TY - JOUR A1 - Deuflhard, Peter A1 - Weiser, Martin A1 - Zachow, Stefan T1 - Mathematics in Facial Surgery JF - AMS Notices Y1 - 2006 VL - 53 IS - 9 SP - 1012 EP - 1016 ER - TY - JOUR A1 - Weiser, Martin A1 - Zachow, Stefan A1 - Deuflhard, Peter T1 - Craniofacial Surgery Planning Based on Virtual Patient Models JF - it - Information Technology Y1 - 2010 U6 - https://doi.org/10.1524/itit.2010.0600 VL - 52 IS - 5 SP - 258 EP - 263 PB - Oldenbourg Verlagsgruppe ER - TY - CHAP A1 - Weiser, Martin A1 - Scacchi, Simone T1 - Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation T2 - G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014 N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-23413-7_42 SP - 321 EP - 328 PB - Springer ER - TY - GEN A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An affine covariant composite step method for optimization with PDEs as equality constraints N2 - 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. T3 - ZIB-Report - 15-09 KW - composite step methods KW - cubic regularization KW - affine covariant KW - optimization with PDEs Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53954 SN - 1438-0064 ER - TY - GEN A1 - Weiser, Martin A1 - Ghosh, Sunayana T1 - Theoretically optimal inexact SDC methods N2 - 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. T3 - ZIB-Report - 16-52 KW - Spectral deferred correction, initial value problems, error propagation, adaptive control of tolerances Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53140 SN - 1438-0064 ER - TY - CHAP A1 - Sagnol, Guillaume A1 - Hege, Hans-Christian A1 - Weiser, Martin T1 - Using sparse kernels to design computer experiments with tunable precision T2 - 22nd Intern. Conf. on Computational Statistics - COMPSTAT 2016, Oviedo, Spain, 23-26 August 2016, Proceedings ISBN 978-90-73592-36-0 Y1 - 2016 SP - 397 EP - 408 ER - TY - CHAP A1 - Götschel, Sebastian A1 - Höhne, Christian A1 - Kolkoori, Sanjeevareddy A1 - Mitzscherling, Steffen A1 - Prager, Jens A1 - Weiser, Martin T1 - Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing T2 - Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016) Y1 - 2016 UR - https://www.wcndt2016.com/portals/wcndt/bb/Fr1H4.pdf ER - TY - CHAP A1 - Götschel, Sebastian A1 - Maierhofer, Christiane A1 - Müller, Jan A1 - Rothbart, Nick A1 - Weiser, Martin T1 - Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites T2 - Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016) Y1 - 2016 UR - https://www.wcndt2016.com/portals/wcndt/bb/Th4C4.pdf ER - TY - CHAP A1 - Müller, Jan A1 - Götschel, Sebastian A1 - Maierhofer, Christiane A1 - Weiser, Martin T1 - Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography T2 - AIP Conference Proceedings Y1 - 2017 U6 - https://doi.org/10.1063/1.4974671 VL - 1806 ER - TY - GEN A1 - Fischer, Lisa A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy data compression reduces communication time in hybrid time-parallel integrators N2 - 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. T3 - ZIB-Report - 17-25 KW - parallel-in-time integration KW - hybrid parareal KW - convergence KW - lossy compression KW - MPI Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63961 SN - 1438-0064 ER - TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita A1 - Zachow, Stefan T1 - Uncertainty in Temperature-Based Determination of Time of Death N2 - 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. T3 - ZIB-Report - 17-18 KW - forensic medicine KW - determination of time of death KW - heat transfer equation KW - sensitivity i.r.t. thermal parameters KW - sensitivity i.r.t. geometric resolution Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63818 SN - 1438-0064 ER - TY - JOUR A1 - Fischer, Lisa A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy data compression reduces communication time in hybrid time-parallel integrators JF - Comput. Vis. Sci. N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/s00791-018-0293-2 VL - 19 IS - 1 SP - 19 EP - 30 ER - TY - GEN A1 - Weiser, Martin A1 - Scacchi, Simone T1 - Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation N2 - 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. T3 - ZIB-Report - 14-22 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50695 SN - 1438-0064 ER - TY - GEN A1 - Deuflhard, Peter A1 - Kornhuber, Ralf A1 - Sander, Oliver A1 - Schiela, Anton A1 - Weiser, Martin ED - Deuflhard, Peter ED - Grötschel, Martin ED - Hömberg, Dietmar ED - Horst, Ulrich ED - Kramer, Jürg ED - Mehrmann, Volker ED - Polthier, Konrad ED - Schmidt, Frank ED - Schütte, Christof ED - Skutella, Martin ED - Sprekels, Jürgen T1 - Mathematics cures virtual patients T2 - MATHEON-Mathematics for Key Technologies Y1 - 2014 VL - 1 SP - 7 EP - 25 PB - European Mathematical Society ER - TY - JOUR A1 - Moualeu-Ngangue, Dany Pascal A1 - Weiser, Martin A1 - Ehrig, Rainald A1 - Deuflhard, Peter T1 - Optimal control for a tuberculosis model with undetected cases in Cameroon JF - Communications in Nonlinear Science and Numerical Simulation N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1016/j.cnsns.2014.06.037 VL - 20 IS - 3 SP - 986 EP - 1003 ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Maierhofer, Christiane A1 - Richter, Regina ED - Cardone, Gennaro T1 - Data Enhancement for Active Thermography T2 - E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples N2 - 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. Y1 - 2012 ER - TY - JOUR A1 - Weiser, Martin T1 - On goal-oriented adaptivity for elliptic optimal control problems JF - Opt. Meth. Softw. N2 - 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. Y1 - 2013 VL - 28 IS - 13 SP - 969 EP - 992 ER - TY - JOUR A1 - Deuflhard, Peter A1 - Schiela, Anton A1 - Weiser, Martin T1 - Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia JF - Acta Numerica N2 - 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. Y1 - 2012 VL - 21 SP - 307 EP - 378 ER - TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Schiela, Anton ED - Dedner, A. ED - Flemisch, B. ED - Klöfkorn, R. T1 - Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox T2 - Advances in DUNE N2 - 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. Y1 - 2012 SP - 101 EP - 112 PB - Springer ER - TY - JOUR A1 - Weiser, Martin T1 - Faster SDC convergence on non-equidistant grids by DIRK sweeps JF - BIT Numerical Mathematics N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1007/s10543-014-0540-y VL - 55 IS - 4 SP - 1219 EP - 1241 ER - TY - JOUR A1 - Weiser, Martin A1 - Götschel, Sebastian T1 - State Trajectory Compression for Optimal Control with Parabolic PDEs JF - SIAM J. Sci. Comput. N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1137/11082172X VL - 34 IS - 1 SP - A161 EP - A184 ER - TY - GEN A1 - Nadobny, Johanna A1 - Weihrauch, Mirko A1 - Weiser, Martin A1 - Gellermann, Johanna A1 - Wlodarczyk, Waldemar A1 - Budach, Volker A1 - Wust, Peter T1 - Advances in the Planning and Control of the MR-guided Regional Hyperthermia Applications T2 - Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy Y1 - 2007 SP - 1010 EP - 1013 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - State Trajectory Compression in Optimal Control JF - PAMM N2 - In optimal control problems with nonlinear time-dependent 3D PDEs, the computation of the reduced gradient by adjoint methods requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. Since the state enters into the adjoint equation, the storage of a 4D discretization is necessary. We propose a lossy compression algorithm using a cheap predictor for the state data, with additional entropy coding of prediction errors. Analytical and numerical results indicate that compression factors around 30 can be obtained without exceeding the FE discretization error. Y1 - 2010 U6 - https://doi.org/10.1002/pamm.201010282 VL - 10 IS - 1 SP - 579 EP - 580 ER - TY - GEN A1 - Weiser, Martin T1 - Delayed Residual Compensation for Bidomain Equations T2 - AIP Conference Proceedings N2 - The biodomain model of cardioelectric excitation consists of a reaction‐diffusion equation, an elliptic algebraic constraint, and a set of pointwise ODEs. Fast reaction enforces small time steps, such that for common mesh sizes the reaction‐diffusion equation is easily solved implicitly due to a dominating mass matrix. In contrast, the elliptic constraint does not benefit from small time steps and requires a comparably expensive solution. We propose a delayed residual compensation that improves the solution of the elliptic constraint and thus alleviates the need for long iteration times. Y1 - 2010 U6 - https://doi.org/10.1063/1.3498495 VL - 1281 SP - 419 EP - 422 ER - TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Deuflhard, Peter ED - Wilson, E. ED - Fitt, A. ED - Ockendon, H. ED - Norbury, J. T1 - On Efficiency and Accuracy in Cardioelectric Simulation T2 - Progress in Industrial Mathematics at ECMI 2008 N2 - Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy. Y1 - 2010 SP - 371 EP - 376 PB - Springer ER - TY - JOUR A1 - Wilhelms, Mathias A1 - Seemann, Gunnar A1 - Weiser, Martin A1 - Dössel, Olaf T1 - Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling JF - Biomed. Engineer. Y1 - 2010 U6 - https://doi.org/10.1515/BMT.2010.712 VL - 55 SP - 99 EP - 102 ER - TY - GEN A1 - Wust, Peter A1 - Weihrauch, Mirko A1 - Weiser, Martin A1 - Gellermann, Johanna A1 - Eisenhardt, Steffen A1 - Chobrok, Thorsten A1 - Budach, Volker ED - Dössel, O. ED - Schlegel, W. ED - Magjarevic, R. T1 - Optimization of clinical radiofrequency hyperthermia by use of MR-thermography in a hybrid system T2 - World Congress on Medical Physics and Biomedical Engineering, September 2009, Munich, Germany Y1 - 2010 SP - 174 EP - 175 PB - Springer ER - TY - JOUR A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An optimal control problem in polyconvex hyperelasticity JF - SIAM J. Control Opt. N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1137/120876629 VL - 52 IS - 3 SP - 1403 EP - 1422 ER - TY - JOUR A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin T1 - Flexible Shape Matching with Finite Element Based LDDMM JF - International Journal of Computer Vision N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1007/s11263-012-0599-3 VL - 105 IS - 2 SP - 128 EP - 143 ER - TY - GEN A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin ED - Pennec, X. ED - Joshi, S. ED - Nielsen, M. T1 - Direct LDDMM of Discrete Currents with Adaptive Finite Elements T2 - Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability N2 - 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. Y1 - 2011 SP - 1 EP - 14 ER - TY - GEN A1 - Schiela, Anton A1 - Weiser, Martin ED - Diehl, M. ED - Glineur, F. ED - Jarlebring, E. ED - Michiels, W. T1 - Barrier methods for a control problem from hyperthermia treatment planning T2 - Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009) N2 - 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. Y1 - 2010 SP - 419 EP - 428 PB - Springer ER - TY - JOUR A1 - Weiser, Martin A1 - Röllig, Mathias A1 - Arndt, Ralf A1 - Erdmann, Bodo T1 - Development and test of a numerical model for pulse thermography in civil engineering JF - Heat and Mass Transfer N2 - 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. Y1 - 2010 VL - 46 IS - 11-12 SP - 1419 EP - 1428 ER - TY - JOUR A1 - Ranneberg, Maximilian A1 - Weiser, Martin A1 - Weihrauch, Mirko A1 - Budach, Volker A1 - Gellermann, Johanna A1 - Wust, Peter T1 - Regularized Antenna Profile Adaptation in Online Hyperthermia Treatment JF - Medical Physics Y1 - 2010 U6 - https://doi.org/10.1118/1.3488896 VL - 37 SP - 5382 EP - 5394 ER - TY - JOUR A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An affine covariant composite step method for optimization with PDEs as equality constraints JF - Optimization Methods and Software N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2016.1241783 VL - 32 IS - 5 SP - 1132 EP - 1161 ER - TY - GEN A1 - Götschel, Sebastian A1 - Maierhofer, Christiane A1 - Müller, Jan P. A1 - Rothbart, Nick A1 - Weiser, Martin T1 - Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites N2 - 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. T3 - ZIB-Report - 16-13 KW - thermography KW - inverse problems KW - parameter identification KW - geometry identification KW - nondestructive testing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58374 UR - https://www.wcndt2016.com/portals/wcndt/bb/Th4C4.pdf SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Höhne, Christian A1 - Kolkoori, Sanjeevareddy A1 - Mitzscherling, Steffen A1 - Prager, Jens A1 - Weiser, Martin T1 - Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing N2 - 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. T3 - ZIB-Report - 16-14 KW - ray tracing KW - ODE boundary value problems KW - ultrasonics KW - nondestructive testing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58386 UR - https://www.wcndt2016.com/portals/wcndt/bb/Fr1H4.pdf SN - 1438-0064 ER - TY - BOOK A1 - Weiser, Martin T1 - Inside Finite Elements N2 - All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms.Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave. Y1 - 2016 PB - De Gruyter ER - TY - GEN A1 - Volkwein, Stefan A1 - Weiser, Martin T1 - Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods N2 - 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. T3 - ZIB-Report - 00-56 KW - nonlinear programming KW - multiplier methods KW - affine invariant norms KW - Burgers' equation Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6243 ER - TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter T1 - The Central Path towards the Numerical Solution of Optimal Control Problems N2 - 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. T3 - ZIB-Report - 01-12 KW - optimal control KW - interior point methods KW - affine invariance Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6380 ER - TY - GEN A1 - Weiser, Martin T1 - Linear convergence of an interior point method for linear control constrained optimal control problems N2 - The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a recent paper of Weiser and Deuflhard, where convergence rates have not been derived. The choice of free parameters, i.e. the corrector accuracy and the number of corrector steps, is discussed. T3 - ZIB-Report - 02-13 KW - linear optimal control KW - infinite dimensional KW - interior point methods KW - inexact Newton methods Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6809 ER - TY - GEN A1 - Weiser, Martin T1 - Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations N2 - 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. T3 - ZIB-Report - 07-45 KW - reaction-diffusion equations KW - travelling waves KW - nonlinear scaling KW - discretization error Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10493 SN - 1438-0064 ER - TY - GEN A1 - Schenk, Olaf A1 - Wächter, Andreas A1 - Weiser, Martin T1 - Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization N2 - 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. T3 - ZIB-Report - 07-32 KW - nonconvex constrained optimization KW - interior-point method KW - inertia KW - multilevel incomplete factorization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10314 SN - 1438-0064 ER - TY - GEN A1 - Griesse, Roland A1 - Weiser, Martin T1 - On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control N2 - This paper is concerned with the sensitivities of function space oriented interior point approximations in parameter dependent problems. For an abstract setting that covers control constrained optimal control problems, the convergence of interior point sensitivities to the sensitivities of the optimal solution is shown. Error bounds for $L_q$ norms are derived and illustrated with numerical examples. T3 - ZIB-Report - 05-44 KW - interior point methods KW - parametric sensitivity KW - optimal control Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8773 ER - TY - GEN A1 - Weiser, Martin A1 - Hubig, Michael A1 - Shanmugam Subramaniam, Jayant T1 - Reconstructing Ambient Temperature Changes in Death Time Estimation with a Bayesian Double-Exponential Approach T2 - Zenodo N2 - Code and data for the reconstruction of ambient temperature drop in time of death estimation We provide Octave code and temperature measurement data for - empirircally estimating thermal sensor likelihood - estimating time and amplitude of a single sudden ambient temperature drop from temperature measurement data in two thermally different compartments. Y1 - 2025 U6 - https://doi.org/10.5281/zenodo.17702240 ER - TY - GEN A1 - Villani, Paolo A1 - Weiser, Martin T1 - Adaptive Gaussian process regression for inverse problems. ALGORITMY 2024 N2 - This submission contains the code used for the proceedings paper for ALGORITMY 2024, concerning surrogate model-based inverse problems. Version 2 modified plot appearances and fixed some minor typos. Y1 - 2024 ER - TY - CHAP A1 - Semler, Phillip A1 - Weiser, Martin ED - Fackeldey, Konstantin ED - Kannan, Aswin ED - Pokutta, Sebastian ED - Sharma, Kartikey ED - Walter, Daniel ED - Walther, Andrea ED - Weiser, Martin T1 - Adaptive gradient-enhanced Gaussian process surrogates for inverse problems T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 N2 - Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational budget. We address not only the choice of evaluation points but also of required simulation accuracy, both of values and gradients of the forward model. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs as well as a clear benefit of including gradient information into the surrogate training. Y1 - 2025 U6 - https://doi.org/10.1515/9783111376776-005 SP - 59 EP - 78 PB - De Gruyter ER - TY - CHAP A1 - Villani, Paolo A1 - Unger, Jörg F. A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Bayesian inverse problems T2 - Proceedings of the Conference Algoritmy 2024 N2 - We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems. Y1 - 2024 SP - 214 EP - 224 ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - A Bayesian Framework for Simulation-based Digital Twins of Bridges JF - EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability N2 - Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management. Y1 - 2023 U6 - https://doi.org/10.1002/cepa.2177 VL - 6 IS - 5 SP - 734 EP - 740 ER - TY - CHAP A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins T2 - 5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering N2 - In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed. Y1 - 2023 UR - https://2023.uncecomp.org/proceedings/pdf/19795.pdf SP - 1 EP - 15 ER - TY - JOUR A1 - Maier, Kristina A1 - Weiser, Martin A1 - Conrad, Tim T1 - Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology JF - Proceedings of the Royal Society A N2 - This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of PDEs and the computational efficiency of ODEs, the model enables rapid evaluation of public health interventions. Applied to synthetic environments and real-world scenarios in Lombardy, Italy, and Berlin, Germany, the model highlights how interactions between PDE and ODE regions affect infection dynamics, especially in high-density areas. Key findings reveal that the placement of model boundaries in densely populated regions can lead to inaccuracies in infection spread, suggesting that boundaries should be positioned in areas of lower population density to better reflect transmission dynamics. Additionally, regions with low population density hinder infection flow, indicating a need for incorporating, e.g., jumps in the model to enhance its predictive capabilities. Results indicate that the hybrid model achieves a balance between computational speed and accuracy, making it a valuable tool for policymakers in real-time decision-making and scenario analysis in epidemiology and potentially in other fields requiring similar modeling approaches. Y1 - 2025 U6 - https://doi.org/10.1098/rspa.2024.0421 VL - 481 IS - 2306 PB - Royal Society ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - Model bias identification for Bayesian calibration of stochastic digital twins of bridges JF - Applied Stochastic Models in Business and Industry N2 - Simulation-based digital twins must provide accurate, robust and reliable digital representations of their physical counterparts. Quantifying the uncertainty in their predictions plays, therefore, a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must be then carefully implemented. When applied to complex standing structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aiming to infer the model parameters often fail at compensating for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for such models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of such approaches in the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error and provides further insight into the system by including additional pre-existing information without modifying the computational model. Y1 - 2024 U6 - https://doi.org/10.1002/asmb.2897 VL - 41 IS - 3 ER - TY - JOUR A1 - Göbel, Fritz A1 - Huynh, Ngoc Mai Monica A1 - Chegini, Fatemeh A1 - Pavarino, Luca A1 - Weiser, Martin A1 - Scacchi, Simone A1 - Anzt, Hartwig T1 - A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions JF - SIAM J. Sci. Comput. N2 - We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments. Y1 - 2025 ER -