@misc{Weiser2009, author = {Weiser, Martin}, title = {On goal-oriented adaptivity for elliptic optimal control problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11192}, number = {09-08}, year = {2009}, abstract = {The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of interest. Finally, the efficiency of the error estimator and generated meshes are demonstrated on numerical examples.}, language = {en} } @misc{SchielaWeiser2009, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11567}, number = {09-36}, year = {2009}, 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{Weiser2008, author = {Weiser, Martin}, title = {Optimization and Identification in Regional Hyperthermia}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10916}, number = {08-40}, year = {2008}, abstract = {Regional hyperthermia is a cancer therapy aiming at heating tumors using phased array applicators. This article provides an overview over current mathematical challenges of delivering individually optimal treatments. The focus is on therapy planning and identification of technical as well as physiological quantities from MR thermometry measurements.}, language = {en} } @misc{WeiserRoelligArndtetal.2008, author = {Weiser, Martin and R{\"o}llig, Mathias and Arndt, Ralf and Erdmann, Bodo}, title = {Development and test of a numerical model for pulse thermography in civil engineering}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10980}, number = {08-45}, year = {2008}, abstract = {Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.}, language = {en} } @misc{PruefertSchiela2008, author = {Pr{\"u}fert, Uwe and Schiela, Anton}, title = {The minimization of an L^{\infty}-functional subject to an elliptic PDE and state constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10714}, number = {08-17}, year = {2008}, abstract = {We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.}, language = {en} } @misc{KlapprothDeuflhardSchiela2008, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10793}, number = {08-27}, year = {2008}, abstract = {This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.}, language = {en} } @misc{GoetschelWeiserSchiela2010, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11909}, number = {10-25}, year = {2010}, 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{WeiserGoetschel2010, author = {Weiser, Martin and G{\"o}tschel, Sebastian}, title = {State Trajectory Compression for Optimal Control with Parabolic PDEs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11676}, number = {10-05}, year = {2010}, abstract = {In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.}, 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}, doi = {10.1007/s11263-012-0599-3}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13090}, number = {11-22}, 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{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{LubkollSchielaWeiser2012, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An optimal control problem in polyconvex hyperelasticity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14745}, number = {12-08}, year = {2012}, abstract = {We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented.}, 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{PruefertTroeltzschWeiser2004, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8223}, number = {04-47}, year = {2004}, abstract = {The paper addresses primal interior point method for state constrained PDE optimal control problems. By a Lavrentiev regularization, the state constraint is transformed to a mixed control-state constraint with bounded Lagrange multiplier. Existence and convergence of the central path are established, and linear convergence of a short-step pathfollowing method is shown. The behaviour of the regularizations are demonstrated by numerical examples.}, 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{WeiserGaenzlerSchiela2004, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A Control Reduced Primal Interior Point Method for PDE Constrained Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8138}, number = {04-38}, year = {2004}, abstract = {A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the innermost loop when solving linear equations. The a priori elimination of the least regular control permits to obtain the required accuracy with comparable coarse meshes. Convergence of the method and discretization errors are studied, and the method is illustrated at two numerical examples.}, language = {en} } @misc{Schiela2007, author = {Schiela, Anton}, title = {Barrier Methods for Optimal Control Problems with State Constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9504}, number = {07-07}, year = {2007}, abstract = {We study barrier methods for state constrained optimal control problems with PDEs. In the focus of our analysis is the path of minimizers of the barrier subproblems with the aim to provide a solid theoretical basis for function space oriented path-following algorithms. We establish results on existence, continuity and convergence of this path. Moreover, we consider the structure of barrier subdifferentials, which play the role of dual variables.}, language = {en} } @misc{GoetschelNagaiahKunischetal.2013, author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18566}, year = {2013}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @misc{GoetschelWeiser2013, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy Compression for PDE-constrained Optimization: Adaptive Error Control}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18575}, year = {2013}, abstract = {For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.}, language = {en} } @misc{Weiser2013, author = {Weiser, Martin}, title = {Faster SDC convergence on non-equidistant grids by DIRK sweeps}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18662}, year = {2013}, abstract = {Spectral deferred correction methods for solving stiff ODEs are known to converge rapidly towards the collocation limit solution on equidistant grids, but show a much less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples.}, 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} } @misc{Lehmann2013, author = {Lehmann, Felix}, title = {Inexaktheit in Newton-Lagrange-Verfahren f{\"u}r Optimierungsprobleme mit Elliptischen PDGL-Nebenbedingungen}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41972}, year = {2013}, abstract = {Bei der numerischen L{\"o}sung von Optimalsteuerungsproblemen mit elliptischen partiellen Differentialgleichungen als Nebenbedingung treten unvermeidlich Diskretisierungs- und Iterationsfehler auf. Man ist aus Aufwandsgr{\"u}nden daran interessiert die dabei entstehenden Fehler nicht sehr klein w{\"a}hlen zu m{\"u}ssen. In der Folge werden die linearisierten Nebenbedingungen in einem Composite-Step-Verfahren nicht exakt erf{\"u}llt. In dieser Arbeit wird der Einfluss dieser Ungenauigkeit auf das Konvergenzverhalten von Newton-Lagrange-Verfahren untersucht. Dabei sollen mehrere einschl{\"a}gige lokale Konvergenzresultate diskutiert werden. Anschließend wird ein konkretes Composite-Step-Verfahren formuliert, in dem die Genauigkeit der inneren Iterationsverfahren adaptiv gesteuert werden kann. Am Ende der Arbeit wird an zwei Musterproblemen die hohe {\"U}bereinstimmung der analytischen Voraussagen und der tats{\"a}chlichen Performanz der dargestellten Methoden demonstriert.}, language = {de} } @misc{GoetschelMinion2019, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71490}, year = {2019}, abstract = {To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE constrained optimization. In order to develop an efficient fully time-parallel algorithm we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a non-linear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.}, language = {en} } @misc{GoetschelvonTycowiczPolthieretal.2013, author = {G{\"o}tschel, Sebastian and von Tycowicz, Christoph and Polthier, Konrad and Weiser, Martin}, title = {Reducing Memory Requirements in Scientific Computing and Optimal Control}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42695}, year = {2013}, abstract = {In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data.}, language = {en} } @article{PowellWeiser2000, author = {Powell, Gary and Weiser, Martin}, title = {Views, A new form of container adaptors}, volume = {18}, journal = {C/C++ Users Journal}, number = {4}, pages = {40 -- 51}, year = {2000}, abstract = {The C++ standard template library has many useful containers for data. The standard library includes two adpators, queue, and stack. The authors have extended this model along the lines of relational database semantics. Sometimes the analogy is striking, and we will point it out occasionally. An adaptor allows the standard algorithms to be used on a subset or modification of the data without having to copy the data elements into a new container. The authors provide many useful adaptors which can be used together to produce interesting views of data in a container.}, language = {en} } @misc{Sali2016, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60508}, year = {2016}, abstract = {The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model.}, language = {en} } @misc{Sali2016, type = {Master Thesis}, author = {Sali, Adrian}, title = {Coupling of Monodomain and Eikonal Models for Cardiac Electrophysiology}, pages = {63}, year = {2016}, abstract = {The primary goal of this paper is to study the coupling of monodomain and eikonal models for the numerical simulation of cardiac electrophysiology. Eikonal models are nonlinear elliptic equations describing the excitation time of the cardiac tissue. They are often used as very fast approximations for monodomain or bidomain models - parabolic reaction-diffusion systems describing the excitation wavefront in terms of ionic currents. The excitation front is a thin region with high gradients, whereas excitation times vary over larger domains. Hence, eikonal equations can be solved on much coarser grids than monodomain equations. Moreover, as eikonal models are not time-dependent, no time integration is needed. Eikonal models are derived from monodomain models making additional assumptions and using certain approximations. While generally the approximation is rather good, several specific situations are not well captured by eikonal models. We consider coupling the two models, i.e. using the monodomain model in regions where more accurate results or the shape of the wavefront are needed, and the eikonal model in the remaining parts of the domain, where the excitation time is sufficient. Restricting the monodomain simulation to a small subdomain reduces the computational effort considerably. Numerical methods for the simulation of the individual models are presented, with the finite element method as the main ingredient. Coupling conditions as well as algorithms for implementing the coupling are explained. The approximation quality and efficiency of the coupled model is illustrated on simple geometries using an Aliev-Panfilov membrane model.}, language = {en} } @article{WeiserGhosh2018, author = {Weiser, Martin and Ghosh, Sunayana}, title = {Theoretically optimal inexact SDC methods}, journal = {Communications in Applied Mathematics and Computational Science}, number = {13-1}, doi = {10.2140/camcos.2018.13.53}, pages = {53 -- 86}, year = {2018}, abstract = {In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples.}, 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}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15243}, 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} } @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} } @article{HellerDudaEhrigetal.2005, author = {Heller, Markus O. and Duda, Georg and Ehrig, Rainald and Schell, H. and Seebeck, P. and Taylor, William R.}, title = {Muskuloskeletale Belastungen im Schafshinterlauf}, journal = {Materialwissenschaft und Werkstofftechnik}, number = {36}, pages = {775 -- 780}, year = {2005}, language = {en} } @inproceedings{HellerDudaKoenigetal.2005, author = {Heller, Markus O. and Duda, G. and K{\"o}nig, Christian and Taylor, William R. and Ehrig, Rainald and Hinterwimmer, S. and Graichen, H.}, title = {Validation of a New Model of Human Knee Kinematics against in Vivo Data under Physiologic Neuromuscular Activation Patterns}, booktitle = {Proceedings of the 51th Annual Meeting of the Orthopedic Society}, address = {Washington}, year = {2005}, language = {en} } @article{HellmichKoberErdmann2008, author = {Hellmich, Christian and Kober, Cornelia and Erdmann, Bodo}, title = {Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible}, volume = {36}, journal = {Annals of Biomedical Engineering}, number = {1}, doi = {10.1007/s10439-007-9393-8}, pages = {108 -- 122}, year = {2008}, language = {en} } @article{HellerKratzensteinEhrigetal.2011, author = {Heller, Markus O. and Kratzenstein, Stefan and Ehrig, Rainald and Wassilew, Georgi and Duda, Georg and Taylor, William R.}, title = {The weighted optimal common shape technique improves identification of the hip joint centre of rotation in vivo}, volume = {29}, journal = {Journal of Orthopedic Research}, pages = {1470 -- 5}, year = {2011}, language = {en} } @article{GellermannWeihrauchChoetal.2006, author = {Gellermann, Johanna and Weihrauch, Mirko and Cho, C. and Wlodarczyk, Waldemar and F{\"a}hling, Horst and Felix, Roland and Budach, Volker and Weiser, Martin and Nadobny, Johanna and Wust, Peter}, title = {Comparison of MR-thermography and planning calculations in phantoms}, volume = {33}, journal = {Medical Physics}, pages = {3912 -- 3920}, year = {2006}, language = {en} } @article{HellerKoenigGraichenetal.2007, author = {Heller, Markus O. and K{\"o}nig, Christian and Graichen, F. and Hinterwimmer, S. and Ehrig, Rainald and Duda, G. and Taylor, William R.}, title = {A new model to predict in vivo human knee kinematics under physiological-like muscle activation}, journal = {Journal of Biomechanics}, pages = {45 -- 53}, year = {2007}, language = {en} } @techreport{GladilinPeckarRohretal.1999, author = {Gladilin, Evgeny and Peckar, W. and Rohr, K. and Stiehl, H.}, title = {A Comparsion Between BEM and FEM for Elastic Registration of Medical Images}, number = {FBI-HH-M-287/99}, publisher = {FB Informatik}, address = {Hamburg, Germany}, year = {1999}, language = {en} } @article{GaenzlerVolkweinWeiser2006, author = {G{\"a}nzler, Tobias and Volkwein, S. and Weiser, Martin}, title = {SQP methods for parameter identification problems arising in hyperthermia}, volume = {21}, journal = {Optim. Methods Softw.}, number = {6}, pages = {869 -- 887}, year = {2006}, language = {en} } @article{EhrigHellerKratzensteinetal.2011, author = {Ehrig, Rainald and Heller, Markus O. and Kratzenstein, Stefan and Duda, Georg and Trepczynski, Adam and Taylor, William R.}, title = {The SCoRE residual: A quality index to assess the accuracy of joint estimations}, volume = {44}, journal = {Journal of Biomechanics}, number = {7}, doi = {10.1016/j.jbiomech.2010.12.009}, pages = {1400 -- 1404}, year = {2011}, language = {en} } @inproceedings{ErdmannKoberLangetal.2002, author = {Erdmann, Bodo and Kober, C. and Lang, Jens and Deuflhard, Peter and Zeilhofer, J. and Sader, Robert}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, booktitle = {proceedings of 9th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2002}, language = {en} } @article{ErdmannLjubijankicNytschGeusen2007, author = {Erdmann, Bodo and Ljubijankic, M. and Nytsch-Geusen, C.}, title = {Entwicklung einer Toolbox zur zwei- und dreidimensionalen instation{\"a}ren thermischen Bauteilsimulation mit KARDOS}, volume = {29}, journal = {Bauphsik}, number = {1}, pages = {33 -- 39}, year = {2007}, language = {en} } @inproceedings{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments}, booktitle = {CHT'97}, editor = {de Vahl Davis, G. and Leonardi, E.}, address = {Cesme, Turkey}, pages = {103 -- 110}, year = {1997}, language = {en} } @inproceedings{ErdmannLangSeebass1998, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Optimization of Temperature Distributions for Regional Hyperthermia based on a Nonlinear Heat Transfer Model}, volume = {858}, booktitle = {Biotransport}, editor = {Diller, K.}, pages = {36 -- 46}, year = {1998}, language = {en} } @article{ErdmannLangSeebass1999, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {The Impact of a Nonlinear Heat Transfer Model for Temperature Control in Regional Hyperthermia}, volume = {49}, journal = {IEEE Transactions on Biomedical Engineering}, number = {9}, pages = {1129 -- 1138}, year = {1999}, language = {en} } @article{EhrigTaylorDudaetal.2006, author = {Ehrig, Rainald and Taylor, William R. and Duda, G. and Heller, Markus O.}, title = {A Survey for Formal Methods for Determining the Centre of Ball Joints}, journal = {Journal of Biomechanics}, number = {39}, pages = {2798 -- 2809}, year = {2006}, language = {en} } @inproceedings{EhrigTaylorDudaetal.2006, author = {Ehrig, Rainald and Taylor, William R. and Duda, G. and Heller, Markus O.}, title = {A New Approach for the Determination of Joint Axes}, booktitle = {Proceedings of the 52th Annual Meeting of the Orthopedic Society}, address = {Chicago}, year = {2006}, language = {en} } @article{EhrigTaylorDudaetal.2007, author = {Ehrig, Rainald and Taylor, William R. and Duda, Georg and Heller, Markus O.}, title = {A Survey for Formal Methods for Determining Functional Joint Axes}, journal = {Journal of Biomechanics}, pages = {2150 -- 2157}, year = {2007}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {A nonlinear soft tissue model for craniofacial surgery simulations}, booktitle = {Proc. of Modeling and Simulation for Computer-aided Medicine and Surgery (MS4CMS}, publisher = {INRIA}, address = {Paris, France}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Biomechanical modeling of individual facial emotion expressions}, booktitle = {Proc. of Visualization, Imaging, and Image Processing (VIIP)}, address = {Malaga, Spain}, pages = {7 -- 11}, year = {2002}, language = {en} } @inproceedings{GladilinZachowDeuflhardetal.2002, author = {Gladilin, Evgeny and Zachow, Stefan and Deuflhard, Peter and Hege, Hans-Christian}, title = {Biomechanisches Modell zur Absch{\"a}tzung der individuellen Gesichtsmimik}, booktitle = {Proc.of Workshop Bildverarbeitung f{\"u}r die Medizin (BVM)}, editor = {Meiler, M. and Saupe, D. and Krugel, F. and Handels, H. and Lehmann, T.}, address = {Leipzig, Germany}, pages = {25 -- 28}, year = {2002}, language = {en} } @phdthesis{Gladilin2003, author = {Gladilin, Evgeny}, title = {Biomechanical Modeling of Soft Tissue and Facial Expressions for Craniofacial Surgery Planning}, address = {Germany}, year = {2003}, language = {en} } @inproceedings{Gladilin2004, author = {Gladilin, Evgeny}, title = {A contour based approach for invariant shape description}, volume = {5370}, booktitle = {SPIE Medical Imaging Conference}, address = {San Diego, USA}, pages = {1282 -- 1291}, year = {2004}, language = {en} } @incollection{LangErdmannKoberetal.2003, author = {Lang, Jens and Erdmann, Bodo and Kober, Cornelia and Deuflhard, Peter and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Effiziente und zuverl{\"a}ssige Finite-Elemente-Methoden zur Simulation des menschlichen Unterkiefers}, volume = {1}, booktitle = {Berichte des IZWR - Interdisziplin{\"a}res Zentrum f{\"u}r Wissenschaftliches Rechnen}, editor = {Alt, Walter and Hermann, Martin}, publisher = {Universit{\"a}t Jena}, address = {Germany}, pages = {49 -- 57}, year = {2003}, language = {en} } @inproceedings{KornaropoulosTaylorDudaetal.2009, author = {Kornaropoulos, Evgenios I. and Taylor, William R. and Duda, Georg and Ehrig, Rainald and Matziolis, Georg and M{\"u}ller, Michael and Wassilew, Georgi and Asbach, Patrick and Perka, Carsten and Heller, Markus O.}, title = {An imageless method to quantify the mechanical femoral-tibial angle based on the functional determination of joint centers and axes}, booktitle = {Annual meeting of the ESMAC 2009}, address = {London}, year = {2009}, language = {en} } @article{KornaropoulosTaylorDudaetal.2010, author = {Kornaropoulos, Evgenios I. and Taylor, William R. and Duda, Georg and Ehrig, Rainald and Matziolis, Georg and M{\"u}ller, Michael and Wassilew, Georgi and Asbach, Patrick and Perka, Carsten and Heller, Markus O.}, title = {Frontal plane alignment: An imageless method to predict the mechanical femoral-tibial angle (mFTA) based on functional determination of joint centres and axes}, volume = {31}, journal = {Gait \& Posture}, number = {2}, doi = {10.1016/j.gaitpost.2009.10.006}, pages = {204 -- 208}, year = {2010}, language = {en} } @inproceedings{KratzensteinTaylorEhrigetal.2009, author = {Kratzenstein, Stefan and Taylor, William R. and Ehrig, Rainald and Heller, Markus O.}, title = {Reduction of the influence of skin marker artefacts using the optimal common shape technique}, booktitle = {Annual meeting of the ESMAC 2009}, address = {London}, year = {2009}, language = {en} } @inproceedings{KassiTaylorSchwarzkopfetal.2004, author = {Kassi, J.-P. and Taylor, William R. and Schwarzkopf, J. and Schell, H. and Duda, G. and Ehrig, Rainald}, title = {Wie sind Osteosynthesesysteme und Defektzonen in vivo belastet?}, booktitle = {68. Jahrestagung der Deutschen Gesellschaft f{\"u}r Unfallchirurgie in Verbindung mit dem Deutschen Orthop{\"a}denkongress}, address = {Berlin}, year = {2004}, language = {en} } @inproceedings{KratzensteinEhrigHelleretal.2010, author = {Kratzenstein, Stefan and Ehrig, Rainald and Heller, Markus O. and Duda, Georg and Taylor, William R.}, title = {A Quantification of Accuracy in Estimating Joint Centers}, booktitle = {17th Congress of the European Society of Biomechanics}, address = {Edinburgh}, year = {2010}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Geiger, M. and Sader, Robert and Zeilhofer, Hans-Florian}, title = {How does the periodontal ligament influence overall stress/strain profiles of a partially edentulous mandible?}, booktitle = {Proc. of 8th Int. Conference on Biological Mechanisms of Tooth Eruption, Resorption and Movement, Phuket, Thailand}, editor = {Davidovitch, Z. and Mah, J. and Suthanarak, S.}, address = {Harvard Society of the Advancement of Orthodontics, Boston, Massachusetts, USA}, year = {2005}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2004, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Anisotropic Simulation of the Human Mandible}, booktitle = {Proc. of 17th ASCE Engineering Mechanics Conference}, publisher = {Univ. of Delaware}, year = {2004}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Consideration of Bone Inhomogeneity and Anisotropy in Deformation Analysis of a Human Mandible}, volume = {1}, booktitle = {Proc. of BMT2005, 39th Annual Congress of the German Society of Biomedical Engineering, Nuremberg, Germany}, editor = {Boenick, U. and Bolz, A.}, publisher = {VDE}, address = {Nuremberg, Germany}, pages = {814 -- 815}, year = {2005}, language = {en} } @inproceedings{KoberErdmannHellmichetal.2005, author = {Kober, C. and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {The Influence of the Periodontal Ligament on Overall Stress/Strain Profiles of a Human Mandible}, booktitle = {Proc. of 23rd CADFEM Users' Meeting, Int. Congress on FEM Technology, Biomechanics}, editor = {CADFEM GmbH, Grafing}, address = {Bonn, Germany}, pages = {1 -- 10}, year = {2005}, language = {en} } @inproceedings{KoberErdmannLangetal.2004, author = {Kober, C. and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Sensitivity of the Temporomandibular Joint Capsule for the Structural Behaviour of the Human Mandible}, volume = {49-2}, booktitle = {Proc. BMT 2004}, address = {Ilmenau, Deutschland}, pages = {372 -- 373}, year = {2004}, language = {en} } @article{KlapprothDeuflhardSchiela2009, author = {Klapproth, Corinna and Deuflhard, Peter and Schiela, Anton}, title = {A Perturbation Result for Dynamical Contact Problems}, volume = {2}, journal = {Numer. Math}, pages = {237 -- 257}, year = {2009}, language = {en} } @phdthesis{Klapproth2012, author = {Klapproth, Corinna}, title = {Adaptive numerical integration for dynamical contact problems}, year = {2012}, language = {en} } @inproceedings{KoberSaderZeilhoferetal.2003, author = {Kober, C. and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {An Individual Anisotropic and Inhomogeneous Material Description of the Human Mandible}, booktitle = {Mathematical Modelling and Computing in Biology and Medicine}, editor = {Capasso, Vincenzo}, publisher = {ESTMB}, pages = {103 -- 109}, year = {2003}, language = {en} } @article{DeuflhardErdmannRoitzschetal.2009, author = {Deuflhard, Peter and Erdmann, Bodo and Roitzsch, Rainer and Lines, Glenn Terje}, title = {Adaptive Finite Element Simulation of Ventricular Dynamics}, volume = {12}, journal = {J. Computing and Visualization in Science}, pages = {201 -- 205}, year = {2009}, language = {en} } @inproceedings{KoberErdmannLangetal.2004, author = {Kober, C. and Erdmann, Bodo and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Adaptive Finite Element Simulation of the Human Mandible Using a New Physiological Model of the Masticatory Muscles}, volume = {4}, booktitle = {Proc. of 75th Annual Meeting of the GAMM}, number = {1}, pages = {332 -- 333}, year = {2004}, language = {en} } @inproceedings{KoberErdmannSaderetal.2003, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Simulation of the Human Mandible}, booktitle = {Proceedings of 10th Workshop on The Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields}, address = {Ulm, Germany}, year = {2003}, language = {en} } @article{KoberErdmannSaderetal.2003, author = {Kober, C. and Erdmann, Bodo and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Belastungssimulation beim menschlichen Biss im Vergleich mit der Dichtestruktur im Unterkieferknochen}, volume = {48}, journal = {Biomedizinische Technik}, number = {Erg{\"a}nzungsband 1}, pages = {268 -- 269}, year = {2003}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2009, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Schr{\"o}der, J{\"o}rg H. and Taylor, William R.}, title = {Die Bestimmung der Genauigkeit nicht-invasiver Techniken zur Ermittlung der H{\"u}ftgelenksposition in-vivo}, booktitle = {6th annual meeting of the German Society for Biomechanics (DGfB)}, address = {M{\"u}nster}, year = {2009}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2009, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Schr{\"o}der, J{\"o}rg H. and Taylor, William R.}, title = {Der Vergleich von nicht-invasiven Techniken zur Bestimmung der H{\"u}ftgelenksposition}, booktitle = {Annual meeting of the German Society of Orthopaedics and Trauma Surgery}, address = {Berlin}, year = {2009}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2010, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Taylor, William R.}, title = {The Residual: A Reliable Measure of Accuracy in the Determination of Joint Centers}, booktitle = {Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society}, address = {New Orleans}, year = {2010}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2010, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Duda, Georg and Taylor, William R.}, title = {The Hip Joint Centre can be determined to within 3 mm}, booktitle = {17th Congress of the European Society of Biomechanics}, address = {Edinburgh}, year = {2010}, language = {en} } @inproceedings{KratzensteinHellerEhrigetal.2010, author = {Kratzenstein, Stefan and Heller, Markus O. and Ehrig, Rainald and Wassilew, Georgi and Duda, Georg and Taylor, William R.}, title = {A new approach for optimally reducing skin marker artifact allows determination of the hip joint center within 3mm}, booktitle = {Transactions Vol. 35, 2010 Annual Meeting of the Orthopedic Society}, address = {New Orleans}, year = {2010}, language = {en} } @article{SchielaGuenther2011, author = {Schiela, Anton and G{\"u}nther, Andreas}, title = {An Interior Point Algorithm with Inexact Step Computation in Function Space for State Constrained Optimal Control}, volume = {119}, journal = {Numer. Math.}, number = {2}, publisher = {Springer Berlin / Heidelberg}, doi = {10.1007/s00211-011-0381-4}, pages = {373 -- 407}, year = {2011}, language = {en} } @article{SchielaWeiser2008, author = {Schiela, Anton and Weiser, Martin}, title = {Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization}, volume = {39}, journal = {Computational Optimization and Applications}, number = {3}, pages = {369 -- 393}, year = {2008}, 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}, volume = {55}, journal = {Int. J. Oncology Biol. Phys.}, number = {2}, pages = {407 -- 419}, year = {2003}, language = {en} } @inproceedings{TaylorEhrigDudaetal.2006, author = {Taylor, William R. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {The determination of joint axes}, booktitle = {5. World Congress of Biomechanics, Munich, Journal of Biomechanics}, number = {39, Suppl. 1}, pages = {S571 -- S572}, year = {2006}, language = {en} } @incollection{ZachowWeiserHegeetal.2005, author = {Zachow, Stefan and Weiser, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {Soft Tissue Prediction in Computer Assisted Maxillofacial Surgery Planning}, booktitle = {Biomechanics Applied to Computer Assisted Surgery}, editor = {Payan, Y.}, publisher = {Research Signpost}, pages = {277 -- 298}, year = {2005}, language = {en} } @incollection{ZachowWeiserDeuflhard2008, author = {Zachow, Stefan and Weiser, Martin and Deuflhard, Peter}, title = {Modellgest{\"u}tzte Operationsplanung in der Kopfchirurgie}, booktitle = {Modellgest{\"u}tzte Therapie}, editor = {Niederlag, Wolfgang and Lemke, Heinz and Meixensberger, J{\"u}rgen and Baumann, Michael}, publisher = {Health Academy}, pages = {140 -- 156}, year = {2008}, language = {en} } @article{HinzeSchiela2011, author = {Hinze, Michael and Schiela, Anton}, title = {Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: optimal error estimates and parameter adjustment}, volume = {48}, journal = {Comp. Opt. and Appl.}, number = {3}, publisher = {Springer}, doi = {10.1007/s10589-009-9278-x}, pages = {581 -- 600}, year = {2011}, language = {en} } @article{Weiser2009, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion Equations}, volume = {59}, journal = {Appl. Num. Math.}, number = {8}, pages = {1858 -- 1869}, year = {2009}, language = {en} } @article{WeihrauchWustWeiseretal.2007, author = {Weihrauch, Mirko and Wust, Peter and Weiser, Martin and Nadobny, Johanna and Eisenhardt, Steffen and Budach, Volker and Gellermann, Johanna}, title = {Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system}, volume = {34}, journal = {Medical Physics}, number = {12}, pages = {4717 -- 4725}, year = {2007}, language = {en} } @article{Weiser2005, author = {Weiser, Martin}, title = {Interior point methods in function space}, volume = {44}, journal = {SIAM J. Control Optimization}, number = {5}, pages = {1766 -- 1786}, year = {2005}, language = {en} } @inproceedings{TaylorKassiSchwarzkopfetal.2005, author = {Taylor, William R. and Kassi, J.-P. and Schwarzkopf, J. and Ehrig, Rainald and Schell, H. and Duda, G.}, title = {The Profile of Mechanical Loading is Independent of Fracture Fixation Principle}, booktitle = {Proceedings of the 51th Annual Meeting of the Orthopedic Society}, address = {Washington}, year = {2005}, language = {en} } @article{TaylorPoepplauKoenigetal.2011, author = {Taylor, William R. and P{\"o}pplau, Berry M. and K{\"o}nig, Christian and Ehrig, Rainald and Zachow, Stefan and Duda, Georg and Heller, Markus O.}, title = {The medial-lateral force distribution in the ovine stifle joint during walking}, volume = {29}, journal = {Journal of Orthopaedic Research}, number = {4}, doi = {10.1002/jor.21254}, pages = {567 -- 571}, year = {2011}, language = {en} } @article{BoethDudaHelleretal.2013, author = {Boeth, Heide and Duda, Georg and Heller, Markus O. and Ehrig, Rainald and Doyscher, Ralf and Jung, Tobias and Moewis, Philippe and Scheffler, Sven and Taylor, William R.}, title = {Anterior cruciate ligament-deficient patients with passive knee joint laxity have a decreased range of anterior-posterior motion during active movements}, volume = {41}, journal = {The American Journal of Sports Medicine}, number = {5}, doi = {10.1177/0363546513480465}, pages = {1051 -- 7}, year = {2013}, language = {en} } @inproceedings{TaylorEhrigDudaetal.2006, author = {Taylor, William R. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {The Symmetrical Axis of Rotation Approach (SARA) for Determination of Joint Axes in Clinical Gait Analysis}, booktitle = {1st Joint ESMAC-GCMAS Meeting, Amsterdam}, year = {2006}, language = {en} } @inproceedings{TaylorEhrigHelleretal.2004, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Duda, G.}, title = {Can Skin Markers Determine the Kinematics of Underlying Bones?}, booktitle = {Proceedings of the 50th Annual Meeting of the Orthopedic Society}, address = {San Francisco}, year = {2004}, language = {en} } @article{TaylorEhrigHelleretal.2005, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Klein, P. and Duda, G.}, title = {On the Influence of Soft Tissue Coverage in the Determination of Bone Kinematics using Bone Markers}, journal = {Journal of Orthopedic Research}, number = {23}, pages = {726 -- 734}, year = {2005}, language = {en} } @inproceedings{TaylorEhrigHelleretal.2005, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Seebeck, P. and Duda, G.}, title = {Animal Models for Knee Injury Frequently Underestimate the Mechanical Conditions of the Clinical Situation}, booktitle = {Proceedings of the 51th Annual Meeting of the Orthopedic Society}, address = {Washington}, year = {2005}, language = {en} } @article{TaylorEhrigHelleretal.2006, author = {Taylor, William R. and Ehrig, Rainald and Heller, Markus O. and Schell, H. and Seebeck, P. and Duda, G.}, title = {Tibio-femoral Joint Contact Forces in Sheep}, journal = {Journal of Biomechanics}, number = {39}, pages = {791 -- 798}, year = {2006}, language = {en} } @inproceedings{TaylorKornaropoulosEhrigetal.2009, author = {Taylor, William R. and Kornaropoulos, Evgenios I. and Ehrig, Rainald and Heller, Markus O. and Duda, Georg}, title = {Reproducibility of a functional approach to gait analysis}, booktitle = {Annual meeting of the ESMAC 2009}, address = {London}, year = {2009}, language = {en} } @inproceedings{TaylorKratzensteinKornaropoulosetal.2009, author = {Taylor, William R. and Kratzenstein, Stefan and Kornaropoulos, Evgenios I. and Ehrig, Rainald and Moewis, Philippe and Heller, Markus O.}, title = {Non-invasive Assessment of Skeletal Kinematics}, booktitle = {Measurement and Sensing in Medicine and Health}, address = {London}, year = {2009}, language = {en} } @inproceedings{TaylorKornaropoulosKratzensteinetal.2011, author = {Taylor, William R. and Kornaropoulos, Evgenios I. and Kratzenstein, Stefan and Ehrig, Rainald and Plank, F. and Heller, Markus O.}, title = {Targeted Marker Placement for the Functional Identification of the Hip Joint Centre}, booktitle = {Transactions Vol. 36, 2011 Annual Meeting of the Orthopedic Society}, address = {Long Beach}, year = {2011}, language = {en} } @inproceedings{TaylorKoenigSpeirsetal.2006, author = {Taylor, William R. and K{\"o}nig, Christian and Speirs, A. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {The medio-lateral force distribution in the sheep knee during walking}, booktitle = {5. World Congress of Biomechanics, Munich, Journal of Biomechanics}, number = {39, Suppl. 1}, pages = {S491}, year = {2006}, language = {en} } @inproceedings{TaylorKoenigSpeirsetal.2006, author = {Taylor, William R. and K{\"o}nig, Christian and Speirs, A. and Ehrig, Rainald and Duda, G. and Heller, Markus O.}, title = {Die medio-laterale Kraftverteilung im Schafsknie}, booktitle = {Deutscher Kongress f{\"u}r Orthp{\"a}die und Unfallchirurgie, Berlin}, year = {2006}, language = {en} } @article{VolkweinWeiser2002, author = {Volkwein, S. and Weiser, Martin}, title = {Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian SQP Methods}, volume = {41}, journal = {SIAM J. Control Optim.}, number = {3}, pages = {875 -- 899}, year = {2002}, language = {en} } @techreport{VolkweinWeiser2004, author = {Volkwein, S. and Weiser, Martin}, title = {Optimality Conditions for a Constrained Parameter Identification Problem in Hyperthermia}, number = {305}, publisher = {University of Graz, SFB F003}, address = {Graz, Austria}, year = {2004}, language = {en} } @article{WeiserGaenzlerSchiela2008, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A control reduced primal interior point method for a class of control constrained optimal control problems}, volume = {41}, journal = {Comput. Optim. Appl.}, number = {1}, pages = {127 -- 145}, year = {2008}, language = {en} } @article{WeiserSchiela2004, author = {Weiser, Martin and Schiela, Anton}, title = {Function space interior point methods for PDE constrained optimization}, volume = {4}, journal = {PAMM}, number = {1}, pages = {43 -- 46}, year = {2004}, language = {en} }