 U6 - https://doi.org/10.2140/camcos.2018.13.53 IS - 13-1 SP - 53 EP - 86 ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Maierhofer, Christiane A1 - Richter, Regina T1 - Data Enhancement for Active Thermography N2 - 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. T3 - ZIB-Report - 12-20 KW - data enhancement KW - active thermography KW - quantitative reconstruction KW - Green's functions Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15243 UR - http://qirt.gel.ulaval.ca/archives/qirt2012/papers/QIRT-2012-167.pdf SN - 1438-0064 ER - TY - JOUR A1 - Hochmuth, Reinhard A1 - Deuflhard, Peter T1 - Multiscale Analysis for the Bio-Heat-Transfer Equation - The Nonisolated Case JF - Mathematical Models and Methods in Applied Sciences (M$^3$AS) Y1 - 2004 VL - 14 IS - 11 SP - 1621 EP - 1634 ER - TY - JOUR A1 - Heller, Markus O. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Schell, H. A1 - Seebeck, P. A1 - Taylor, William R. T1 - Muskuloskeletale Belastungen im Schafshinterlauf JF - Materialwissenschaft und Werkstofftechnik Y1 - 2005 IS - 36 SP - 775 EP - 780 ER - TY - CHAP A1 - Heller, Markus O. A1 - Duda, G. A1 - König, Christian A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Hinterwimmer, S. A1 - Graichen, H. T1 - Validation of a New Model of Human Knee Kinematics against in Vivo Data under Physiologic Neuromuscular Activation Patterns T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Hellmich, Christian A1 - Kober, Cornelia A1 - Erdmann, Bodo T1 - Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible JF - Annals of Biomedical Engineering Y1 - 2008 U6 - https://doi.org/10.1007/s10439-007-9393-8 VL - 36 IS - 1 SP - 108 EP - 122 ER - TY - JOUR A1 - Heller, Markus O. A1 - Kratzenstein, Stefan A1 - Ehrig, Rainald A1 - Wassilew, Georgi A1 - Duda, Georg A1 - Taylor, William R. T1 - The weighted optimal common shape technique improves identification of the hip joint centre of rotation in vivo JF - Journal of Orthopedic Research Y1 - 2011 VL - 29 SP - 1470 EP - 5 ER - TY - JOUR A1 - Gellermann, Johanna A1 - Weihrauch, Mirko A1 - Cho, C. A1 - Wlodarczyk, Waldemar A1 - Fähling, Horst A1 - Felix, Roland A1 - Budach, Volker A1 - Weiser, Martin A1 - Nadobny, Johanna A1 - Wust, Peter T1 - Comparison of MR-thermography and planning calculations in phantoms JF - Medical Physics Y1 - 2006 VL - 33 SP - 3912 EP - 3920 ER - TY - JOUR A1 - Heller, Markus O. A1 - König, Christian A1 - Graichen, F. A1 - Hinterwimmer, S. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Taylor, William R. T1 - A new model to predict in vivo human knee kinematics under physiological-like muscle activation JF - Journal of Biomechanics Y1 - 2007 SP - 45 EP - 53 ER - TY - RPRT A1 - Gladilin, Evgeny A1 - Peckar, W. A1 - Rohr, K. A1 - Stiehl, H. T1 - A Comparsion Between BEM and FEM for Elastic Registration of Medical Images Y1 - 1999 IS - FBI-HH-M-287/99 PB - FB Informatik CY - Hamburg, Germany ER - TY - JOUR A1 - Gänzler, Tobias A1 - Volkwein, S. A1 - Weiser, Martin T1 - SQP methods for parameter identification problems arising in hyperthermia JF - Optim. Methods Softw. Y1 - 2006 VL - 21 IS - 6 SP - 869 EP - 887 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Kratzenstein, Stefan A1 - Duda, Georg A1 - Trepczynski, Adam A1 - Taylor, William R. T1 - The SCoRE residual: A quality index to assess the accuracy of joint estimations JF - Journal of Biomechanics Y1 - 2011 U6 - https://doi.org/10.1016/j.jbiomech.2010.12.009 VL - 44 IS - 7 SP - 1400 EP - 1404 ER - TY - CHAP A1 - Erdmann, Bodo A1 - Kober, C. A1 - Lang, Jens A1 - Deuflhard, Peter A1 - Zeilhofer, J. A1 - Sader, Robert T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible T2 - proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields Y1 - 2002 CY - Ulm, Germany ER - TY - JOUR A1 - Erdmann, Bodo A1 - Ljubijankic, M. A1 - Nytsch-Geusen, C. T1 - Entwicklung einer Toolbox zur zwei- und dreidimensionalen instationären thermischen Bauteilsimulation mit KARDOS JF - Bauphsik Y1 - 2007 VL - 29 IS - 1 SP - 33 EP - 39 ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin ED - de Vahl Davis, G. ED - Leonardi, E. T1 - Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments T2 - CHT’97 Y1 - 1997 SP - 103 EP - 110 CY - Cesme, Turkey ER - TY - CHAP A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin ED - Diller, K. T1 - Optimization of Temperature Distributions for Regional Hyperthermia based on a Nonlinear Heat Transfer Model T2 - Biotransport Y1 - 1998 VL - 858 SP - 36 EP - 46 ER - TY - JOUR A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - The Impact of a Nonlinear Heat Transfer Model for Temperature Control in Regional Hyperthermia JF - IEEE Transactions on Biomedical Engineering Y1 - 1999 VL - 49 IS - 9 SP - 1129 EP - 1138 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, G. A1 - Heller, Markus O. T1 - A Survey for Formal Methods for Determining the Centre of Ball Joints JF - Journal of Biomechanics Y1 - 2006 IS - 39 SP - 2798 EP - 2809 ER - TY - CHAP A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, G. A1 - Heller, Markus O. T1 - A New Approach for the Determination of Joint Axes T2 - Proceedings of the 52th Annual Meeting of the Orthopedic Society Y1 - 2006 CY - Chicago ER - TY - JOUR A1 - Ehrig, Rainald A1 - Taylor, William R. A1 - Duda, Georg A1 - Heller, Markus O. T1 - A Survey for Formal Methods for Determining Functional Joint Axes JF - Journal of Biomechanics Y1 - 2007 SP - 2150 EP - 2157 ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - A nonlinear soft tissue model for craniofacial surgery simulations T2 - Proc. of Modeling and Simulation for Computer-aided Medicine and Surgery (MS4CMS Y1 - 2002 PB - INRIA CY - Paris, France ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Biomechanical modeling of individual facial emotion expressions T2 - Proc. of Visualization, Imaging, and Image Processing (VIIP) Y1 - 2002 SP - 7 EP - 11 CY - Malaga, Spain ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - Meiler, M. ED - Saupe, D. ED - Krugel, F. ED - Handels, H. ED - Lehmann, T. T1 - Biomechanisches Modell zur Abschätzung der individuellen Gesichtsmimik T2 - Proc.of Workshop Bildverarbeitung für die Medizin (BVM) Y1 - 2002 SP - 25 EP - 28 CY - Leipzig, Germany ER - TY - THES A1 - Gladilin, Evgeny T1 - Biomechanical Modeling of Soft Tissue and Facial Expressions for Craniofacial Surgery Planning Y1 - 2003 CY - Germany ER - TY - CHAP A1 - Gladilin, Evgeny T1 - A contour based approach for invariant shape description T2 - SPIE Medical Imaging Conference Y1 - 2004 VL - 5370 SP - 1282 EP - 1291 CY - San Diego, USA ER - TY - CHAP A1 - Lang, Jens A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Deuflhard, Peter A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Alt, Walter ED - Hermann, Martin T1 - Effiziente und zuverlässige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers T2 - Berichte des IZWR - Interdisziplinäres Zentrum für Wissenschaftliches Rechnen Y1 - 2003 VL - 1 SP - 49 EP - 57 PB - Universität Jena CY - Germany ER - TY - CHAP A1 - Kornaropoulos, Evgenios I. A1 - Taylor, William R. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Matziolis, Georg A1 - Müller, Michael A1 - Wassilew, Georgi A1 - Asbach, Patrick A1 - Perka, Carsten A1 - Heller, Markus O. T1 - An imageless method to quantify the mechanical femoral-tibial angle based on the functional determination of joint centers and axes T2 - Annual meeting of the ESMAC 2009 Y1 - 2009 CY - London ER - TY - JOUR A1 - Kornaropoulos, Evgenios I. A1 - Taylor, William R. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Matziolis, Georg A1 - Müller, Michael A1 - Wassilew, Georgi A1 - Asbach, Patrick A1 - Perka, Carsten A1 - Heller, Markus O. T1 - Frontal plane alignment: An imageless method to predict the mechanical femoral–tibial angle (mFTA) based on functional determination of joint centres and axes JF - Gait & Posture Y1 - 2010 U6 - https://doi.org/10.1016/j.gaitpost.2009.10.006 VL - 31 IS - 2 SP - 204 EP - 208 ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. T1 - Reduction of the influence of skin marker artefacts using the optimal common shape technique T2 - Annual meeting of the ESMAC 2009 Y1 - 2009 CY - London ER - TY - CHAP A1 - Kassi, J.-P. A1 - Taylor, William R. A1 - Schwarzkopf, J. A1 - Schell, H. A1 - Duda, G. A1 - Ehrig, Rainald T1 - Wie sind Osteosynthesesysteme und Defektzonen in vivo belastet? T2 - 68. Jahrestagung der Deutschen Gesellschaft für Unfallchirurgie in Verbindung mit dem Deutschen Orthopädenkongress Y1 - 2004 CY - Berlin ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Duda, Georg A1 - Taylor, William R. T1 - A Quantification of Accuracy in Estimating Joint Centers T2 - 17th Congress of the European Society of Biomechanics Y1 - 2010 CY - Edinburgh ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Geiger, M. A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Davidovitch, Z. ED - Mah, J. ED - Suthanarak, S. T1 - How does the periodontal ligament influence overall stress/strain profiles of a partially edentulous mandible? T2 - Proc. of 8th Int. Conference on Biological Mechanisms of Tooth Eruption, Resorption and Movement, Phuket, Thailand Y1 - 2005 CY - Harvard Society of the Advancement of Orthodontics, Boston, Massachusetts, USA ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Anisotropic Simulation of the Human Mandible T2 - Proc. of 17th ASCE Engineering Mechanics Conference Y1 - 2004 PB - Univ. of Delaware ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - Boenick, U. ED - Bolz, A. T1 - Consideration of Bone Inhomogeneity and Anisotropy in Deformation Analysis of a Human Mandible T2 - Proc. of BMT2005, 39th Annual Congress of the German Society of Biomedical Engineering, Nuremberg, Germany Y1 - 2005 VL - 1 SP - 814 EP - 815 PB - VDE CY - Nuremberg, Germany ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian ED - CADFEM GmbH, Grafing T1 - The Influence of the Periodontal Ligament on Overall Stress/Strain Profiles of a Human Mandible T2 - Proc. of 23rd CADFEM Users’ Meeting, Int. Congress on FEM Technology, Biomechanics Y1 - 2005 SP - 1 EP - 10 CY - Bonn, Germany ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Sensitivity of the Temporomandibular Joint Capsule for the Structural Behaviour of the Human Mandible T2 - Proc. BMT 2004 Y1 - 2004 VL - 49-2 SP - 372 EP - 373 CY - Ilmenau, Deutschland ER - TY - JOUR A1 - Klapproth, Corinna A1 - Deuflhard, Peter A1 - Schiela, Anton T1 - A Perturbation Result for Dynamical Contact Problems JF - Numer. Math Y1 - 2009 VL - 2 SP - 237 EP - 257 ER - TY - THES A1 - Klapproth, Corinna T1 - Adaptive numerical integration for dynamical contact problems Y1 - 2012 ER - TY - CHAP A1 - Kober, C. A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian A1 - Deuflhard, Peter ED - Capasso, Vincenzo T1 - An Individual Anisotropic and Inhomogeneous Material Description of the Human Mandible T2 - Mathematical Modelling and Computing in Biology and Medicine Y1 - 2003 SP - 103 EP - 109 PB - ESTMB ER - TY - JOUR A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Roitzsch, Rainer A1 - Lines, Glenn Terje T1 - Adaptive Finite Element Simulation of Ventricular Dynamics JF - J. Computing and Visualization in Science Y1 - 2009 VL - 12 SP - 201 EP - 205 ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Adaptive Finite Element Simulation of the Human Mandible Using a New Physiological Model of the Masticatory Muscles T2 - Proc. of 75th Annual Meeting of the GAMM Y1 - 2004 VL - 4 IS - 1 SP - 332 EP - 333 ER - TY - CHAP A1 - Kober, C. A1 - Erdmann, Bodo A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Simulation of the Human Mandible T2 - Proceedings of 10th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields Y1 - 2003 CY - Ulm, Germany ER - TY - JOUR A1 - Kober, C. A1 - Erdmann, Bodo A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Belastungssimulation beim menschlichen Biss im Vergleich mit der Dichtestruktur im Unterkieferknochen JF - Biomedizinische Technik Y1 - 2003 VL - 48 IS - Ergänzungsband 1 SP - 268 EP - 269 ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Schröder, Jörg H. A1 - Taylor, William R. T1 - Die Bestimmung der Genauigkeit nicht-invasiver Techniken zur Ermittlung der Hüftgelenksposition in-vivo T2 - 6th annual meeting of the German Society for Biomechanics (DGfB) Y1 - 2009 CY - Münster ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Schröder, Jörg H. A1 - Taylor, William R. T1 - Der Vergleich von nicht-invasiven Techniken zur Bestimmung der Hüftgelenksposition T2 - Annual meeting of the German Society of Orthopaedics and Trauma Surgery Y1 - 2009 CY - Berlin ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Taylor, William R. T1 - The Residual: A Reliable Measure of Accuracy in the Determination of Joint Centers T2 - Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society Y1 - 2010 CY - New Orleans ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Duda, Georg A1 - Taylor, William R. T1 - The Hip Joint Centre can be determined to within 3 mm T2 - 17th Congress of the European Society of Biomechanics Y1 - 2010 CY - Edinburgh ER - TY - CHAP A1 - Kratzenstein, Stefan A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Wassilew, Georgi A1 - Duda, Georg A1 - Taylor, William R. T1 - A new approach for optimally reducing skin marker artifact allows determination of the hip joint center within 3mm T2 - Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society Y1 - 2010 CY - New Orleans ER - TY - JOUR A1 - Schiela, Anton A1 - Günther, Andreas T1 - An Interior Point Algorithm with Inexact Step Computation in Function Space for State Constrained Optimal Control JF - Numer. Math. Y1 - 2011 U6 - https://doi.org/10.1007/s00211-011-0381-4 VL - 119 IS - 2 SP - 373 EP - 407 PB - Springer Berlin / Heidelberg ER - TY - JOUR A1 - Schiela, Anton A1 - Weiser, Martin T1 - Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization JF - Computational Optimization and Applications Y1 - 2008 VL - 39 IS - 3 SP - 369 EP - 393 ER - TY - JOUR A1 - Sreenivasa, G. A1 - Gellermann, Johanna A1 - Nadobny, Johanna A1 - Schlag, P. A1 - Deuflhard, Peter A1 - Felix, Roland A1 - Wust, Peter T1 - Clinical Use of the Hyperthermia Treatment Planning System Hyperplan to Predict Effectiveness and Toxicity JF - Int. J. Oncology Biol. Phys. Y1 - 2003 VL - 55 IS - 2 SP - 407 EP - 419 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The determination of joint axes T2 - 5. World Congress of Biomechanics, Munich, Journal of Biomechanics Y1 - 2006 IS - 39, Suppl. 1 SP - S571 EP - S572 ER - TY - CHAP A1 - Zachow, Stefan A1 - Weiser, Martin A1 - Hege, Hans-Christian A1 - Deuflhard, Peter ED - Payan, Y. T1 - Soft Tissue Prediction in Computer Assisted Maxillofacial Surgery Planning T2 - Biomechanics Applied to Computer Assisted Surgery Y1 - 2005 SP - 277 EP - 298 PB - Research Signpost ER - TY - CHAP A1 - Zachow, Stefan A1 - Weiser, Martin A1 - Deuflhard, Peter ED - Niederlag, Wolfgang ED - Lemke, Heinz ED - Meixensberger, Jürgen ED - Baumann, Michael T1 - Modellgestützte Operationsplanung in der Kopfchirurgie T2 - Modellgestützte Therapie Y1 - 2008 SP - 140 EP - 156 PB - Health Academy ER - TY - JOUR A1 - Hinze, Michael A1 - Schiela, Anton T1 - Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: optimal error estimates and parameter adjustment JF - Comp. Opt. and Appl. Y1 - 2011 U6 - https://doi.org/10.1007/s10589-009-9278-x VL - 48 IS - 3 SP - 581 EP - 600 PB - Springer ER - TY - JOUR A1 - Weiser, Martin T1 - Pointwise Nonlinear Scaling for Reaction-Diffusion Equations JF - Appl. Num. Math. Y1 - 2009 VL - 59 IS - 8 SP - 1858 EP - 1869 ER - TY - JOUR A1 - Weihrauch, Mirko A1 - Wust, Peter A1 - Weiser, Martin A1 - Nadobny, Johanna A1 - Eisenhardt, Steffen A1 - Budach, Volker A1 - Gellermann, Johanna T1 - Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system JF - Medical Physics Y1 - 2007 VL - 34 IS - 12 SP - 4717 EP - 4725 ER - TY - JOUR A1 - Weiser, Martin T1 - Interior point methods in function space JF - SIAM J. Control Optimization Y1 - 2005 VL - 44 IS - 5 SP - 1766 EP - 1786 ER - TY - CHAP A1 - Taylor, William R. A1 - Kassi, J.-P. A1 - Schwarzkopf, J. A1 - Ehrig, Rainald A1 - Schell, H. A1 - Duda, G. T1 - The Profile of Mechanical Loading is Independent of Fracture Fixation Principle T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Taylor, William R. A1 - Pöpplau, Berry M. A1 - König, Christian A1 - Ehrig, Rainald A1 - Zachow, Stefan A1 - Duda, Georg A1 - Heller, Markus O. T1 - The medial-lateral force distribution in the ovine stifle joint during walking JF - Journal of Orthopaedic Research Y1 - 2011 U6 - https://doi.org/10.1002/jor.21254 VL - 29 IS - 4 SP - 567 EP - 571 ER - TY - JOUR A1 - Boeth, Heide A1 - Duda, Georg A1 - Heller, Markus O. A1 - Ehrig, Rainald A1 - Doyscher, Ralf A1 - Jung, Tobias A1 - Moewis, Philippe A1 - Scheffler, Sven A1 - Taylor, William R. T1 - Anterior cruciate ligament-deficient patients with passive knee joint laxity have a decreased range of anterior-posterior motion during active movements JF - The American Journal of Sports Medicine Y1 - 2013 U6 - https://doi.org/10.1177/0363546513480465 VL - 41 IS - 5 SP - 1051 EP - 7 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The Symmetrical Axis of Rotation Approach (SARA) for Determination of Joint Axes in Clinical Gait Analysis T2 - 1st Joint ESMAC-GCMAS Meeting, Amsterdam Y1 - 2006 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Duda, G. T1 - Can Skin Markers Determine the Kinematics of Underlying Bones? T2 - Proceedings of the 50th Annual Meeting of the Orthopedic Society Y1 - 2004 CY - San Francisco ER - TY - JOUR A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Klein, P. A1 - Duda, G. T1 - On the Influence of Soft Tissue Coverage in the Determination of Bone Kinematics using Bone Markers JF - Journal of Orthopedic Research Y1 - 2005 IS - 23 SP - 726 EP - 734 ER - TY - CHAP A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Seebeck, P. A1 - Duda, G. T1 - Animal Models for Knee Injury Frequently Underestimate the Mechanical Conditions of the Clinical Situation T2 - Proceedings of the 51th Annual Meeting of the Orthopedic Society Y1 - 2005 CY - Washington ER - TY - JOUR A1 - Taylor, William R. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Schell, H. A1 - Seebeck, P. A1 - Duda, G. T1 - Tibio-femoral Joint Contact Forces in Sheep JF - Journal of Biomechanics Y1 - 2006 IS - 39 SP - 791 EP - 798 ER - TY - CHAP A1 - Taylor, William R. A1 - Kornaropoulos, Evgenios I. A1 - Ehrig, Rainald A1 - Heller, Markus O. A1 - Duda, Georg T1 - Reproducibility of a functional approach to gait analysis T2 - Annual meeting of the ESMAC 2009 Y1 - 2009 CY - London ER - TY - CHAP A1 - Taylor, William R. A1 - Kratzenstein, Stefan A1 - Kornaropoulos, Evgenios I. A1 - Ehrig, Rainald A1 - Moewis, Philippe A1 - Heller, Markus O. T1 - Non-invasive Assessment of Skeletal Kinematics T2 - Measurement and Sensing in Medicine and Health Y1 - 2009 CY - London ER - TY - CHAP A1 - Taylor, William R. A1 - Kornaropoulos, Evgenios I. A1 - Kratzenstein, Stefan A1 - Ehrig, Rainald A1 - Plank, F. A1 - Heller, Markus O. T1 - Targeted Marker Placement for the Functional Identification of the Hip Joint Centre T2 - Transactions Vol. 36, 2011 Annual Meeting of the Orthopedic Society Y1 - 2011 CY - Long Beach ER - TY - CHAP A1 - Taylor, William R. A1 - König, Christian A1 - Speirs, A. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - The medio-lateral force distribution in the sheep knee during walking T2 - 5. World Congress of Biomechanics, Munich, Journal of Biomechanics Y1 - 2006 IS - 39, Suppl. 1 SP - S491 ER - TY - CHAP A1 - Taylor, William R. A1 - König, Christian A1 - Speirs, A. A1 - Ehrig, Rainald A1 - Duda, G. A1 - Heller, Markus O. T1 - Die medio-laterale Kraftverteilung im Schafsknie T2 - Deutscher Kongress für Orthpädie und Unfallchirurgie, Berlin Y1 - 2006 ER - TY - JOUR A1 - Volkwein, S. A1 - Weiser, Martin T1 - Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian SQP Methods JF - SIAM J. Control Optim. Y1 - 2002 VL - 41 IS - 3 SP - 875 EP - 899 ER - TY - RPRT A1 - Volkwein, S. A1 - Weiser, Martin T1 - Optimality Conditions for a Constrained Parameter Identification Problem in Hyperthermia Y1 - 2004 IS - 305 PB - University of Graz, SFB F003 CY - Graz, Austria ER - TY - JOUR A1 - Weiser, Martin A1 - Gänzler, Tobias A1 - Schiela, Anton T1 - A control reduced primal interior point method for a class of control constrained optimal control problems JF - Comput. Optim. Appl. Y1 - 2007 VL - 41 IS - 1 SP - 127 EP - 145 ER - TY - JOUR A1 - Weiser, Martin A1 - Schiela, Anton T1 - Function space interior point methods for PDE constrained optimization JF - PAMM Y1 - 2004 VL - 4 IS - 1 SP - 43 EP - 46 ER - TY - JOUR A1 - Weiser, Martin A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Asymptotic Mesh Independence of Newton’s Method Revisited JF - SIAM J. Num. Anal. Y1 - 2005 VL - 42 IS - 5 SP - 1830 EP - 1845 ER - TY - JOUR A1 - Weiser, Martin T1 - Optimization and Identification in Regional Hyperthermia JF - Int. J. Appl. Electromagn. and Mech. Y1 - 2009 VL - 30 SP - 265 EP - 275 ER - TY - THES A1 - Massing, Andre T1 - 1D-Reduktion thermal signifikanter Aderstränge in der Hyperthermie-Modellierung Y1 - 2007 CY - Fachbereich Mathematik ER - TY - JOUR A1 - Meyer, Christian A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi T1 - On two numerical methods for state-constrained elliptic control problems JF - Optimization Methods and Software Y1 - 2007 UR - http://www.math.tu-berlin.de/~pruefert/Publicat/index_en.html UR - /homes/numerik/pruefert/WWW/Publicat/on2numerical.pdf VL - 22 IS - 6 SP - 871 EP - 899 ER - TY - JOUR A1 - Prüfert, Uwe A1 - Schiela, Anton T1 - The Minimization of a maximum-norm functional subject to an elliptic PDE and state constraints JF - Z. angew. Math. Mech. Y1 - 2009 VL - 89 IS - 7 SP - 536 EP - 551 ER - TY - JOUR A1 - Schiela, Anton T1 - A Simplified Approach to Semismooth Newton Methods in Function Space JF - SIAM J. on Optimization Y1 - 2008 VL - 19 IS - 3 SP - 369 EP - 393 ER - TY - THES A1 - Schiela, Anton T1 - The Control Reduced Interior Point Method. A Function Space Oriented Algorithmic Approach Y1 - 2006 CY - Fachbereich Mathematik ER - TY - CHAP A1 - Schiela, Anton T1 - An Extended Mathematical Framework for Barrier Methods in Function Space T2 - Domain Decomposition Methods in Science and Engineering XVIII Y1 - 2009 VL - 70 ER - TY - JOUR A1 - Schiela, Anton T1 - Barrier Methods for Optimal Control Problems with State Constraints JF - SIAM J. on Optimization Y1 - 2009 VL - 20 IS - 2 SP - 1002 EP - 1031 ER - TY - JOUR A1 - Schiela, Anton T1 - State constrained optimal control problems with states of low regularity JF - SIAM J. on Control and Optimization Y1 - 2009 VL - 48 IS - 4 SP - 2407 EP - 2432 ER - TY - THES A1 - Schräer, Ingo T1 - Modellreduktion in der Hyperthermie mittels POD Y1 - 2008 CY - Fachbereich Mathematik ER - TY - JOUR A1 - Prüfert, Uwe A1 - Tröltzsch, Fredi A1 - Weiser, Martin T1 - The convergence of an interior point method for an elliptic control problem with mixed control-state constraints JF - Comput. Optim. Appl. Y1 - 2008 VL - 39 IS - 2 SP - 183 EP - 218 ER - TY - CHAP A1 - Götschel, Sebastian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad A1 - Weiser, Martin ED - Carraro, T. ED - Geiger, M. ED - Koerkel, S. ED - Rannacher, R. T1 - Reducing Memory Requirements in Scientific Computing and Optimal Control T2 - Multiple Shooting and Time Domain Decomposition Methods Y1 - 2015 SP - 263 EP - 287 PB - Springer ER - TY - JOUR A1 - Götschel, Sebastian A1 - Nagaiah, Chamakuri A1 - Kunisch, Karl A1 - Weiser, Martin T1 - Lossy Compression in Optimal Control of Cardiac Defibrillation JF - J. Sci. Comput. N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1007/s10915-013-9785-x VL - 60 IS - 1 SP - 35 EP - 59 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Maierhofer, Christiane A1 - Richter, Regina A1 - Röllig, Mathias T1 - Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography JF - Nondestructive Testing of Materials and Structures Y1 - 2013 VL - 6 SP - 83 EP - 89 ER - TY - THES A1 - Lubkoll, Lars T1 - Optimal Control in Implant Shape Design KW - optimal control Y1 - 2011 ER - TY - THES A1 - Lehmann, Felix T1 - Inexaktheit in Newton-Lagrange-Verfahren für Optimierungsprobleme mit Elliptischen PDGL-Nebenbedingungen N2 - Bei der numerischen Lösung von Optimalsteuerungsproblemen mit elliptischen partiellen Differentialgleichungen als Nebenbedingung treten unvermeidlich Diskretisierungs- und Iterationsfehler auf. Man ist aus Aufwandsgründen daran interessiert die dabei entstehenden Fehler nicht sehr klein wählen zu müssen. In der Folge werden die linearisierten Nebenbedingungen in einem Composite-Step-Verfahren nicht exakt erfüllt. In dieser Arbeit wird der Einfluss dieser Ungenauigkeit auf das Konvergenzverhalten von Newton-Lagrange-Verfahren untersucht. Dabei sollen mehrere einschlägige 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 Übereinstimmung der analytischen Voraussagen und der tatsächlichen Performanz der dargestellten Methoden demonstriert. KW - PDE KW - adaptive Newton KW - inexact Newton-Lagrange Y1 - 2013 UR - urn:nbn:de:0297-zib-41972 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy Compression for PDE-constrained Optimization: Adaptive Error Control JF - Comput. Optim. Appl. N2 - 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. Y1 - 2015 VL - 62 IS - 1 SP - 131 EP - 155 PB - Springer ER - TY - CHAP A1 - Kornaropoulos, Evgenios I. A1 - Taylor, William R. A1 - Duda, Georg A1 - Ehrig, Rainald A1 - Heller, Markus O. T1 - Frontal plane lower limb alignment using functionally determined joint centers and axes T2 - International Conference on Computational Bioengineering Y1 - 2009 ER - TY - JOUR A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Erdmann, Bodo A1 - Weiser, Martin A1 - Zachow, Stefan A1 - Heinrich, Andreas A1 - Güttler, Felix Victor A1 - Teichgräber, Ulf A1 - Mall, Gita T1 - Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis JF - International Journal of Legal Medicine N2 - 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. KW - temperature based death time estimation KW - finite element method KW - CT segmentation KW - sensitivity analysis Y1 - 2017 U6 - https://doi.org/doi:10.1007/s00414-016-1523-0 VL - 131 IS - 3 SP - 699 EP - 712 ER - TY - JOUR A1 - Weiser, Martin A1 - Freytag, Yvonne A1 - Erdmann, Bodo A1 - Hubig, Michael A1 - Mall, Gita T1 - Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine JF - Inverse Problems N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1088/1361-6420/aae7a5 VL - 34 IS - 12 SP - 125005 ER - TY - GEN A1 - Binkowski, Felix T1 - On the convergence behavior of spectral deferred correction methods for convection-diffusion equations N2 - Spectral deferred correction (SDC) Methoden, vorgestellt von Dutt, Greengard und Rokhlin in [1], sind iterative Verfahren zur numerischen Lösung von Anfangswertproblemen für gewöhnliche Differentialgleichungen. Wenn diese Methoden konvergieren, dann wird unter Verwendung von Zeitschrittverfahren niedriger Ordnung eine Kollokationslösung berechnet. Die Lösung von steifen Anfangswertproblemen ist eine relevante Problemstellung in der numerischen Mathematik. SDC-Methoden, speziell für steife Probleme, werden von Martin Weiser in [2] konstruiert. Die Theorie und die Experimente beziehen sich dabei auf Probleme, die aus räumlich semidiskretisierten Reaktions-Diffusions-Gleichungen entstehen. In dieser Arbeit werden die Ansätze 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] eingeführten SDC-Methoden möglich ist. Die Untersuchungen ergeben weiterhin, dass das auch für 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. T3 - ZIB-Report - 17-53 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66016 SN - 1438-0064 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Minion, Michael L. T1 - An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs JF - SIAM J. Sci. Comput. N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1137/19M1239313 VL - 41 IS - 6 SP - C603 EP - C626 ER -