@misc{BoerStoetzelRoeblitzetal.2010, author = {Boer, H. Marike T. and St{\"o}tzel, Claudia and R{\"o}blitz, Susanna and Deuflhard, Peter and Veerkamp, Roel F. and Woelders, Henri}, title = {A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11682}, number = {10-06}, year = {2010}, abstract = {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.}, language = {en} } @misc{RoeblitzStoetzelDeuflhardetal.2011, author = {R{\"o}blitz, Susanna and St{\"o}tzel, Claudia and Deuflhard, Peter and Jones, Hannah M. and Azulay, David-Olivier and van der Graaf, Piet and Martin, Steven}, title = {A mathematical model of the human menstrual cycle for the administration of GnRH analogues}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12732}, number = {11-16}, year = {2011}, abstract = {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.}, language = {en} } @misc{DeuflhardSchielaWeiser2011, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14204}, number = {11-39}, year = {2011}, abstract = {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.}, language = {en} } @misc{SanderKlapprothYouettetal.2012, author = {Sander, Oliver and Klapproth, Corinna and Youett, Jonathan and Kornhuber, Ralf and Deuflhard, Peter}, title = {Towards an Efficient Numerical Simulation of Complex 3D Knee Joint Motion}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14512}, number = {12-06}, year = {2012}, abstract = {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.}, language = {en} } @misc{KlapprothSchielaDeuflhard2010, author = {Klapproth, Corinna and Schiela, Anton and Deuflhard, Peter}, title = {Adaptive Timestep Control for the Contact-Stabilized Newmark Method}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11714}, number = {10-09}, year = {2010}, abstract = {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.}, language = {en} } @misc{FranzoneDeuflhardErdmannetal.2005, author = {Franzone, Piero Colli and Deuflhard, Peter and Erdmann, Bodo and Lang, Jens and Pavarino, Luca Franco}, title = {Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8649}, number = {05-30}, year = {2005}, abstract = {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.}, language = {en} } @misc{WeberWalterKubeetal.2006, author = {Weber, Marcus and Walter, Lionel and Kube, Susanna and Deuflhard, Peter}, title = {Stable computation of probability densities for metastable dynamical systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9331}, number = {06-39}, year = {2006}, abstract = {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.}, language = {en} } @misc{DeuflhardKrauseErtel2006, author = {Deuflhard, Peter and Krause, Rolf and Ertel, Susanne}, title = {A Contact-Stabilized Newmark Method for Dynamical Contact Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9361}, number = {06-42}, year = {2006}, abstract = {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).}, language = {en} } @misc{WeiserDeuflhardErdmann2004, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7768}, number = {04-01}, year = {2004}, abstract = {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.}, language = {en} } @misc{DeuflhardChairs2003, author = {Deuflhard, Peter and (Chairs), Hyung Yong Ra}, title = {Korean-German Bilateral Symposium on Scientific Computing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7778}, number = {04-02}, year = {2003}, abstract = {Collection of abstracts of the Korean-German Bilateral Symposium on Scientific Computing, Berlin January 15/16, 2004}, language = {en} } @misc{DeuflhardErdmannRoitzschetal.2006, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9431}, number = {06-49}, year = {2006}, abstract = {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).}, language = {en} } @misc{DeuflhardHuisingaJahnkeetal.2007, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9471}, number = {07-04}, year = {2007}, abstract = {\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}}, language = {en} } @misc{ReineckeDeuflhard2006, author = {Reinecke, Isabel and Deuflhard, Peter}, title = {A Complex Mathematical Model of the Human Menstrual Cycle}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9112}, number = {06-18}, year = {2006}, abstract = {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.}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Validation of a Linear Elastic Model for Soft Tissue Simulation in Craniofacial Surgery}, volume = {4319}, booktitle = {Proc. SPIE Medical Imaging 2001}, editor = {Mun, Seong}, address = {San Diego, USA}, doi = {10.1117/12.428061}, pages = {27 -- 35}, year = {2001}, language = {en} } @inproceedings{GladilinZachowHegeetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {FE-based heuristic approach for the estimation of person-specific facial mimics}, booktitle = {Proceedings of Euro-Par 2001: 5-th International Symposium on Computer Methods}, address = {Rome, Italy}, year = {2001}, language = {en} } @article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebaß, Martin}, title = {A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia}, volume = {3}, journal = {Comput. Visual. Sci.}, doi = {10.1007/PL00013546}, pages = {1 -- 6}, year = {2000}, language = {en} } @inproceedings{GladilinZachowHegeetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Towards a Realistic Simulation of Individual Facial Mimics}, booktitle = {Vision Modeling and Visualization 2001 (VMV)}, address = {Stuttgart, Germany}, pages = {129 -- 134}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {A Biomechanical Model for Soft Tissue Simulation in Craniofacial Surgery}, booktitle = {Medical Imaging and Augmented Reality (MIAR)}, address = {Hong Kong, China}, doi = {10.1109/MIAR.2001.930276}, pages = {137 -- 141}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Virtual Fibers: A Robust Approach for Muscle Simulation}, booktitle = {IX Mediterranean Conference on Medical and Biological Engineering and Computing (MEDICON)}, address = {Pula, Croatia}, pages = {961 -- 964}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2001, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Validierung eines linear elastischen Modells f{\"u}r die Weichgewebesimulation in der Mund-Kiefer-Gesichtschirurgie}, booktitle = {Bildverarbeitung f{\"u}r die Medizin (BVM)}, address = {L{\"u}beck, Germany}, pages = {57 -- 61}, year = {2001}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2003, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Realistic prediction of individual facial emotion expressions for craniofacial surgery simulations}, volume = {5029}, booktitle = {Proc. SPIE medical Imaging 2003}, editor = {Galloway, Robert}, address = {San Diego, CA, USA}, doi = {10.1117/12.479584}, pages = {520 -- 527}, year = {2003}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2003, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {On constitutive modeling of soft tissue for the long-term prediction of cranio-maxillofacial surgery outcome}, volume = {1256}, booktitle = {International Congress Series, CARS2003, Computer Assisted Radiology and Surgery, Proceedings of the 17th International Congress and Exhibition}, doi = {10.1016/S0531-5131(03)00500-4}, pages = {343 -- 348}, year = {2003}, language = {en} } @inproceedings{LameckerSeebassHegeetal.2004, author = {Lamecker, Hans and Seebaß, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {A 3D statistical shape model of the pelvic bone for segmentation}, booktitle = {Proceedings of SPIE - Volume 5370 Medical Imaging 2004}, editor = {Fitzpatrick, J. and Sonka, Milan}, doi = {10.1117/12.534145}, pages = {1341 -- 1351}, year = {2004}, language = {en} } @article{GladilinZachowDeuflhardetal.2004, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Anatomy- and physics-based facial animation for craniofacial surgery simulations}, volume = {42(2)}, journal = {Med Biol Eng Comput.}, doi = {10.1007/BF02344627}, pages = {167 -- 170}, year = {2004}, language = {en} } @inproceedings{ZachowGladilinHegeetal.2002, author = {Zachow, Stefan and Gladilin, Evgeny and Hege, Hans-Christian and Deuflhard, Peter}, title = {Towards Patient Specific, Anatomy Based Simulation of Facial Mimics for Surgical Nerve Rehabilitation}, booktitle = {Computer Assisted Radiology and Surgery (CARS)}, publisher = {Springer Verlag}, pages = {3 -- 6}, year = {2002}, language = {en} } @inproceedings{ZachowErdmannHegeetal.2004, author = {Zachow, Stefan and Erdmann, Bodo and Hege, Hans-Christian and Deuflhard, Peter}, title = {Advances in 3D osteotomy planning with 3D soft tissue prediction}, booktitle = {Proc. 2nd International Symposium on Computer Aided Surgery around the Head, Abstract}, address = {Bern}, pages = {31}, year = {2004}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Adaptive Nonlinear Elastic FEM for Realistic Prediction of Soft Tissue in Craniofacial Surgery Simulations}, volume = {4681}, booktitle = {Proc. SPIE Medical Imaging 2002}, editor = {K. Mun, Seong}, address = {San Diego, USA}, doi = {10.1117/12.466906}, pages = {1 -- 8}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Shape-based Modeling Approach for the Estimation of Individual Facial Mimics in Craniofacial Surgery Planning}, volume = {4681}, booktitle = {Proc. SPIE Medical Imaging 2002: Visualization, Image-Guided Procedures, and Display}, editor = {Mun, Seong}, address = {San Diego, USA target}, pages = {242 -- 248}, year = {2002}, language = {en} } @article{ZachowHegeDeuflhard2006, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Computer assisted planning in cranio-maxillofacial surgery}, volume = {14(1)}, journal = {Journal of Computing and Information Technology}, pages = {53 -- 64}, year = {2006}, language = {en} } @inproceedings{ZachowGladilinHegeetal.2000, author = {Zachow, Stefan and Gladilin, Evgeny and Hege, Hans-Christian and Deuflhard, Peter}, title = {Finite-Element Simulation of Soft Tissue Deformation}, booktitle = {Computer Assisted Radiology and Surgey (CARS)}, publisher = {Elsevier Science B.V.}, pages = {23 -- 28}, year = {2000}, language = {en} } @inproceedings{DeuflhardHegeSeebass2000, author = {Deuflhard, Peter and Hege, Hans-Christian and Seebaß, Martin}, title = {Progress Towards a Combined MRI/Hyperthermia System}, booktitle = {Proceedings Second International Congress HIGH CARE 2000}, address = {Bochum}, year = {2000}, language = {en} } @inproceedings{DeuflhardSeebassStallingetal.1997, author = {Deuflhard, Peter and Seebaß, Martin and Stalling, Detlev and Beck, Rudolf and Hege, Hans-Christian}, title = {Hyperthermia Treatment Planning in Clinical Therapy}, booktitle = {Computational Physics, Chemistry and Biology (Proceedings of the 15th IMACS World Congress 1997 on Scientific Computation 3, Modelling and Applied Mathematics)}, editor = {Sydow, Achim}, publisher = {Wissenschaft und Technik Verlag}, pages = {9 -- 17}, year = {1997}, language = {en} } @incollection{BeckDeuflhardHegeetal.1996, author = {Beck, Rudolf and Deuflhard, Peter and Hege, Hans-Christian and Seebaß, Martin and Stalling, Detlev}, title = {Numerical Algorithms and Visualization in Medical Treatment Planning}, booktitle = {Visualization and Mathematics 1997}, editor = {Hege, Hans-Christian and Polthier, Konrad}, publisher = {Springer, Heidelberg}, pages = {303 -- 328}, year = {1996}, language = {en} } @inproceedings{DeuflhardHege1994, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Scientific Computing in der Theoretischen Physik - Collected Abstracts}, booktitle = {Tagung organisiert von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem GAMM Fachausschuss Scientific Computing}, address = {Berlin}, year = {1994}, language = {en} } @inproceedings{DeuflhardSeebass1998, author = {Deuflhard, Peter and Seebaß, Martin}, title = {Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyerthermia}, booktitle = {Proc. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering}, editor = {Lai, Choi-Hong and Bjorstad, Petter and Cross, Mark and Widlund, Olof}, address = {Greenwich, UK}, pages = {410 -- 421}, year = {1998}, language = {en} } @misc{MoualeuNgangueRoeblitzEhrigetal.2013, author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification for a Tuberculosis Model in Cameroon}, issn = {1438-0064}, doi = {10.1371/journal.pone.0120607}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43087}, year = {2013}, abstract = {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.}, language = {en} } @misc{MoualeuNgangueWeiserEhrigetal.2013, author = {Moualeu-Ngangue, Dany Pascal and Weiser, Martin and Ehrig, Rainald and Deuflhard, Peter}, title = {Optimal control for a tuberculosis model with undetected cases in Cameroon}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-43142}, year = {2013}, abstract = {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}, language = {en} } @article{Deuflhard2018, author = {Deuflhard, Peter}, title = {The Grand Four. Affine Invariant Globalizations of Newton's Method}, volume = {46}, journal = {Vietnam Journal of Mathematics}, number = {4}, doi = {10.1007/s10013-018-0301-3}, pages = {761 -- 777}, year = {2018}, language = {en} } @misc{NaegelDeuflhardWittum2018, author = {N{\"a}gel, Arne and Deuflhard, Peter and Wittum, Gabriel}, title = {Efficient Stiff Integration of Density Driven Flow Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-70891}, year = {2018}, abstract = {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.}, language = {en} } @article{HochmuthDeuflhard2004, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {Multiscale Analysis for the Bio-Heat-Transfer Equation - The Nonisolated Case}, volume = {14}, journal = {Mathematical Models and Methods in Applied Sciences (M\$^3\$AS)}, number = {11}, pages = {1621 -- 1634}, year = {2004}, language = {en} } @inproceedings{GalliatDeuflhardRoitzschetal.2002, author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic Identification of Metastable Conformations via Self-Organized Neural Networks}, booktitle = {Computational Methods for Macromolecules}, number = {24}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, year = {2002}, language = {en} } @inproceedings{GalliatHuisingaDeuflhard2000, author = {Galliat, Tobias and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification}, booktitle = {Neural Computation, ICSC Academic Press}, editor = {H. Bothe, R.}, pages = {227 -- 232}, year = {2000}, language = {en} } @article{HochmuthDeuflhard2003, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {On the thermoregulation in the human microvascular system}, volume = {3}, journal = {PAMM}, pages = {378 -- 379}, year = {2003}, language = {en} } @inproceedings{FrieseDeuflhardSchmidt1999, author = {Friese, T. and Deuflhard, Peter and Schmidt, Frank}, title = {A Multigrid Method for the Complex Helmholtz Eigenvalue Problem}, booktitle = {Procs. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), UK}, editor = {Lai, Choi-Hong and Bj{\o}rstad, Petter E. and Cross, Mark and Widlund, Olof}, publisher = {DDM.org}, pages = {19 -- 26}, year = {1999}, language = {en} } @inproceedings{GalliatDeuflhardRoitzschetal.2002, author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic identification of metastable conformations via self-organized neural networks}, booktitle = {Proceedings of the 3rd International Workshop on Algorithms for Macromolecular Modelling}, year = {2002}, language = {en} } @article{DeuflhardWulkow1989, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Computational treatment of polyreaction kinetics by orthogonal polynomials of a discrete variable}, volume = {1}, journal = {IMPACT Comput. Sci. Eng.}, number = {3}, pages = {269 -- 301}, year = {1989}, language = {en} } @incollection{DeuflhardWulkow1995, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Simulationsverfahren f{\"u}r die Polymerchemie}, booktitle = {Mathematik in der Praxis. Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin}, editor = {et al. Bachem, Achim}, publisher = {Berlin: Springer-Verlag}, pages = {117 -- 136}, year = {1995}, language = {en} } @incollection{Deuflhard2007, author = {Deuflhard, Peter}, title = {Painters, Murderers, Mathematicians}, booktitle = {Mathematics and Culture in Europe. Mathematics in Art, Technology, Cinema, and Theatre}, publisher = {Springer-Verlag}, pages = {141 -- 152}, year = {2007}, language = {en} } @inproceedings{FischerSchuetteDeuflhardetal.2002, author = {Fischer, Alexander and Sch{\"u}tte, Christof and Deuflhard, Peter and Cordes, Frank}, title = {Hierarchical Uncoupling-Coupling of Metastable Conformations}, booktitle = {Computational Methods for Macromolecules}, number = {24}, editor = {Schlick, T. and Gan, H.}, publisher = {Springer}, pages = {235 -- 259}, year = {2002}, language = {en} } @inproceedings{FroehlichDeuflhard1996, author = {Fr{\"o}hlich, Jochen and Deuflhard, Peter}, title = {An adaptive Galerkin method for the PDF transport equation of turbulent reactive flows}, booktitle = {Progress in Industrial Mathematics, Proc. 8th Conference of the European Consortium for Mathematics in Industry (ECMI 94)}, editor = {Neunzert, H.}, publisher = {Wiley \& Teubner}, pages = {176 -- 184}, year = {1996}, language = {en} } @incollection{EhrigNowakOeverdiecketal.1999, author = {Ehrig, Rainald and Nowak, Ulrich and Oeverdieck, Lars and Deuflhard, Peter}, title = {Advanced Extrapolation Methods for Large Scale Differential Algebraic Problems}, volume = {8}, booktitle = {High Performance Scientific and Engineering Computing}, editor = {H.-J. Bungartz, F.}, publisher = {Springer Verlag}, pages = {233 -- 244}, year = {1999}, language = {en} }