TY - GEN A1 - Klapproth, Corinna A1 - Deuflhard, Peter A1 - Schiela, Anton T1 - A Perturbation Result for Dynamical Contact Problems N2 - This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition. T3 - ZIB-Report - 08-27 KW - Dynamical contact problems KW - stability KW - (visco-)elasticity KW - Signorini condition KW - Newmark method Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10793 SN - 1438-0064 ER - TY - GEN A1 - Deuflhard, Peter A1 - Schiela, Anton A1 - Weiser, Martin T1 - Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia N2 - This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator. T3 - ZIB-Report - 11-39 KW - hyperthermia therapy planning KW - mathematical modelling KW - Maxwell equations KW - state constraints KW - parameter identification Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14204 SN - 1438-0064 ER - TY - GEN A1 - Franzone, Piero Colli 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 N2 - Adaptive numerical methods in space and time are introduced and studied for multiscale cardiac reaction-diffusion models in three dimensions. The evolution of a complete heartbeat, from the excitation to the recovery phase, is simulated with both the anisotropic Bidomain and Monodomain models, coupled with either a variant of the simple FitzHugh-Nagumo model or the more complex phase-I Luo-Rudy ionic model. The simulations are performed with the {\sc kardos} library, that employs adaptive finite elements in space and adaptive linearly implicit methods in time. The numerical results show that this adaptive method successfully solves these complex cardiac reaction-diffusion models on three-dimensional domains of moderate sizes. By automatically adapting the spatial meshes and time steps to the proper scales in each phase of the heartbeat, the method accurately resolves the evolution of the intra- and extra-cellular potentials, gating variables and ion concentrations during the excitation, plateau and recovery phases. T3 - ZIB-Report - 05-30 KW - reaction-diffusion equations KW - cardiac Bidomain and Monodomain models KW - adaptive finite elements KW - adaptive time integration Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8649 ER - TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter A1 - Erdmann, Bodo T1 - Affine conjugate adaptive Newton methods for nonlinear elastomechanics N2 - The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning. T3 - ZIB-Report - 04-01 KW - affine conjugate Newton methods KW - nonconvex minimization KW - nonlinear elastomechnics KW - cranio-maxillofacial surgery KW - soft tissue simulation KW - multilev Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7768 ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Weiser, Martin A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Optimal control for a tuberculosis model with undetected cases in Cameroon N2 - This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years T3 - ZIB-Report - 13-73 KW - Tuberculosis KW - Optimal control KW - Nonlinear dynamical systems Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43142 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 - 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 - 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 - 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 -