@article{NadobnySullivanWustetal.1998, author = {Nadobny, Jacek and Sullivan, Dennis and Wust, Peter and Seebaß, Martin and Deuflhard, Peter and Felix, Roland}, title = {A High-Resolution Interpolation at Arbitary Interfaces for the FDTD Method}, series = {IEEE Trans. Microwave Theory Tech.}, volume = {46}, journal = {IEEE Trans. Microwave Theory Tech.}, number = {11}, doi = {10.1109/22.734576}, pages = {1759 -- 1766}, year = {1998}, language = {en} } @inproceedings{NadobnyWustFaehlingetal.1998, author = {Nadobny, Jacek and Wust, Peter and F{\"a}hling, Horst and Stalling, Detlev and Seebaß, Martin and Deuflhard, Peter and Felix, Roland}, title = {Numerical and Experimental Evaluation of E-Field and Absorbed Power in the Pelvic Region Using a Bone-Equivalent Phantom}, series = {Proc. PIERS Progress in Electromagnetic Research Symposium}, booktitle = {Proc. PIERS Progress in Electromagnetic Research Symposium}, address = {Nantes}, pages = {264}, year = {1998}, language = {en} } @article{WustGellermannBeieretal.1998, author = {Wust, Peter and Gellermann, Johanna and Beier, J{\"u}rgen and Wegner, Susan and Tilly, Wolfgang and Tr{\"o}ger, Jens and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Evaluation of Segmentation Algorithms for Generation of Patient Models in Radiofrequency Hyperthermia}, series = {Phys. Med. Biol.}, volume = {43 (11)}, journal = {Phys. Med. Biol.}, doi = {10.1088/0031-9155/43/11/009}, pages = {3295 -- 3307}, year = {1998}, language = {en} } @inproceedings{DeuflhardHege1994, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Scientific Computing in der Theoretischen Physik - Collected Abstracts}, series = {Tagung organisiert von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem GAMM Fachausschuss Scientific Computing}, booktitle = {Tagung organisiert von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem GAMM Fachausschuss Scientific Computing}, address = {Berlin}, year = {1994}, language = {en} } @inproceedings{NadobnyWustWlodarczyketal.1996, author = {Nadobny, Jacek and Wust, Peter and Wlodarczyk, Waldemar and Seebaß, Martin and Deuflhard, Peter and M{\"o}nich, Gerhard and Felix, Roland}, title = {Simulation Studies for Combination of Hyperthermia and Magnetic Resonance Systems}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {549 -- 551}, year = {1996}, language = {en} } @inproceedings{SeebassStallingNadobnyetal.1996, author = {Seebaß, Martin and Stalling, Detlev and Nadobny, Jacek and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Three-Dimensional Finite Elements Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {547 -- 548}, year = {1996}, language = {en} } @inproceedings{StallingSeebassHegeetal.1996, author = {Stalling, Detlev and Seebaß, Martin and Hege, Hans-Christian and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {HyperPlan - an Integrated System for Treatment Planning in Regional Hyperthermia}, series = {Proceedings of the 17th Congress on Hyperthermic Oncology}, volume = {2}, booktitle = {Proceedings of the 17th Congress on Hyperthermic Oncology}, address = {Rome, Italy}, pages = {552 -- 554}, year = {1996}, language = {en} } @article{WustSeebassNadobnyetal.1996, author = {Wust, Peter and Seebaß, Martin and Nadobny, Jacek and Deuflhard, Peter and M{\"o}nich, Gerhard and Felix, Roland}, title = {Simulation Studies Promote Technological Development of Radiofrequency Phased Array Hyperthermia}, series = {Int. Journal of Hyperthermia}, volume = {12}, journal = {Int. Journal of Hyperthermia}, pages = {477 -- 494}, year = {1996}, language = {en} } @misc{WeiserErdmannDeuflhard, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, series = {Progress in Industrial Mathematics at ECMI 2008}, journal = {Progress in Industrial Mathematics at ECMI 2008}, editor = {Wilson, E. and Fitt, A. and Ockendon, H. and Norbury, J.}, publisher = {Springer}, pages = {371 -- 376}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @article{DeuflhardSchielaWeiser, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, series = {Acta Numerica}, volume = {21}, journal = {Acta Numerica}, pages = {307 -- 378}, 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{DeuflhardHege, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Raumtiefe in Malerei und Computergrafik}, series = {R{\"a}ume - Bilder - Kulturen}, journal = {R{\"a}ume - Bilder - Kulturen}, editor = {Lepper, Verena and Deuflhard, Peter and Markschies, Christoph}, publisher = {Walter De Gruyter}, isbn = {978-3-11-035993-0}, pages = {33 -- 46}, abstract = {Einf{\"u}hrung: Die Tiefenwirkung dreidimensionaler R{\"a}ume in einem zweidimensionalen Bild einzufangen, ist ein Faszinosum nahezu aller Kulturen der Menschheitsgeschichte. Der vorliegende Aufsatz folgt den Spuren dieses Faszinosums, vergleichend in der Malerei und der mathematisierten Computergrafik. Die Entdeckung der Zentralperspektive in der italienischen Renaissance zeigt bereits den engen Zusammenhang von Malerei und Mathematik. Auf der Suche nach Maltechniken, mit denen Raumtiefe bildnerisch dargestellt werden kann, beginnen wir in Kap. 2 mit einem chronologischen Gang durch verschiedene Epochen der europ{\"a}ischen Malerei. Hieraus abgeleitete Prinzipien, soweit sie im Rechner realisierbar scheinen, stellen wir in Kap. 3 am Beispiel moderner Methoden der mathematischen Visualisierung vor.}, language = {de} } @book{OPUS4-5717, title = {R{\"a}ume - Bilder - Kulturen}, editor = {Lepper, Verena and Deuflhard, Peter and Markschies, Christoph}, publisher = {De Gruyter}, isbn = {978-3-11-035993-0}, language = {de} } @book{OPUS4-5024, title = {MATHEON - Mathematics for Key Technologies}, volume = {1}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, isbn = {978-3-03719-137-8}, doi = {10.4171/137}, language = {en} } @misc{Deuflhard, author = {Deuflhard, Peter}, title = {The Grand Four}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66038}, abstract = {This paper gives a concise synopsis and some new insights concerning four affine invariant globalizations of the local Newton method. The invariance classes include: affine covariance, affine contravariance, affine conjugacy, and affine similarity. In view of algorithmic robustness, each of these classes of algorithms is particularly suitable for some corresponding problem class.}, language = {en} } @article{WustNadobnySeebassetal.1999, author = {Wust, Peter and Nadobny, Johanna and Seebass, Martin and Stalling, Detlev and Gellermann, Johanna and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Influence of patient models and numerical methods on predicted power deposition patterns}, series = {Int. J. Hyperthermia}, volume = {15}, journal = {Int. J. Hyperthermia}, number = {6}, pages = {519 -- 540}, year = {1999}, language = {en} } @article{WustSeebassNadobnyetal.1996, author = {Wust, Peter and Seebass, Martin and Nadobny, Johanna and Deuflhard, Peter and M{\"o}nich, Gerhard and Felix, Roland}, title = {Simulation studies promote technological development of radiofrequency phased array hyperthermia}, series = {Int J Hyperthermia}, volume = {12}, journal = {Int J Hyperthermia}, number = {4}, pages = {477 -- 494}, year = {1996}, language = {en} } @techreport{DeuflhardFiedlerKunkel1984, author = {Deuflhard, Peter and Fiedler, B. and Kunkel, P.}, title = {Efficient numerical pathfollowing beyond critical points}, number = {278}, publisher = {Universit{\"a}t Heidelberg}, year = {1984}, language = {en} } @article{RoeblitzStoetzelDeuflhardetal.2013, 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}, series = {Journal of Theoretical Biology}, volume = {321}, journal = {Journal of Theoretical Biology}, doi = {10.1016/j.jtbi.2012.11.020}, pages = {8 -- 27}, year = {2013}, language = {en} } @inproceedings{SeebassStallingNadobnyetal.1996, author = {Seebass, Martin and Stalling, Detlev and Nadobny, Johanna and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Three-Dimensional Finite Element Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, volume = {2}, booktitle = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, editor = {Franconi, Cafiero}, pages = {547 -- 548}, year = {1996}, language = {en} } @inproceedings{SeebassStallingZoeckleretal.1997, author = {Seebass, Martin and Stalling, Detlev and Z{\"o}ckler, M. and Hege, Hans-Christian and Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {Surface Mesh Generation for Numerical Simulations of Hyperthermia Treatments}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {146}, year = {1997}, language = {en} } @inproceedings{WlodarczykNadobnyWustetal.1999, author = {Wlodarczyk, Waldemar and Nadobny, Johanna and Wust, Peter and M{\"o}nich, Gerhard and Deuflhard, Peter and Felix, Roland}, title = {Systematic design of antennas for cylindrical 3D phased array hyperthermia applicator}, series = {Proc. IEEE Antennas Propagat. Soc. Intern. Symposium, July 11-16, 1999, Orlando, FL, USA,}, booktitle = {Proc. IEEE Antennas Propagat. Soc. Intern. Symposium, July 11-16, 1999, Orlando, FL, USA,}, pages = {1004 -- 1007}, year = {1999}, language = {en} } @incollection{WulkowDeuflhard1992, author = {Wulkow, Michael and Deuflhard, Peter}, title = {Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions}, series = {Computational Ordinary Differential Equations}, booktitle = {Computational Ordinary Differential Equations}, editor = {Fatunla, S.}, publisher = {University Press, Nigeria}, pages = {287 -- 306}, year = {1992}, language = {en} } @article{WustFahlingWlodarczyketal.2001, author = {Wust, Peter and Fahling, Horst and Wlodarczyk, Waldemar and Seebass, Martin and Gellermann, Johanna and Deuflhard, Peter and Nadobny, Johanna}, title = {Antenna arrays in the SIGMA-eye applicator}, series = {Med Phys}, volume = {28}, journal = {Med Phys}, number = {8}, pages = {1793 -- 1805}, year = {2001}, language = {en} } @misc{WustFelixDeuflhard1999, author = {Wust, Peter and Felix, Roland and Deuflhard, Peter}, title = {K{\"u}nstliches Fieber gegen Krebs}, publisher = {Spektrum der Wissenschaft, pp. 78-84 (December 1999).}, year = {1999}, language = {en} } @article{WustGellermannBeieretal.1998, author = {Wust, Peter and Gellermann, Johanna and Beier, J{\"u}rgen and Wegner, S. and Tilly, Wolfgang and Troger, J. and Stalling, Detlev and Oswald, H. and Hege, Hans-Christian and Deuflhard, Peter and Felix, Roland}, title = {Evaluation of segmentation algorithms for generation of patient models in radiofrequency hyperthermia}, series = {Phys Med Biol}, volume = {43}, journal = {Phys Med Biol}, pages = {3295 -- 3307}, year = {1998}, language = {en} } @article{WustNadobnyFelixetal.1989, author = {Wust, Peter and Nadobny, Johanna and Felix, Roland and Deuflhard, Peter and John, W. and Louis, Alfred}, title = {Numerical approaches to treatment planning in deep RF-hyperthermia}, series = {Strahlenther Onkol}, volume = {165}, journal = {Strahlenther Onkol}, number = {10}, pages = {751 -- 757}, year = {1989}, language = {en} } @article{WustNadobnyFelixetal.1991, author = {Wust, Peter and Nadobny, Johanna and Felix, Roland and Deuflhard, Peter and Louis, Alfred and John, W.}, title = {Strategies for optimized application of annular-phased-array systems in clinical hyperthermia}, series = {Int J Hyperthermia}, volume = {7}, journal = {Int J Hyperthermia}, pages = {157 -- 173}, year = {1991}, language = {en} } @inproceedings{WustNadobnyGellermannetal.1997, author = {Wust, Peter and Nadobny, Johanna and Gellermann, Johanna and Seebass, Martin and Stalling, Detlev and Hege, Hans-Christian and Deuflhard, Peter and Budach, Volker and Felix, Roland}, title = {Patient Models and Algorithms for Hyperthermia Planning}, series = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, booktitle = {Proc. 16th Ann. Meeting Europ. Soc. Hyperthermic Oncology (ESHO-97), Berlin, Germany, April 1997}, pages = {75}, year = {1997}, language = {en} } @article{SchaberOfenlochEhrigetal.2004, author = {Schaber, Karlheinz and Ofenloch, Oliver and Ehrig, Rainald and Deuflhard, Peter}, title = {Aerosolbildung in Gas/Fl{\"u}ssigkeits-Kontaktapparaten - Modellierungsstrategien und Simulation}, series = {Chemie Ingenieur Technik}, volume = {76}, journal = {Chemie Ingenieur Technik}, number = {9}, pages = {1358 -- 1359}, year = {2004}, language = {en} } @article{SreenivasaGellermannNadobnyetal.2003, author = {Sreenivasa, G. and Gellermann, Johanna and Nadobny, Johanna and Schlag, P. and Deuflhard, Peter and Felix, Roland and Wust, Peter}, title = {Clinical Use of the Hyperthermia Treatment Planning System Hyperplan to Predict Effectiveness and Toxicity}, series = {Int. J. Oncology Biol. Phys.}, volume = {55}, journal = {Int. J. Oncology Biol. Phys.}, number = {2}, pages = {407 -- 419}, year = {2003}, language = {en} } @inproceedings{StallingSeebassHegeetal.1996, author = {Stalling, Detlev and Seebass, Martin and Hege, Hans-Christian and Wust, Peter and Deuflhard, Peter and Felix, Roland}, title = {HyperPlan - an integrated system for treatment planning in regional hyperthermia}, series = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, volume = {2}, booktitle = {Proc. of the 7th Int. Congress on Hyperthermic Oncology, Rome, Italy, April 1996}, editor = {Franconi, Cafiero}, pages = {552 -- 554}, year = {1996}, language = {en} } @article{WeberKubeWalteretal.2007, author = {Weber, Marcus and Kube, Susanna and Walter, Lionel and Deuflhard, Peter}, title = {Stable Computation of Probability Densities of Metastable Dynamical Systems}, series = {SIAM J. Multiscale Model. Simul.}, volume = {6}, journal = {SIAM J. Multiscale Model. Simul.}, number = {2}, pages = {396 -- 416}, year = {2007}, language = {en} } @article{WeiserSchielaDeuflhard2005, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, series = {SIAM J. Num. Anal.}, volume = {42}, journal = {SIAM J. Num. Anal.}, number = {5}, pages = {1830 -- 1845}, year = {2005}, language = {en} } @article{WeiserDeuflhardErdmann2007, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, series = {Opt. Meth. Softw.}, volume = {22}, journal = {Opt. Meth. Softw.}, number = {3}, pages = {413 -- 431}, year = {2007}, language = {en} } @article{WixSchaberOfenlochetal.2007, author = {Wix, A. and Schaber, Karlheinz and Ofenloch, O. and Ehrig, Rainald and Deuflhard, Peter}, title = {Simulation of Aerosol Formation in Gas-Liquid Contact Devices}, series = {Chem. Eng. Comm.}, volume = {194}, journal = {Chem. Eng. Comm.}, pages = {565 -- 577}, year = {2007}, language = {en} } @book{DeuflhardRoeblitz, author = {Deuflhard, Peter and R{\"o}blitz, Susanna}, title = {A guide to numerical modelling in systems biology}, volume = {12}, publisher = {Springer}, isbn = {978-3-319-20058-3}, doi = {10.1007/978-3-319-20059-0}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2008, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {Mehr Mathematik wagen in der Medizin}, series = {acatech diskutiert, Produktionsfaktor Mathematik - Wie Mathematik Technik und Wirtschaft bewegt}, booktitle = {acatech diskutiert, Produktionsfaktor Mathematik - Wie Mathematik Technik und Wirtschaft bewegt}, publisher = {Springer}, doi = {10.1007/978-3-540-89435-3}, pages = {435 -- 459}, year = {2008}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2010, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {More Mathematics into Medicine!}, series = {Production Factor Mathematics}, booktitle = {Production Factor Mathematics}, publisher = {Springer}, pages = {357 -- 378}, year = {2010}, language = {en} } @article{ZachowDeuflhard2008, author = {Zachow, Stefan and Deuflhard, Peter}, title = {Computergest{\"u}tzte Planung in der kraniofazialen Chirurgie}, series = {Face 01/08, Int. Mag. of Orofacial Esthetics}, journal = {Face 01/08, Int. Mag. of Orofacial Esthetics}, publisher = {Oemus Journale Leipzig}, pages = {43 -- 49}, year = {2008}, language = {en} } @article{WeiserZachowDeuflhard2010, author = {Weiser, Martin and Zachow, Stefan and Deuflhard, Peter}, title = {Craniofacial Surgery Planning Based on Virtual Patient Models}, series = {it - Information Technology}, volume = {52}, journal = {it - Information Technology}, number = {5}, publisher = {Oldenbourg Verlagsgruppe}, doi = {10.1524/itit.2010.0600}, pages = {258 -- 263}, year = {2010}, language = {en} } @article{ZachowHegeDeuflhard2006, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Computer assisted planning in cranio-maxillofacial surgery}, series = {Journal of Computing and Information Technology}, volume = {14(1)}, journal = {Journal of Computing and Information Technology}, pages = {53 -- 64}, year = {2006}, language = {en} } @article{DeuflhardRoeblitzStoetzel, author = {Deuflhard, Peter and R{\"o}blitz, Susanna and St{\"o}tzel, Claudia}, title = {Mathematical Systems Biology at Zuse Institute Berlin (ZIB)}, series = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, volume = {39}, journal = {BioTOPics - Journal of Biotechnology in Berlin-Brandenburg}, language = {en} } @misc{DeuflhardWeber, author = {Deuflhard, Peter and Weber, Marcus}, title = {Mathematics without pain}, series = {MATHEON-Mathematics for Key Technologies}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {26 -- 28}, language = {en} } @misc{MoualeuNgangueRoeblitzEhrigetal., 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}, 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., 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}, 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{MoualeuNgangueRoeblitzEhrigetal., author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification in a Tuberculosis Model for Cameroon}, series = {PLOS ONE}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0120607}, abstract = {A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as 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 the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.}, language = {en} } @book{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3. Adaptive L{\"o}sung partieller Differentialgleichungen}, edition = {2}, publisher = {de Gruyter}, isbn = {978-3-11-069168-9}, doi = {10.1515/9783110689655}, pages = {456}, language = {de} } @article{Deuflhard, author = {Deuflhard, Peter}, title = {The Grand Four. Affine Invariant Globalizations of Newton's Method}, series = {Vietnam Journal of Mathematics}, volume = {46}, journal = {Vietnam Journal of Mathematics}, number = {4}, doi = {10.1007/s10013-018-0301-3}, pages = {761 -- 777}, language = {en} } @misc{NaegelDeuflhardWittum, 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}, 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} } @misc{FranzoneDeuflhardErdmannetal., 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}, 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} }