@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} } @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{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} } @misc{Binkowski2017, author = {Binkowski, Felix}, title = {On the convergence behavior of spectral deferred correction methods for convection-diffusion equations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66016}, pages = {64}, year = {2017}, abstract = {Spectral deferred correction (SDC) Methoden, vorgestellt von Dutt, Greengard und Rokhlin in [1], sind iterative Verfahren zur numerischen L{\"o}sung von Anfangswertproblemen f{\"u}r gew{\"o}hnliche Differentialgleichungen. Wenn diese Methoden konvergieren, dann wird unter Verwendung von Zeitschrittverfahren niedriger Ordnung eine Kollokationsl{\"o}sung berechnet. Die L{\"o}sung von steifen Anfangswertproblemen ist eine relevante Problemstellung in der numerischen Mathematik. SDC-Methoden, speziell f{\"u}r steife Probleme, werden von Martin Weiser in [2] konstruiert. Die Theorie und die Experimente beziehen sich dabei auf Probleme, die aus r{\"a}umlich semidiskretisierten Reaktions-Diffusions-Gleichungen entstehen. In dieser Arbeit werden die Ans{\"a}tze aus [2] auf Konvektions-Diffusions-Gleichungen angewendet und das resultierende Konvergenzverhalten von SDC-Methoden untersucht. Basierend auf einem einfachen Konvektions-Diffusions-Operator, dessen spektrale Eigenschaften umfassend studiert werden, wird ein Schema zur Verbesserung dieses Verhaltens entwickelt. Numerische Experimente zeigen, dass eine Verbesserung der in [1] eingef{\"u}hrten SDC-Methoden m{\"o}glich ist. Die Untersuchungen ergeben weiterhin, dass das auch f{\"u}r komplexere Konvektions-Diffusions-Probleme gilt. [1] Alok Dutt, Leslie Greengard, und Vladimir Rokhlin. "Spectral deferred correction methods for ordinary differential equations." In: BIT 40.2 (2000), pp. 241-266. [2] Martin Weiser. "Faster SDC convergence on non-equidistant grids by DIRK sweeps." In: BIT 55.4 (2015), pp. 1219-1241.}, language = {en} } @misc{WeiserFreytagErdmannetal.2018, author = {Weiser, Martin and Freytag, Yvonne and Erdmann, Bodo and Hubig, Michael and Mall, Gita}, title = {Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-67247}, year = {2018}, abstract = {Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements.}, language = {en} } @misc{GoetschelWeiser2019, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy Compression for Large Scale PDE Problems}, issn = {1438-0064}, doi = {10.1101/506378}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73817}, year = {2019}, abstract = {Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to relatively small arithmetic intensity, and increasingly so due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers during the last decades. This paper surveys data compression challenges and corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to main memory. Exemplarily, we illustrate concepts at particular methods, and give references to alternatives.}, language = {en} } @misc{GoetschelSchielaWeiser2019, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 -- a Flexible Finite Element Toolbox}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74616}, year = {2019}, abstract = {Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the Dune interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.}, language = {en} } @misc{Schiela2008, author = {Schiela, Anton}, title = {State constrained optimal control problems with states of low regularity}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-509}, number = {08-24}, year = {2008}, abstract = {We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.}, language = {en} } @misc{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Adaptive Solutions of Nonlinear Parabolic Equations with Application to Hyperthermia Treatments}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3130}, number = {SC-97-44}, year = {1997}, abstract = {We present a self-adaptive finite element method to solve nonlinear evolution problems in 3D. An implicit time integrator of Rosenbrock type is coupled with a multilevel approach in space. The proposed method is applied to hyperthermia treatments to demonstrate its potential for the solving of complicated problems.}, language = {en} } @misc{Weiser2003, author = {Weiser, Martin}, title = {Interior Point Methods in Function Space}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7578}, number = {03-35}, year = {2003}, abstract = {A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established.}, language = {en} } @misc{WeiserSchielaDeuflhard2003, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7352}, number = {03-13}, year = {2003}, abstract = {The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.}, language = {en} } @misc{Deuflhard2002, author = {Deuflhard, Peter}, title = {A Comparison of Related Concepts in Computational Chemistry and Mathematics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7138}, number = {02-46}, year = {2002}, abstract = {This article studies the relation of the two scientific languages Chemistry and Mathematics via three selected comparisons: (a) QSSA versus dynamic ILDM in reaction kinetics, (b) lumping versus discrete Galerkin methods in polymer chemistry, and (c) geometrical conformations versus metastable conformations in drug design. The common clear message from these comparisons is that chemical intuition may pave the way for mathematical concepts just as chemical concepts may gain from mathematical precisioning. Along this line, significant improvements in chemical research and engineering have already been possible -- and can be further expected in the future from the dialogue between the two scientific languages.}, language = {en} } @misc{Deuflhard2002, author = {Deuflhard, Peter}, title = {From Molecular Dynamics to Conformational Dynamics in Drug Design}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6878}, number = {02-20}, year = {2002}, abstract = {Computational drug design studies molecular recognition in the {\em virtual lab}. The arising Hamiltonian dynamics is known to be chaotic and ill-conditioned already after picoseconds, whereas times are \$msec\$ up to \$min\$. Classical molecular dynamics with long term trajectory computation gives, at best, information about time and statistical ensemble averages. The present paper surveys a recent new modeling approach called {\em conformational dynamics}, which is due to the author and Ch. Sch{\"u}tte. This approach achieves information about the dy time scales by telescoping a short term deterministic model with a statistical model. Examples of small biomolecules are included.}, language = {en} } @misc{DeuflhardHochmuth2002, author = {Deuflhard, Peter and Hochmuth, Reinhard}, title = {Multiscale Analysis of Thermoregulation in the Human Microvascular System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6985}, number = {02-31}, year = {2002}, abstract = {The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the deduction of the Helmholtz term in the bio-heat transfer equation is not co role. In view of a future numerical application of this new mathematical model to treatment planning in hyperthermia we derive asymptotic estimates for first and second order correctors.}, language = {en} } @misc{DeuflhardNowakWeiser2002, author = {Deuflhard, Peter and Nowak, Ulrich and Weiser, Martin}, title = {Affine Invariant Adaptive Newton Codes for Discretized PDEs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7005}, number = {02-33}, year = {2002}, abstract = {The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs.}, language = {en} } @misc{PowellWeiser1999, author = {Powell, Gary and Weiser, Martin}, title = {Container Adaptors}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4308}, number = {SC-99-41}, year = {1999}, 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{ErdmannLangSeebass1997, author = {Erdmann, Bodo and Lang, Jens and Seebass, Martin}, title = {Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Transfer Model}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3283}, number = {SC-97-59}, year = {1997}, abstract = {We describe an optimization process specially designed for regional hyperthermia of deap seated tumors in order to achieve desired steady--state temperature distributions. A nonlinear three--dimensional heat--transfer model based on temperature--dependent blood perfusion is applied to predict the temperature. Optimal heating is obtained by minimizing an integral object function which measures the distance between desired and model predicted temperatures. Sequential minima are calculated from successively improved constant--rate perfusion models employing a damped Newton method in an inner iteration. Numerical results for a Sigma 60 applicator are presented. This work has been supported by Deutsche Forschungsgemeinschaft (DFG) within the Sonderforschungsbereich 273 \glqq Hyperthermie: Methodik und Klinik \grqq .}, language = {en} } @misc{SchielaWeiser2005, author = {Schiela, Anton and Weiser, Martin}, title = {Superlinear Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8490}, number = {05-15}, year = {2005}, abstract = {A thorough convergence analysis of the Control Reduced Interior Point Method in function space is performed. This recently proposed method is a primal interior point pathfollowing scheme with the special feature, that the control variable is eliminated from the optimality system. Apart from global linear convergence we show, that this method converges locally almost quadratically, if the optimal solution satisfies a function space analogue to a non-degeneracy condition. In numerical experiments we observe, that a prototype implementation of our method behaves in compliance with our theoretical results.}, language = {en} } @misc{KoberErdmannHellmichetal.2004, author = {Kober, Cornelia and Erdmann, Bodo and Hellmich, Christian and Sader, Robert and Zeilhofer, Hans-Florian}, title = {Anisotropic Simulation of the Human Mandible}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7873}, number = {04-12}, year = {2004}, abstract = {We focus on the role of anisotropic elasticity in the simulation of the load distribution in a human mandible due to a lateral bite on the leftmost premolar. Based on experimental evidence, we adopt ``local''" orthotropy of the elastic properties of the bone tissue. Since the trajectories of anisotropic elasticity are not accessible from Computer Tomographic (CT) data, they will be reconstructed from (i) the organ's geometry and (ii) from coherent structures which can be recognized from the spatial distribution of the CT values. A sensitivity analysis comprising various 3D FE simulations reveals the relevance of elastic anisotropy for the load carrying behavior of a human mandible: Comparison of the load distributions in isotropic and anisotropic simulations indicates that anisotropy seems to ``spare''" the mandible from loading. Moreover, a maximum degree of anisotropy leads to kind of an load minimization of the mandible, expressed by a minimum of different norms of local strain, evaluated throughout the organ. Thus, we may suggest that anisotropy is not only relevant, but also in some sense ``optimal''.}, language = {en} } @misc{KoberErdmannLangetal.2004, author = {Kober, Cornelia 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}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7917}, number = {04-16}, year = {2004}, abstract = {Structural mechanics simulation of bony organs is of general medical and biomechanical interest, because of the interdependence of the inner architecture of bone and its functional loading already stated by Wolff in 1892. This work is part of a detailed research project concerning the human mandible. By adaptive finite element techniques, stress/strain profiles occurring in the bony structure under biting were simulated. Estimates of the discretization errors, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. In general, our simulation requires a representation of the organ's geometry, an appropriate material description, and the load case due to teeth, muscle, or joint forces. In this paper, we want to focus on the influence of the masticatory system. Our goal is to capture the physiological situation as far as possible. By means of visualization techniques developed by the group, we are able to extract individual muscle fibres from computed tomography data. By a special algorithm, the fibres are expanded to fanlike (esp. for the musc. temporalis) coherent vector fields similar to the anatomical reality. The activity of the fibres can be adapted according to compartmentalisation of the muscles as measured by electromyological experiments. A refined sensitivity analysis proved remarkable impact of the presented approach on the simulation results.}, language = {en} } @misc{WeiserSchiela2004, author = {Weiser, Martin and Schiela, Anton}, title = {Function space interior point methods for PDE constrained optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8027}, number = {04-27}, year = {2004}, abstract = {A primal-dual interior point method for optimal control problems with PDE constraints is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed. Numerical results from an inexact continuation method applied to a model problem are shown.}, language = {en} } @misc{LubkollSchielaWeiser2015, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An affine covariant composite step method for optimization with PDEs as equality constraints}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53954}, year = {2015}, abstract = {We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery.}, language = {en} } @misc{WeiserGhosh2016, author = {Weiser, Martin and Ghosh, Sunayana}, title = {Theoretically optimal inexact SDC methods}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53140}, year = {2016}, abstract = {In several inital value problems with particularly expensive right hand side computation, there is a trade-off between accuracy and computational effort in evaluating the right hand sides. We consider inexact spectral deferred correction (SDC) methods for solving such non-stiff 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 an error model bounding the total error in terms of the right hand side 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 tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance.}, language = {en} } @misc{Freytag2017, author = {Freytag, Yvonne}, title = {Optimal Experimental Design to Estimate the Time of Death in a Bayesian Context}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62475}, year = {2017}, abstract = {This thesis is devoted to the interdisciplinary work between mathematicians and forensic experts: the modeling of the human body cooling process after death laying the foundation for the estimation of the time of death. An inverse problem needs to be solved. In this thesis the inverse problem computes the time of death given the measured body temperature and the Forward Model that simulates the body cooling process. The Forward Model is based on the heat equation established by Fourier. This differential equation is numerically solved by the discretization over space by the Finite Element Method and the discretization over time by the Implicit Euler Method. The applications in this thesis demand a fast computation time. A model reduction is achieved by the Proper Orthogonal Decomposition in combination with the Galerkin Method. For reasons of simplification the computations and the measurements are restricted to a cylindrical phantom that is made out of homogeneous polyethylene. The estimate of the time of death is accompanied by an uncertainty. The inverse problem is incorporated by Bayesian inference to interpret the quality of the estimate and the effciency of the experiment. The uncertainty of the estimate of the time of death is minimized by approaching the Optimal Design of the Experiment. An objective function measures the certainty of the data and lays the foundation of the optimization problem. Solving the optimization problem is successfully done by relaxing the complex discrete NP-hard problem and applying a gradient-based method. The results of this thesis clearly show that the design of an experiment has a great in- uence on the outcome of the quality of the estimate. The comparison of the estimate and its properties based on different designs and conditions reveals the effciency of the Design of Experiment in the context of the estimation of the time of death.}, language = {en} } @misc{FischerGoetschelWeiser2017, author = {Fischer, Lisa and G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy data compression reduces communication time in hybrid time-parallel integrators}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63961}, year = {2017}, abstract = {Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups.}, language = {en} } @misc{WeiserErdmannSchenkletal.2017, author = {Weiser, Martin and Erdmann, Bodo and Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Mall, Gita and Zachow, Stefan}, title = {Uncertainty in Temperature-Based Determination of Time of Death}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63818}, year = {2017}, abstract = {Temperature-based estimation of time of death (ToD) can be per- formed either with the help of simple phenomenological models of corpse cooling or with detailed mechanistic (thermodynamic) heat transfer mod- els. The latter are much more complex, but allow a higher accuracy of ToD estimation as in principle all relevant cooling mechanisms can be taken into account. The potentially higher accuracy depends on the accuracy of tissue and environmental parameters as well as on the geometric resolution. We in- vestigate the impact of parameter variations and geometry representation on the estimated ToD based on a highly detailed 3D corpse model, that has been segmented and geometrically reconstructed from a computed to- mography (CT) data set, differentiating various organs and tissue types. From that we identify the most crucial parameters to measure or estimate, and obtain a local uncertainty quantifcation for the ToD.}, language = {en} } @misc{GoetschelMinion2017, author = {G{\"o}tschel, Sebastian and Minion, Michael L.}, title = {Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64989}, year = {2017}, 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{WeiserScacchi2014, author = {Weiser, Martin and Scacchi, Simone}, title = {Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50695}, year = {2014}, abstract = {We investigate spectral deferred correction (SDC) methods for time stepping and their interplay with spatio-temporal adaptivity, applied to the solution of the cardiac electro-mechanical coupling model. This model consists of the Monodomain equations, a reaction-diffusion system modeling the cardiac bioelectrical activity, coupled with a quasi-static mechanical model describing the contraction and relaxation of the cardiac muscle. The numerical approximation of the cardiac electro-mechanical coupling is a challenging multiphysics problem, because it exhibits very different spatial and temporal scales. Therefore, spatio-temporal adaptivity is a promising approach to reduce the computational complexity. SDC methods are simple iterative methods for solving collocation systems. We exploit their flexibility for combining them in various ways with spatio-temporal adaptivity. The accuracy and computational complexity of the resulting methods are studied on some numerical examples.}, language = {en} } @misc{GoetschelMaierhoferMuelleretal.2016, author = {G{\"o}tschel, Sebastian and Maierhofer, Christiane and M{\"u}ller, Jan P. and Rothbart, Nick and Weiser, Martin}, title = {Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58374}, year = {2016}, abstract = {Carbon-fiber reinforced composites are becoming more and more important in the production of light-weight structures, e.g., in the automotive and aerospace industry. Thermography is often used for non-destructive testing of these products, especially to detect delaminations between different layers of the composite. In this presentation, we aim at methods for defect reconstruction from thermographic measurements of such carbon-fiber reinforced composites. The reconstruction results shall not only allow to locate defects, but also give a quantitative characterization of the defect properties. We discuss the simulation of the measurement process using finite element methods, as well as the experimental validation on flat bottom holes. Especially in pulse thermography, thin boundary layers with steep temperature gradients occurring at the heated surface need to be resolved. Here we use the combination of a 1D analytical solution combined with numerical solution of the remaining defect equation. We use the simulations to identify material parameters from the measurements. Finally, fast heuristics for reconstructing defect geometries are applied to the acquired data, and compared for their accuracy and utility in detecting different defects like back surface defects or delaminations.}, language = {en} } @misc{GoetschelHoehneKolkoorietal.2016, author = {G{\"o}tschel, Sebastian and H{\"o}hne, Christian and Kolkoori, Sanjeevareddy and Mitzscherling, Steffen and Prager, Jens and Weiser, Martin}, title = {Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58386}, year = {2016}, abstract = {The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave propagation through the material, in particular travel times between two points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points. In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the eikonal equation. The implementation of such a two point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools. As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value problem allows a straightforward derivation of the ray path from a given transducer position to any pixel in the reconstruction area and reduces the computational cost considerably.}, language = {en} } @misc{Makarenko2017, type = {Master Thesis}, author = {Makarenko, Oleksandra}, title = {Square Root Approximation und statistische Umgewichtungstechnik f{\"u}r das Faltungsverhalten von Polymerb{\"u}rsten}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65283}, year = {2017}, language = {de} } @misc{VolkweinWeiser2000, author = {Volkwein, Stefan and Weiser, Martin}, title = {Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6243}, number = {00-56}, year = {2000}, abstract = {An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solves. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation.}, language = {en} } @misc{WeiserDeuflhard2001, author = {Weiser, Martin and Deuflhard, Peter}, title = {The Central Path towards the Numerical Solution of Optimal Control Problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6380}, number = {01-12}, year = {2001}, abstract = {A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem.}, language = {en} } @misc{ErdmannKoberLangetal.2001, author = {Erdmann, Bodo and Kober, Cornelia and Lang, Jens and Sader, Robert and Zeilhofer, Hans-Florian and Deuflhard, Peter}, title = {Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6403}, number = {01-14}, year = {2001}, abstract = {By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.}, language = {en} } @misc{HinzeSchiela2007, 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}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10414}, number = {07-40}, year = {2007}, abstract = {An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.}, language = {en} } @misc{Weiser2007, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10493}, number = {07-45}, year = {2007}, abstract = {Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples.}, language = {en} } @misc{SchenkWaechterWeiser2007, author = {Schenk, Olaf and W{\"a}chter, Andreas and Weiser, Martin}, title = {Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10314}, number = {07-32}, year = {2007}, abstract = {Fast nonlinear programming methods following the all-at-once approach usually employ Newton's method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is only guaranteed to be a descent direction if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints, otherwise some modifications to Newton's method are necessary. This condition can be verified using the signs of the KKT's eigenvalues (inertia), which are usually available from direct solvers for the arising linear saddle point problems. Iterative solvers are mandatory for very large-scale problems, but in general do not provide the inertia. Here we present a preconditioner based on a multilevel incomplete \$LBL^T\$ factorization, from which an approximation of the inertia can be obtained. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale 3D PDE-constrained optimal control problems, as well as 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with \$150^3\$ state variables and \$150^2\$ control variables, both subject to bound constraints.}, language = {en} } @misc{Schiela2008, author = {Schiela, Anton}, title = {An Extended Mathematical Framework for Barrier Methods in Function Space}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10593}, number = {08-07}, year = {2008}, abstract = {An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.}, language = {en} } @misc{BorndoerferDaneckerWeiser2023, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91309}, year = {2023}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @misc{SagnolHegeWeiser2016, author = {Sagnol, Guillaume and Hege, Hans-Christian and Weiser, Martin}, title = {Using sparse kernels to design computer experiments with tunable precision}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59605}, year = {2016}, abstract = {Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate. In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples). We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave. On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem.}, language = {en} } @misc{BorndoerferDaneckerWeiser2020, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, issn = {1438-0064}, doi = {10.3390/a14010004}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-81343}, year = {2020}, abstract = {We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.}, language = {en} }