TY - GEN A1 - Boer, H. Marike T. A1 - Stötzel, Claudia A1 - Röblitz, Susanna A1 - Deuflhard, Peter A1 - Veerkamp, Roel F. A1 - Woelders, Henri T1 - A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions N2 - Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences. T3 - ZIB-Report - 10-06 KW - cow KW - reproduction KW - hormone patterns KW - ordinary differential equations KW - systems biology Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11682 SN - 1438-0064 ER - TY - GEN A1 - Röblitz, Susanna A1 - Stötzel, Claudia A1 - Deuflhard, Peter A1 - Jones, Hannah M. A1 - Azulay, David-Olivier A1 - van der Graaf, Piet A1 - Martin, Steven T1 - A mathematical model of the human menstrual cycle for the administration of GnRH analogues N2 - This study presents a differential equation model for the feedback mechanisms between Gonadotropin-releasing Hormone (GnRH), Follicle-Stimulating Hormone (FSH), Luteinizing Hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. In contrast to other models, this model does not involve delay differential equations and is based on deterministic modelling of the GnRH pulse pattern, which allows for faster simulation times and efficient parameter identification. These steps were essential to tackle the task of developing a mathematical model for the administration of GnRH analogues. The focus of this paper is on model development for GnRH receptor binding and the integration of a pharmacokinetic/pharmacodynamic model for the GnRH agonist Nafarelin and the GnRH antagonist Cetrorelix into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle in 12 healthy women. Moreover, it correctly predicts the changes in the cycle following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle. T3 - ZIB-Report - 11-16 KW - human menstrual cycle KW - systems biology KW - mathematical modelling KW - GnRH analogues KW - differential equations Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12732 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 - Sander, Oliver A1 - Klapproth, Corinna A1 - Youett, Jonathan A1 - Kornhuber, Ralf A1 - Deuflhard, Peter T1 - Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion N2 - We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity. Its efficient numerical simulation requires advanced numerical algorithms that have been developed just recently. Up to now, the model comprises bones, cartilage, and the major ligaments (patella and menisci are still missing). Bones (femur, tibia, and fibula) are modelled by linear elastic materials, cartilage by viscoelastic materials, ligaments by one-dimensional so-called Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity in the presence of strict contact inequalities. For the total spatio-temporal discretization we apply a method of layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts, we apply a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet-Neumann method, and the arising large algebraic systems are solved by a recent fast multigrid solver, the truncated non-smooth Newton multigrid method. T3 - ZIB-Report - 12-06 KW - contact problem KW - contact-stabilized Newmark method KW - domain decomposition KW - energy-momentum method KW - geodesic finite elements KW - knee model Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14512 SN - 1438-0064 ER - TY - GEN A1 - Klapproth, Corinna A1 - Schiela, Anton A1 - Deuflhard, Peter T1 - Adaptive Timestep Control for the Contact-Stabilized Newmark Method N2 - The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example. T3 - ZIB-Report - 10-09 KW - dynamical contact problems KW - contact--stabilized Newmark method KW - extrapolation methods KW - adaptivity KW - timestep control Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11714 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 - Weber, Marcus A1 - Walter, Lionel A1 - Kube, Susanna A1 - Deuflhard, Peter T1 - Stable computation of probability densities for metastable dynamical systems N2 - Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples. T3 - ZIB-Report - 06-39 KW - dynamical systems KW - metastability KW - molecular conformations KW - cluster analysis KW - sampling KW - aggregation/disaggregation KW - domain decomposition Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9331 ER - TY - GEN A1 - Deuflhard, Peter A1 - Krause, Rolf A1 - Ertel, Susanne T1 - A Contact-Stabilized Newmark Method for Dynamical Contact Problems N2 - The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact). T3 - ZIB-Report - 06-42 KW - Numerical problems in dynamical systems KW - nonlinear stabilities Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9361 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 - Deuflhard, Peter A1 - (Chairs), Hyung Yong Ra T1 - Korean-German Bilateral Symposium on Scientific Computing N2 - Collection of abstracts of the Korean-German Bilateral Symposium on Scientific Computing, Berlin January 15/16, 2004 T3 - ZIB-Report - 04-02 KW - Abstracts Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7778 ER - TY - GEN A1 - Deuflhard, Peter A1 - Erdmann, Bodo A1 - Roitzsch, Rainer A1 - Lines, Glenn Terje T1 - Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics N2 - The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle). T3 - ZIB-Report - 06-49 KW - reaction-diffusion equations KW - Aliev-Panfilov model KW - electrocardiology KW - adaptive finite elements KW - adaptive time integration KW - adaptive Rothe method Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9431 ER - TY - GEN A1 - Deuflhard, Peter A1 - Huisinga, Wilhelm A1 - Jahnke, Tobias A1 - Wulkow, Michael T1 - Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation N2 - \begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract} T3 - ZIB-Report - 07-04 KW - adaptive discrete Galerkin methods KW - adaptive Rothe method KW - discrete Chebyshev polynomials KW - stochastic reactions kinetics KW - chemical master equation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9471 ER - TY - GEN A1 - Reinecke, Isabel A1 - Deuflhard, Peter T1 - A Complex Mathematical Model of the Human Menstrual Cycle N2 - This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper. T3 - ZIB-Report - 06-18 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9112 ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - Mun, Seong T1 - Validation of a Linear Elastic Model for Soft Tissue Simulation in Craniofacial Surgery T2 - Proc. SPIE Medical Imaging 2001 Y1 - 2001 U6 - https://doi.org/10.1117/12.428061 VL - 4319 SP - 27 EP - 35 CY - San Diego, USA ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - FE-based heuristic approach for the estimation of person-specific facial mimics T2 - Proceedings of Euro-Par 2001: 5-th International Symposium on Computer Methods Y1 - 2001 CY - Rome, Italy ER - TY - JOUR A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Seebaß, Martin T1 - A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia JF - Comput. Visual. Sci. Y1 - 2000 U6 - https://doi.org/10.1007/PL00013546 VL - 3 SP - 1 EP - 6 ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Towards a Realistic Simulation of Individual Facial Mimics T2 - Vision Modeling and Visualization 2001 (VMV) Y1 - 2001 SP - 129 EP - 134 CY - Stuttgart, Germany ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - A Biomechanical Model for Soft Tissue Simulation in Craniofacial Surgery T2 - Medical Imaging and Augmented Reality (MIAR) Y1 - 2001 U6 - https://doi.org/10.1109/MIAR.2001.930276 SP - 137 EP - 141 CY - Hong Kong, China ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Virtual Fibers: A Robust Approach for Muscle Simulation T2 - IX Mediterranean Conference on Medical and Biological Engineering and Computing (MEDICON) Y1 - 2001 SP - 961 EP - 964 CY - Pula, Croatia ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Validierung eines linear elastischen Modells für die Weichgewebesimulation in der Mund-Kiefer-Gesichtschirurgie T2 - Bildverarbeitung für die Medizin (BVM) Y1 - 2001 SP - 57 EP - 61 CY - Lübeck, Germany ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - Galloway, Robert T1 - Realistic prediction of individual facial emotion expressions for craniofacial surgery simulations T2 - Proc. SPIE medical Imaging 2003 Y1 - 2003 U6 - https://doi.org/10.1117/12.479584 VL - 5029 SP - 520 EP - 527 CY - San Diego, CA, USA ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - On constitutive modeling of soft tissue for the long-term prediction of cranio-maxillofacial surgery outcome T2 - International Congress Series, CARS2003, Computer Assisted Radiology and Surgery, Proceedings of the 17th International Congress and Exhibition Y1 - 2003 U6 - https://doi.org/10.1016/S0531-5131(03)00500-4 VL - 1256 SP - 343 EP - 348 ER - TY - CHAP A1 - Lamecker, Hans A1 - Seebaß, Martin A1 - Hege, Hans-Christian A1 - Deuflhard, Peter ED - Fitzpatrick, J. ED - Sonka, Milan T1 - A 3D statistical shape model of the pelvic bone for segmentation T2 - Proceedings of SPIE - Volume 5370 Medical Imaging 2004 Y1 - 2004 U6 - https://doi.org/10.1117/12.534145 SP - 1341 EP - 1351 ER - TY - JOUR A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Anatomy- and physics-based facial animation for craniofacial surgery simulations JF - Med Biol Eng Comput. Y1 - 2004 U6 - https://doi.org/10.1007/BF02344627 VL - 42(2) SP - 167 EP - 170 ER - TY - CHAP A1 - Zachow, Stefan A1 - Gladilin, Evgeny A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Towards Patient Specific, Anatomy Based Simulation of Facial Mimics for Surgical Nerve Rehabilitation T2 - Computer Assisted Radiology and Surgery (CARS) Y1 - 2002 SP - 3 EP - 6 PB - Springer Verlag ER - TY - CHAP A1 - Zachow, Stefan A1 - Erdmann, Bodo A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Advances in 3D osteotomy planning with 3D soft tissue prediction T2 - Proc. 2nd International Symposium on Computer Aided Surgery around the Head, Abstract Y1 - 2004 SP - 31 CY - Bern ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - K. Mun, Seong T1 - Adaptive Nonlinear Elastic FEM for Realistic Prediction of Soft Tissue in Craniofacial Surgery Simulations T2 - Proc. SPIE Medical Imaging 2002 Y1 - 2002 U6 - https://doi.org/10.1117/12.466906 VL - 4681 SP - 1 EP - 8 CY - San Diego, USA ER - TY - CHAP A1 - Gladilin, Evgeny A1 - Zachow, Stefan A1 - Deuflhard, Peter A1 - Hege, Hans-Christian ED - Mun, Seong T1 - Shape-based Modeling Approach for the Estimation of Individual Facial Mimics in Craniofacial Surgery Planning T2 - Proc. SPIE Medical Imaging 2002: Visualization, Image-Guided Procedures, and Display Y1 - 2002 VL - 4681 SP - 242 EP - 248 CY - San Diego, USA target ER - TY - JOUR A1 - Zachow, Stefan A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Computer assisted planning in cranio-maxillofacial surgery JF - Journal of Computing and Information Technology Y1 - 2006 VL - 14(1) SP - 53 EP - 64 ER - TY - CHAP A1 - Zachow, Stefan A1 - Gladilin, Evgeny A1 - Hege, Hans-Christian A1 - Deuflhard, Peter T1 - Finite-Element Simulation of Soft Tissue Deformation T2 - Computer Assisted Radiology and Surgey (CARS) Y1 - 2000 SP - 23 EP - 28 PB - Elsevier Science B.V. ER - TY - CHAP A1 - Deuflhard, Peter A1 - Hege, Hans-Christian A1 - Seebaß, Martin T1 - Progress Towards a Combined MRI/Hyperthermia System T2 - Proceedings Second International Congress HIGH CARE 2000 Y1 - 2000 CY - Bochum ER - TY - CHAP A1 - Deuflhard, Peter A1 - Seebaß, Martin A1 - Stalling, Detlev A1 - Beck, Rudolf A1 - Hege, Hans-Christian ED - Sydow, Achim T1 - Hyperthermia Treatment Planning in Clinical Therapy T2 - Computational Physics, Chemistry and Biology (Proceedings of the 15th IMACS World Congress 1997 on Scientific Computation 3, Modelling and Applied Mathematics) Y1 - 1997 SP - 9 EP - 17 PB - Wissenschaft und Technik Verlag ER - TY - CHAP A1 - Beck, Rudolf A1 - Deuflhard, Peter A1 - Hege, Hans-Christian A1 - Seebaß, Martin A1 - Stalling, Detlev ED - Hege, Hans-Christian ED - Polthier, Konrad T1 - Numerical Algorithms and Visualization in Medical Treatment Planning T2 - Visualization and Mathematics 1997 Y1 - 1996 SP - 303 EP - 328 PB - Springer, Heidelberg ER - TY - CHAP A1 - Deuflhard, Peter A1 - Hege, Hans-Christian T1 - Scientific Computing in der Theoretischen Physik - Collected Abstracts T2 - Tagung organisiert von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem GAMM Fachausschuss Scientific Computing Y1 - 1994 CY - Berlin ER - TY - CHAP A1 - Deuflhard, Peter A1 - Seebaß, Martin ED - Lai, Choi-Hong ED - Bjorstad, Petter ED - Cross, Mark ED - Widlund, Olof T1 - Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyerthermia T2 - Proc. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering Y1 - 1998 SP - 410 EP - 421 CY - Greenwich, UK ER - TY - GEN A1 - Moualeu-Ngangue, Dany Pascal A1 - Röblitz, Susanna A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Parameter Identification for a Tuberculosis Model in Cameroon N2 - A deterministic model of tuberculosis in sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed with respect to its transmission dynamics. The model includes both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and most sensitive parameters of the model are identified using a state-of-the-art Gauss-Newton Method. In particular, parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease. It has been shown that an increase of these parameter values over the time can significantly reduce the disease burden in the population within the next 15 years. T3 - ZIB-Report - 13-72 KW - Tuberculosis, parameter identification, sensitivity analysis, Gauss-Newton method, Nonlinear dynamical systems. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43087 SN - 1438-0064 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 - Deuflhard, Peter T1 - The Grand Four. Affine Invariant Globalizations of Newton's Method JF - Vietnam Journal of Mathematics Y1 - 2018 U6 - https://doi.org/10.1007/s10013-018-0301-3 VL - 46 IS - 4 SP - 761 EP - 777 ER - TY - GEN A1 - Nägel, Arne A1 - Deuflhard, Peter A1 - Wittum, Gabriel T1 - Efficient Stiff Integration of Density Driven Flow Problems N2 - The paper investigates the efficient use of a linearly implicit stiff integrator for the numerical solution of density driven flow problems. Upon choosing a one-step method of extrapolation type (code LIMEX), the use of full Jacobians and reduced approximations are discussed. Numerical experiments include nonlinear density flow problems such as diffusion from a salt dome (2D), a (modified) Elder problem (3D), the saltpool benchmark (3D) and a real life salt dome problem (2D). The arising linear equations are solved using either a multigrid preconditioner from the software package UG4 or the sparse matrix solver SuperLU. T3 - ZIB-Report - 18-54 KW - stiff integration for PDEs KW - linearly implicit Euler discretization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70891 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 - Galliat, Tobias A1 - Deuflhard, Peter A1 - Roitzsch, Rainer A1 - Cordes, Frank ED - Schlick, T. ED - Gan, H. T1 - Automatic Identification of Metastable Conformations via Self-Organized Neural Networks T2 - Computational Methods for Macromolecules Y1 - 2002 UR - http://www.zib.de/PaperWeb/abstracts/ZR-00-51 IS - 24 PB - Springer ER - TY - CHAP A1 - Galliat, Tobias A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter ED - H. Bothe, R. T1 - Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification T2 - Neural Computation, ICSC Academic Press Y1 - 2000 SP - 227 EP - 232 ER - TY - JOUR A1 - Hochmuth, Reinhard A1 - Deuflhard, Peter T1 - On the thermoregulation in the human microvascular system JF - PAMM Y1 - 2003 VL - 3 SP - 378 EP - 379 ER - TY - CHAP A1 - Friese, T. A1 - Deuflhard, Peter A1 - Schmidt, Frank ED - Lai, Choi-Hong ED - Bjørstad, Petter E. ED - Cross, Mark ED - Widlund, Olof T1 - A Multigrid Method for the Complex Helmholtz Eigenvalue Problem T2 - Procs. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), UK Y1 - 1999 SP - 19 EP - 26 PB - DDM.org ER - TY - CHAP A1 - Galliat, Tobias A1 - Deuflhard, Peter A1 - Roitzsch, Rainer A1 - Cordes, Frank T1 - Automatic identification of metastable conformations via self-organized neural networks T2 - Proceedings of the 3rd International Workshop on Algorithms for Macromolecular Modelling Y1 - 2002 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Wulkow, Michael T1 - Computational treatment of polyreaction kinetics by orthogonal polynomials of a discrete variable JF - IMPACT Comput. Sci. Eng. Y1 - 1989 VL - 1 IS - 3 SP - 269 EP - 301 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Wulkow, Michael ED - et al. Bachem, Achim T1 - Simulationsverfahren für die Polymerchemie T2 - Mathematik in der Praxis. Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin Y1 - 1995 SP - 117 EP - 136 PB - Berlin: Springer-Verlag ER - TY - CHAP A1 - Deuflhard, Peter T1 - Painters, Murderers, Mathematicians T2 - Mathematics and Culture in Europe. Mathematics in Art, Technology, Cinema, and Theatre Y1 - 2007 SP - 141 EP - 152 PB - Springer-Verlag ER - TY - CHAP A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank ED - Schlick, T. ED - Gan, H. T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations T2 - Computational Methods for Macromolecules Y1 - 2002 UR - http://www.zib.de/PaperWeb/abstracts/ZR-01-03 IS - 24 SP - 235 EP - 259 PB - Springer ER - TY - CHAP A1 - Fröhlich, Jochen A1 - Deuflhard, Peter ED - Neunzert, H. T1 - An adaptive Galerkin method for the PDF transport equation of turbulent reactive flows T2 - Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94) Y1 - 1996 SP - 176 EP - 184 PB - Wiley & Teubner ER - TY - CHAP A1 - Ehrig, Rainald A1 - Nowak, Ulrich A1 - Oeverdieck, Lars A1 - Deuflhard, Peter ED - H.-J. Bungartz, F. T1 - Advanced Extrapolation Methods for Large Scale Differential Algebraic Problems T2 - High Performance Scientific and Engineering Computing Y1 - 1999 VL - 8 SP - 233 EP - 244 PB - Springer Verlag ER -