@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} }