@article{FischerGoetschelWeiser2018, author = {Fischer, Lisa and G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy data compression reduces communication time in hybrid time-parallel integrators}, volume = {19}, journal = {Comput. Vis. Sci.}, number = {1}, doi = {10.1007/s00791-018-0293-2}, pages = {19 -- 30}, year = {2018}, 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{DeuflhardKornhuberSanderetal.2014, author = {Deuflhard, Peter and Kornhuber, Ralf and Sander, Oliver and Schiela, Anton and Weiser, Martin}, title = {Mathematics cures virtual patients}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {7 -- 25}, year = {2014}, language = {en} } @article{MoualeuNgangueWeiserEhrigetal.2015, author = {Moualeu-Ngangue, Dany Pascal and Weiser, Martin and Ehrig, Rainald and Deuflhard, Peter}, title = {Optimal control for a tuberculosis model with undetected cases in Cameroon}, volume = {20}, journal = {Communications in Nonlinear Science and Numerical Simulation}, number = {3}, doi = {10.1016/j.cnsns.2014.06.037}, pages = {986 -- 1003}, year = {2015}, abstract = {This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 \% in 10 years.}, language = {en} } @misc{GoetschelWeiserMaierhoferetal.2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, journal = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, editor = {Cardone, Gennaro}, year = {2012}, abstract = {Pulse thermography is a non-destructive testing method based on infrared imaging of transient thermal patterns. Heating the surface of the structure under test for a short period of time generates a non-stationary temperature distribution and thus a thermal contrast between the defect and the sound material. Due to measurement noise, preprocessing of the experimental data is necessary, before reconstruction algorithms can be applied. We propose a decomposition of the measured temperature into Green's function solutions to eliminate noise.}, language = {en} } @article{Weiser2013, author = {Weiser, Martin}, title = {On goal-oriented adaptivity for elliptic optimal control problems}, volume = {28}, journal = {Opt. Meth. Softw.}, number = {13}, pages = {969 -- 992}, year = {2013}, abstract = {The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of interest. Finally, the efficiency of the error estimator and generated meshes are demonstrated on numerical examples.}, language = {en} } @article{DeuflhardSchielaWeiser2012, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, volume = {21}, journal = {Acta Numerica}, pages = {307 -- 378}, year = {2012}, abstract = {This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, a virtual lab, including 3D geometry processing of individual virtual patients had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.}, language = {en} } @misc{GoetschelWeiserSchiela2012, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, journal = {Advances in DUNE}, editor = {Dedner, A. and Flemisch, B. and Kl{\"o}fkorn, R.}, publisher = {Springer}, pages = {101 -- 112}, year = {2012}, abstract = {This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.}, language = {en} } @article{Weiser2015, author = {Weiser, Martin}, title = {Faster SDC convergence on non-equidistant grids by DIRK sweeps}, volume = {55}, journal = {BIT Numerical Mathematics}, number = {4}, doi = {10.1007/s10543-014-0540-y}, pages = {1219 -- 1241}, year = {2015}, abstract = {Spectral deferred correction methods for solving stiff ODEs are known to converge rapidly towards the collocation limit solution on equidistant grids, but show a much less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples.}, language = {en} } @article{WeiserGoetschel2012, author = {Weiser, Martin and G{\"o}tschel, Sebastian}, title = {State Trajectory Compression for Optimal Control with Parabolic PDEs}, volume = {34}, journal = {SIAM J. Sci. Comput.}, number = {1}, doi = {10.1137/11082172X}, pages = {A161 -- A184}, year = {2012}, abstract = {In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.}, language = {en} } @misc{NadobnyWeihrauchWeiseretal.2007, author = {Nadobny, Johanna and Weihrauch, Mirko and Weiser, Martin and Gellermann, Johanna and Wlodarczyk, Waldemar and Budach, Volker and Wust, Peter}, title = {Advances in the Planning and Control of the MR-guided Regional Hyperthermia Applications}, journal = {Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy}, pages = {1010 -- 1013}, year = {2007}, language = {en} } @article{GoetschelWeiser2010, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {State Trajectory Compression in Optimal Control}, volume = {10}, journal = {PAMM}, number = {1}, doi = {10.1002/pamm.201010282}, pages = {579 -- 580}, year = {2010}, abstract = {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.}, language = {en} } @misc{Weiser2010, author = {Weiser, Martin}, title = {Delayed Residual Compensation for Bidomain Equations}, volume = {1281}, journal = {AIP Conference Proceedings}, doi = {10.1063/1.3498495}, pages = {419 -- 422}, year = {2010}, abstract = {The biodomain model of cardioelectric excitation consists of a reaction-diffusion equation, an elliptic algebraic constraint, and a set of pointwise ODEs. Fast reaction enforces small time steps, such that for common mesh sizes the reaction-diffusion equation is easily solved implicitly due to a dominating mass matrix. In contrast, the elliptic constraint does not benefit from small time steps and requires a comparably expensive solution. We propose a delayed residual compensation that improves the solution of the elliptic constraint and thus alleviates the need for long iteration times.}, language = {en} } @misc{WeiserErdmannDeuflhard2010, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, journal = {Progress in Industrial Mathematics at ECMI 2008}, editor = {Wilson, E. and Fitt, A. and Ockendon, H. and Norbury, J.}, publisher = {Springer}, pages = {371 -- 376}, year = {2010}, abstract = {Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.}, language = {en} } @article{WilhelmsSeemannWeiseretal.2010, author = {Wilhelms, Mathias and Seemann, Gunnar and Weiser, Martin and D{\"o}ssel, Olaf}, title = {Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling}, volume = {55}, journal = {Biomed. Engineer.}, doi = {10.1515/BMT.2010.712}, pages = {99 -- 102}, year = {2010}, language = {en} } @misc{WustWeihrauchWeiseretal.2010, author = {Wust, Peter and Weihrauch, Mirko and Weiser, Martin and Gellermann, Johanna and Eisenhardt, Steffen and Chobrok, Thorsten and Budach, Volker}, title = {Optimization of clinical radiofrequency hyperthermia by use of MR-thermography in a hybrid system}, journal = {World Congress on Medical Physics and Biomedical Engineering, September 2009, Munich, Germany}, editor = {D{\"o}ssel, O. and Schlegel, W. and Magjarevic, R.}, publisher = {Springer}, pages = {174 -- 175}, year = {2010}, language = {en} } @article{LubkollSchielaWeiser2014, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An optimal control problem in polyconvex hyperelasticity}, volume = {52}, journal = {SIAM J. Control Opt.}, number = {3}, doi = {10.1137/120876629}, pages = {1403 -- 1422}, year = {2014}, abstract = {We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented.}, language = {en} } @article{GuentherLameckerWeiser2013, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Flexible Shape Matching with Finite Element Based LDDMM}, volume = {105}, journal = {International Journal of Computer Vision}, number = {2}, doi = {10.1007/s11263-012-0599-3}, pages = {128 -- 143}, year = {2013}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @misc{GuentherLameckerWeiser2011, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, journal = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, editor = {Pennec, X. and Joshi, S. and Nielsen, M.}, pages = {1 -- 14}, year = {2011}, abstract = {We consider Large Deformation Diffeomorphic Metric Mapping of general \$m\$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete \$m\$-current attributes.}, language = {en} } @misc{SchielaWeiser2010, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, journal = {Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009)}, editor = {Diehl, M. and Glineur, F. and Jarlebring, E. and Michiels, W.}, publisher = {Springer}, pages = {419 -- 428}, year = {2010}, abstract = {We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.}, language = {en} } @article{WeiserRoelligArndtetal.2010, author = {Weiser, Martin and R{\"o}llig, Mathias and Arndt, Ralf and Erdmann, Bodo}, title = {Development and test of a numerical model for pulse thermography in civil engineering}, volume = {46}, journal = {Heat and Mass Transfer}, number = {11-12}, pages = {1419 -- 1428}, year = {2010}, abstract = {Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.}, language = {en} }