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 - TY - GEN 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 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. T3 - ZIB-Report - 18-08 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67247 SN - 1438-0064 ER - TY - THES 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. Y1 - 2017 ER - TY - JOUR A1 - Moldenhauer, Marian A1 - Weiser, Martin A1 - Zachow, Stefan T1 - Adaptive Algorithms for Optimal Hip Implant Positioning JF - PAMM N2 - In an aging society where the number of joint replacements rises, it is important to also increase the longevity of implants. In particular hip implants have a lifetime of at most 15 years. This derives primarily from pain due to implant migration, wear, inflammation, and dislocation, which is affected by the positioning of the implant during the surgery. Current joint replacement practice uses 2D software tools and relies on the experience of surgeons. Especially the 2D tools fail to take the patients’ natural range of motion as well as stress distribution in the 3D joint induced by different daily motions into account. Optimizing the hip joint implant position for all possible parametrized motions under the constraint of a contact problem is prohibitively expensive as there are too many motions and every position change demands a recalculation of the contact problem. For the reduction of the computational effort, we use adaptive refinement on the parameter domain coupled with the interpolation method of Kriging. A coarse initial grid is to be locally refined using goal-oriented error estimation, reducing locally high variances. This approach will be combined with multi-grid optimization such that numerical errors are reduced. Y1 - 2017 U6 - https://doi.org/10.1002/pamm.201710071 VL - 17 IS - 1 SP - 203 EP - 204 ER - TY - GEN A1 - Götschel, Sebastian A1 - Minion, Michael L. T1 - Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST BT - DD 2017. T2 - Domain Decomposition Methods in Science and Engineering XXIV N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-93873-8_34 SP - 363 EP - 371 PB - Springer CY - Cham ER - TY - JOUR A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita A1 - Zachow, Stefan T1 - Uncertainty in Temperature-Based Determination of Time of Death JF - Heat and Mass Transfer N2 - Temperature-based estimation of time of death (ToD) can be per- formed either with the help of simple phenomenological models of corpse cooling or with detailed mechanistic (thermodynamic) heat transfer mod- els. The latter are much more complex, but allow a higher accuracy of ToD estimation as in principle all relevant cooling mechanisms can be taken into account. The potentially higher accuracy depends on the accuracy of tissue and environmental parameters as well as on the geometric resolution. We in- vestigate the impact of parameter variations and geometry representation on the estimated ToD based on a highly detailed 3D corpse model, that has been segmented and geometrically reconstructed from a computed to- mography (CT) data set, differentiating various organs and tissue types. Y1 - 2018 U6 - https://doi.org/10.1007/s00231-018-2324-4 VL - 54 IS - 9 SP - 2815 EP - 2826 PB - Springer ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy Compression for Large Scale PDE Problems N2 - Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to relatively small arithmetic intensity, and increasingly so due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers during the last decades. This paper surveys data compression challenges and corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to main memory. Exemplarily, we illustrate concepts at particular methods, and give references to alternatives. T3 - ZIB-Report - 19-32 KW - partial differential equation KW - data compression KW - floating point compression KW - lossy compression Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73817 SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Schiela, Anton A1 - Weiser, Martin T1 - Kaskade 7 -- a Flexible Finite Element Toolbox N2 - 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. T3 - ZIB-Report - 19-48 KW - finite elements KW - generic programming KW - partial differential equations Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74616 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton T1 - State constrained optimal control problems with states of low regularity N2 - We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties. T3 - ZIB-Report - 08-24 KW - optimal control KW - state constraints KW - optimality conditions Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-509 SN - 1438-0064 ER - TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments N2 - We present a self-adaptive finite element method to solve nonlinear evolution problems in 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. The proposed method is applied to hyperthermia treatments to demonstrate its potential for the solving of complicated problems. T3 - ZIB-Report - SC-97-44 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3130 ER - TY - GEN A1 - Weiser, Martin T1 - Interior Point Methods in Function Space N2 - A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established. T3 - ZIB-Report - 03-35 KW - interior point methods in function space KW - optimal control KW - complementarity functions Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7578 ER - TY - GEN A1 - Weiser, Martin A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Asymptotic Mesh Independence of Newton's Method Revisited N2 - The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems. T3 - ZIB-Report - 03-13 KW - mesh independence KW - nonlinear partial differential equations KW - Newton method KW - finite element method KW - collocation method Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7352 ER - TY - GEN A1 - Deuflhard, Peter T1 - A Comparison of Related Concepts in Computational Chemistry and Mathematics N2 - This article studies the relation of the two scientific languages Chemistry and Mathematics via three selected comparisons: (a) QSSA versus dynamic ILDM in reaction kinetics, (b) lumping versus discrete Galerkin methods in polymer chemistry, and (c) geometrical conformations versus metastable conformations in drug design. The common clear message from these comparisons is that chemical intuition may pave the way for mathematical concepts just as chemical concepts may gain from mathematical precisioning. Along this line, significant improvements in chemical research and engineering have already been possible -- and can be further expected in the future from the dialogue between the two scientific languages. T3 - ZIB-Report - 02-46 KW - dimension reduction KW - model reduction KW - QSSA KW - ILDM KW - reaction kinetics KW - polyreaction kinetics KW - Hamilton systems KW - conformations KW - metastability KW - d Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7138 ER - TY - GEN A1 - Deuflhard, Peter T1 - From Molecular Dynamics to Conformational Dynamics in Drug Design N2 - Computational drug design studies molecular recognition in the {\em virtual lab}. The arising Hamiltonian dynamics is known to be chaotic and ill-conditioned already after picoseconds, whereas times are $msec$ up to $min$. Classical molecular dynamics with long term trajectory computation gives, at best, information about time and statistical ensemble averages. The present paper surveys a recent new modeling approach called {\em conformational dynamics}, which is due to the author and Ch. Schütte. This approach achieves information about the dy time scales by telescoping a short term deterministic model with a statistical model. Examples of small biomolecules are included. T3 - ZIB-Report - 02-20 KW - molecular dynamics KW - conformational dynamics KW - drug design KW - Hamiltonian dynamics KW - almost invariant sets KW - transition operator KW - Markov chain KW - Perro Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6878 ER - TY - GEN A1 - Deuflhard, Peter A1 - Hochmuth, Reinhard T1 - Multiscale Analysis of Thermoregulation in the Human Microvascular System N2 - The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the deduction of the Helmholtz term in the bio-heat transfer equation is not co role. In view of a future numerical application of this new mathematical model to treatment planning in hyperthermia we derive asymptotic estimates for first and second order correctors. T3 - ZIB-Report - 02-31 KW - bio-heat equation KW - hyperthermia KW - homogenization Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6985 ER - TY - GEN A1 - Deuflhard, Peter A1 - Nowak, Ulrich A1 - Weiser, Martin T1 - Affine Invariant Adaptive Newton Codes for Discretized PDEs N2 - The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs. T3 - ZIB-Report - 02-33 KW - Affine invariant Newton methods KW - global Newton methods KW - inexact Newton methods KW - adaptive trust region methods KW - nonlinear partial differential equa Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7005 ER - TY - GEN A1 - Powell, Gary A1 - Weiser, Martin T1 - Container Adaptors N2 - The C++ standard template library has many useful containers for data. The standard library includes two adpators, queue, and stack. The authors have extended this model along the lines of relational database semantics. Sometimes the analogy is striking, and we will point it out occasionally. An adaptor allows the standard algorithms to be used on a subset or modification of the data without having to copy the data elements into a new container. The authors provide many useful adaptors which can be used together to produce interesting views of data in a container. T3 - ZIB-Report - SC-99-41 KW - C++ KW - STL KW - views Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4308 ER - TY - GEN A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Seebass, Martin T1 - Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Transfer Model N2 - We describe an optimization process specially designed for regional hyperthermia of deap seated tumors in order to achieve desired steady--state temperature distributions. A nonlinear three--dimensional heat--transfer model based on temperature--dependent blood perfusion is applied to predict the temperature. Optimal heating is obtained by minimizing an integral object function which measures the distance between desired and model predicted temperatures. Sequential minima are calculated from successively improved constant--rate perfusion models employing a damped Newton method in an inner iteration. Numerical results for a Sigma 60 applicator are presented. This work has been supported by Deutsche Forschungsgemeinschaft (DFG) within the Sonderforschungsbereich 273 \glqq Hyperthermie: Methodik und Klinik \grqq . T3 - ZIB-Report - SC-97-59 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3283 ER - TY - GEN A1 - Schiela, Anton A1 - Weiser, Martin T1 - Superlinear Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization N2 - A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadratically, if the optimal solution satisfies a function space analogue to a non-degeneracy condition. In numerical experiments we observe, that a prototype implementation of our method behaves in compliance with our theoretical results. T3 - ZIB-Report - 05-15 KW - interior point methods in function space KW - optimal control KW - superlinear convergence Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8490 ER - TY - GEN A1 - Kober, Cornelia A1 - Erdmann, Bodo A1 - Hellmich, Christian A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian T1 - Anisotropic Simulation of the Human Mandible N2 - We focus on the role of anisotropic elasticity in the simulation of the load distribution in a human mandible due to a lateral bite on the leftmost premolar. Based on experimental evidence, we adopt ``local''" orthotropy of the elastic properties of the bone tissue. Since the trajectories of anisotropic elasticity are not accessible from Computer Tomographic (CT) data, they will be reconstructed from (i) the organ's geometry and (ii) from coherent structures which can be recognized from the spatial distribution of the CT values. A sensitivity analysis comprising various 3D FE simulations reveals the relevance of elastic anisotropy for the load carrying behavior of a human mandible: Comparison of the load distributions in isotropic and anisotropic simulations indicates that anisotropy seems to ``spare''" the mandible from loading. Moreover, a maximum degree of anisotropy leads to kind of an load minimization of the mandible, expressed by a minimum of different norms of local strain, evaluated throughout the organ. Thus, we may suggest that anisotropy is not only relevant, but also in some sense ``optimal''. T3 - ZIB-Report - 04-12 KW - anisotropy KW - elasticity KW - bony organ simulation KW - human mandible KW - visualization of tissue quality KW - finite element analysis Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7873 ER - TY - GEN A1 - Kober, Cornelia 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 N2 - Structural mechanics simulation of bony organs is of general medical and biomechanical interest, because of the interdependence of the inner architecture of bone and its functional loading already stated by Wolff in 1892. This work is part of a detailed research project concerning the human mandible. By adaptive finite element techniques, stress/strain profiles occurring in the bony structure under biting were simulated. Estimates of the discretization errors, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. In general, our simulation requires a representation of the organ's geometry, an appropriate material description, and the load case due to teeth, muscle, or joint forces. In this paper, we want to focus on the influence of the masticatory system. Our goal is to capture the physiological situation as far as possible. By means of visualization techniques developed by the group, we are able to extract individual muscle fibres from computed tomography data. By a special algorithm, the fibres are expanded to fanlike (esp. for the musc. temporalis) coherent vector fields similar to the anatomical reality. The activity of the fibres can be adapted according to compartmentalisation of the muscles as measured by electromyological experiments. A refined sensitivity analysis proved remarkable impact of the presented approach on the simulation results. T3 - ZIB-Report - 04-16 KW - adaptive finite elements KW - error estimation KW - local grid refinement KW - isotropic linear elasticity KW - human mandible KW - masticatory muscles Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7917 ER - TY - GEN A1 - Weiser, Martin A1 - Schiela, Anton T1 - Function space interior point methods for PDE constrained optimization N2 - A primal-dual interior point method for optimal control problems with PDE constraints is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed. Numerical results from an inexact continuation method applied to a model problem are shown. T3 - ZIB-Report - 04-27 KW - interior point methods in function space KW - optimal control KW - complementarity functions Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8027 ER - TY - JOUR A1 - Schenk, O. A1 - Wächter, Andreas A1 - Weiser, Martin T1 - Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization JF - SIAM J. Sci. Comp. Y1 - 2008 VL - 31 IS - 2 SP - 939 EP - 960 ER - TY - JOUR A1 - Weiser, Martin A1 - Deuflhard, Peter T1 - Inexact central path following algorithms for optimal control problems JF - SIAM J. Control Opt. Y1 - 2007 VL - 46 IS - 3 SP - 792 EP - 815 ER - TY - JOUR A1 - Bergmann, G. A1 - Graichen, F. A1 - Rohlmann, A. A1 - Bender, Alwina A1 - Ehrig, Rainald A1 - Westerhoff, P. A1 - Heinlein, B. T1 - Design and calibration of load sensing orthopaedic implants JF - Journal Biomech. Eng. Y1 - 2008 SP - 02109 EP - 1–02109–9 ER - TY - JOUR A1 - Colli Franzone, Piero A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Lang, Jens A1 - Pavarino, Luca Franco T1 - Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology JF - SIAM J. Sc. Comp. Y1 - 2006 VL - 28 SP - 942 EP - 962 ER - TY - JOUR A1 - Dahlke, S. A1 - Steidl, G. A1 - Teschke, G. T1 - Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to Analyzing Functions on Spheres JF - Adv. Comput.Math. Y1 - 2004 VL - 1-2 IS - 21 SP - 147 EP - 180 ER - TY - JOUR A1 - Dahlke, S. A1 - Steidl, G. A1 - Teschke, G. T1 - Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces JF - Journal of Fourier Analysis and Applications Y1 - 2004 VL - 5 IS - 10 SP - 507 EP - 539 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Numerische Mathematik 3 Y1 - 2011 PB - de Gruyter, Berlin ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Adaptive numerical solution of PDEs Y1 - 2012 PB - de Gruyter CY - Berlin ER - TY - JOUR A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Zachow, Stefan T1 - Mathematics in Facial Surgery JF - AMS Notices Y1 - 2006 VL - 53 IS - 9 SP - 1012 EP - 1016 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Hochmuth, Reinhard T1 - Multiscale analysis of thermoregulation in the human microvascular system JF - Math. Methods Appl. Sci. Y1 - 2004 VL - 27 IS - 8 SP - 971 EP - 989 PB - Wiley Verlag ER -