@misc{BaumannDudaSchielaetal.2026, author = {Baumann, Felix and Duda, Georg and Schiela, Anton and Weiser, Martin}, title = {Identification of Stress in Heterogeneous Contact Models}, volume = {173}, journal = {Non-Smooth and Complementarity-Based Distributed Parameter Systems}, editor = {Hinterm{\"u}ller, Michael and Herzog, Roland and Kanzow, Christian and Ulbrich, Michael and Ulbrich, Stefan}, publisher = {Springer Nature}, year = {2026}, abstract = {We develop a heterogeneous model of the lower limb system to simulate muscle forces and stresses acting on the knee joint. The modelling of the bone dynamics leads to an index-3 DAE, which we discretize by higher order collocation methods. Furthermore, we present an elastomechanical contact knee joint model of the articular cartilage. For the solution of the contact problem we develop an efficient multigrid solver, based on an Augmented-Lagrangian relaxation of the contact constraints. We formulate the identification of joint forces and resulting stresses with respect to different knee joint models as an inverse problem based on medical gait data.}, language = {en} } @misc{MusialSekSchneideretal.2024, author = {Musial, Anna and Sek, Grzegorz and Schneider, Philipp-Immanuel and Reitzenstein, Stephan}, title = {Fiber-coupled solid-state-based single-photon sources}, journal = {Specialty Optical Fibers}, publisher = {Woodhead Publishing}, doi = {10.1016/B978-0-443-18495-6.00004-4}, pages = {345 -- 384}, year = {2024}, language = {de} } @misc{MollenhauerSchusterKlusetal.2020, author = {Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Sch{\"u}tte, Christof}, title = {Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces}, volume = {304}, journal = {Advances om Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, K.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_5}, pages = {109 -- 131}, year = {2020}, language = {en} } @misc{BittracherSchuette2020, author = {Bittracher, Andreas and Sch{\"u}tte, Christof}, title = {A weak characterization of slow variables in stochastic dynamical systems}, volume = {304}, journal = {Advances in Dynamics, Optimization and Computation. Series: Studies in Systems, Decision and Control. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday}, editor = {Junge, Oliver and Sch{\"u}tze, O. and Froyland, Gary and Ober-Blobaum, S. and Padberg-Gehle, E.}, publisher = {Springer International}, isbn = {978-3-030-51264-4}, doi = {10.1007/978-3-030-51264-4_6}, pages = {132 -- 150}, year = {2020}, language = {en} } @misc{OatesCockaynePrangleetal.2020, author = {Oates, Chris and Cockayne, Jon and Prangle, Dennis and Sullivan, T. J. and Girolami, Mark}, title = {Optimality criteria for probabilistic numerical methods}, volume = {27}, journal = {Multivariate Algorithms and Information-Based Complexity}, editor = {Hickernell, F. J. and Kritzer, P.}, publisher = {De Gruyter}, arxiv = {http://arxiv.org/abs/1901.04326}, doi = {10.1515/9783110635461-005}, pages = {65 -- 88}, year = {2020}, abstract = {It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.}, language = {en} } @misc{CiccottiFerrarioSchuette2018, author = {Ciccotti, Giovanni and Ferrario, Mauro and Sch{\"u}tte, Christof}, title = {Molecular Dynamics vs. Stochastic Processes: Are We Heading Anywhere?}, volume = {20}, journal = {Special Issue: Understanding Molecular Dynamics via Stochastic Processes, Entropy}, number = {5}, doi = {10.3390/e20050348}, year = {2018}, language = {en} } @misc{GoetschelMinion2018, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST}, journal = {Domain Decomposition Methods in Science and Engineering XXIV}, publisher = {Springer}, address = {Cham}, doi = {10.1007/978-3-319-93873-8_34}, pages = {363 -- 371}, year = {2018}, abstract = {In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.}, language = {en} } @misc{DeuflhardHege2015, author = {Deuflhard, Peter and Hege, Hans-Christian}, title = {Raumtiefe in Malerei und Computergrafik}, 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}, year = {2015}, 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} } @misc{SarichSchuette2014, author = {Sarich, Marco and Sch{\"u}tte, Christof}, title = {Markov Model Theory}, volume = {797}, journal = {An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation}, editor = {Bowman, Gregory R. and Pande, Vijay S. and No{\´e}, Frank}, publisher = {Springer}, doi = {10.1007/978-94-007-7606-7}, pages = {23 -- 44}, year = {2014}, abstract = {This section reviews the relation between the continuous dynamics of a molecular system in thermal equilibrium and the kinetics given by a Markov State Model (MSM). We will introduce the dynamical propagator, an error-less, alternative description of the continuous dynamics, and show how MSMs result from its discretization. This allows for an precise understanding of the approximation quality of MSMs in comparison to the continuous dynamics. The results on the approximation quality are key for the design of good MSMs. While this section is important for understanding the theory of discretization and related systematic errors, practitioners wishing only to learn how to construct MSMs may skip directly to the discussion of Markov model estimation.}, language = {en} } @misc{DeuflhardWeber2014, author = {Deuflhard, Peter and Weber, Marcus}, title = {Mathematics without pain}, 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}, year = {2014}, language = {en} } @misc{DeuflhardKornhuberSanderetal.2014, author = {Deuflhard, Peter and Kornhuber, Ralf and Sander, Oliver and Schiela, Anton and Weiser, Martin}, title = {Mathematics cures virtual patients}, 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 Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {7 -- 25}, year = {2014}, language = {en} } @misc{BockmayrSiebertRoeblitzetal.2014, author = {Bockmayr, Alexander and Siebert, Heike and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof and Deuflhard, Peter}, title = {Advanced mathematical modeling in systems biology}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutela, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {29 -- 44}, year = {2014}, language = {en} } @misc{SchuetteConrad2014, author = {Sch{\"u}tte, Christof and Conrad, Tim}, title = {Showcase 3: Information-based medicine}, 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}, pages = {66 -- 67}, year = {2014}, language = {en} } @misc{AmiranashviliBandelowBlomeetal.2014, author = {Amiranashvili, Shalva and Bandelow, Uwe and Blome, Mark and Burger, Sven and Schmidt, Frank and Schmidt, Kersten and Zschiedrich, Lin}, title = {Nanophotonics and nonlinear fiber optics}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and et al.,}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {257 -- 275}, year = {2014}, language = {en} } @misc{LockauHammerschmidtBlomeetal.2014, author = {Lockau, Daniel and Hammerschmidt, Martin and Blome, Mark and Schmidt, Frank}, title = {Optics of thin film solar cells}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and et al.,}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {278 -- 279}, year = {2014}, language = {en} } @misc{DeuflhardSchuette2014, author = {Deuflhard, Peter and Sch{\"u}tte, Christof}, title = {Life Sciences}, 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 Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {1 -- 5}, year = {2014}, language = {en} } @misc{SchuetteDeuflhardNoeetal.2014, author = {Sch{\"u}tte, Christof and Deuflhard, Peter and No{\´e}, Frank and Weber, Marcus}, title = {Design of functional molecules}, 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 Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {49 -- 65}, year = {2014}, language = {en} } @misc{NadobnyWeihrauchWeiseretal.2007, author = {Nadobny, Johanna and Weihrauch, Mirko and Weiser, Martin and Gellermann, Johanna and Wlodarczyk, Waldemar and Budach, Volker and Wust, Peter}, title = {Advances in the Planning and Control of the MR-guided Regional Hyperthermia Applications}, journal = {Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy}, pages = {1010 -- 1013}, year = {2007}, language = {en} } @misc{WustWeihrauchWeiseretal.2010, author = {Wust, Peter and Weihrauch, Mirko and Weiser, Martin and Gellermann, Johanna and Eisenhardt, Steffen and Chobrok, Thorsten and Budach, Volker}, title = {Optimization of clinical radiofrequency hyperthermia by use of MR-thermography in a hybrid system}, journal = {World Congress on Medical Physics and Biomedical Engineering, September 2009, Munich, Germany}, editor = {D{\"o}ssel, O. and Schlegel, W. and Magjarevic, R.}, publisher = {Springer}, pages = {174 -- 175}, year = {2010}, language = {en} } @misc{WeiserErdmannDeuflhard2010, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, 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}, year = {2010}, 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} } @misc{Weiser2010, author = {Weiser, Martin}, title = {Delayed Residual Compensation for Bidomain Equations}, volume = {1281}, journal = {AIP Conference Proceedings}, doi = {10.1063/1.3498495}, pages = {419 -- 422}, year = {2010}, abstract = {The biodomain model of cardioelectric excitation consists of a reaction-diffusion equation, an elliptic algebraic constraint, and a set of pointwise ODEs. Fast reaction enforces small time steps, such that for common mesh sizes the reaction-diffusion equation is easily solved implicitly due to a dominating mass matrix. In contrast, the elliptic constraint does not benefit from small time steps and requires a comparably expensive solution. We propose a delayed residual compensation that improves the solution of the elliptic constraint and thus alleviates the need for long iteration times.}, language = {en} } @misc{GoetschelWeiserMaierhoferetal.2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, journal = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, editor = {Cardone, Gennaro}, year = {2012}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @misc{SchielaWeiser2010, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, journal = {Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009)}, editor = {Diehl, M. and Glineur, F. and Jarlebring, E. and Michiels, W.}, publisher = {Springer}, pages = {419 -- 428}, year = {2010}, abstract = {We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.}, language = {en} } @misc{GuentherLameckerWeiser2011, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, journal = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, editor = {Pennec, X. and Joshi, S. and Nielsen, M.}, pages = {1 -- 14}, year = {2011}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @misc{GoetschelWeiserSchiela2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, journal = {Advances in DUNE}, editor = {Dedner, A. and Flemisch, B. and Kl{\"o}fkorn, R.}, publisher = {Springer}, pages = {101 -- 112}, year = {2012}, abstract = {This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.}, language = {en} } @misc{Deuflhard1998, author = {Deuflhard, Peter}, title = {Fast algorithms, fast computers: The Konrad-Zuse-Zentrum Berlin (ZIB)}, journal = {Mathematics in Berlin}, editor = {et al. Begehr, H.}, publisher = {Basel: Birkh{\"a}user}, pages = {183 -- 184}, year = {1998}, language = {en} }