@article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebaß, Martin}, title = {A New Nonlinear Elliptic Multilevel FEM Applied to Regional Hyperthermia}, series = {Comput. Visual. Sci.}, volume = {3}, journal = {Comput. Visual. Sci.}, doi = {10.1007/PL00013546}, pages = {1 -- 6}, year = {2000}, language = {en} } @article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebass, Martin}, title = {A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning}, series = {Comput. Vis. Sci.}, volume = {3}, journal = {Comput. Vis. Sci.}, pages = {115 -- 120}, year = {2000}, 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{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{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{WeiserDeuflhard2007, author = {Weiser, Martin and Deuflhard, Peter}, title = {Inexact central path following algorithms for optimal control problems}, series = {SIAM J. Control Opt.}, volume = {46}, journal = {SIAM J. Control Opt.}, number = {3}, pages = {792 -- 815}, year = {2007}, 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} } @article{DeuflhardWeiserZachow2006, author = {Deuflhard, Peter and Weiser, Martin and Zachow, Stefan}, title = {Mathematics in Facial Surgery}, series = {AMS Notices}, volume = {53}, journal = {AMS Notices}, number = {9}, pages = {1012 -- 1016}, year = {2006}, language = {en} } @article{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}, series = {Communications in Nonlinear Science and Numerical Simulation}, volume = {20}, journal = {Communications in Nonlinear Science and Numerical Simulation}, number = {3}, doi = {10.1016/j.cnsns.2014.06.037}, pages = {986 -- 1003}, 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} }