@article{DeuflhardWeiserSeebass2000, author = {Deuflhard, Peter and Weiser, Martin and Seebass, Martin}, title = {A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning}, series = {Comput. Vis. Sci.}, volume = {3}, journal = {Comput. Vis. Sci.}, pages = {115 -- 120}, year = {2000}, language = {en} } @article{HammerschmidtWeiserSantiagoetal., author = {Hammerschmidt, Martin and Weiser, Martin and Santiago, Xavier Garcia and Zschiedrich, Lin and Bodermann, Bernd and Burger, Sven}, title = {Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion}, series = {Proc. SPIE}, volume = {10330}, journal = {Proc. SPIE}, doi = {10.1117/12.2270596}, pages = {1033004}, language = {en} } @article{HammerschmidtSchneiderSantiagoetal., author = {Hammerschmidt, Martin and Schneider, Philipp-Immanuel and Santiago, Xavier Garcia and Zschiedrich, Lin and Weiser, Martin and Burger, Sven}, title = {Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization}, series = {Proc. SPIE}, volume = {10694}, journal = {Proc. SPIE}, doi = {10.1117/12.2315468}, pages = {1069407}, language = {en} } @article{SchenkWaechterWeiser2008, author = {Schenk, O. and W{\"a}chter, Andreas and Weiser, Martin}, title = {Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization}, series = {SIAM J. Sci. Comp.}, volume = {31}, journal = {SIAM J. Sci. Comp.}, number = {2}, pages = {939 -- 960}, year = {2008}, language = {en} } @article{WeiserDeuflhard2007, author = {Weiser, Martin and Deuflhard, Peter}, title = {Inexact central path following algorithms for optimal control problems}, series = {SIAM J. Control Opt.}, volume = {46}, journal = {SIAM J. Control Opt.}, number = {3}, pages = {792 -- 815}, year = {2007}, language = {en} } @article{SchielaWeiser2008, author = {Schiela, Anton and Weiser, Martin}, title = {Superlinear convergence of the Control Reduced Interior Point Method for PDE Constrained Optimization}, series = {Computational Optimization and Applications}, volume = {39}, journal = {Computational Optimization and Applications}, number = {3}, pages = {369 -- 393}, year = {2008}, language = {en} } @article{GaenzlerVolkweinWeiser2006, author = {G{\"a}nzler, Tobias and Volkwein, S. and Weiser, Martin}, title = {SQP methods for parameter identification problems arising in hyperthermia}, series = {Optim. Methods Softw.}, volume = {21}, journal = {Optim. Methods Softw.}, number = {6}, pages = {869 -- 887}, year = {2006}, language = {en} } @article{GellermannWeihrauchChoetal.2006, author = {Gellermann, Johanna and Weihrauch, Mirko and Cho, C. and Wlodarczyk, Waldemar and F{\"a}hling, Horst and Felix, Roland and Budach, Volker and Weiser, Martin and Nadobny, Johanna and Wust, Peter}, title = {Comparison of MR-thermography and planning calculations in phantoms}, series = {Medical Physics}, volume = {33}, journal = {Medical Physics}, pages = {3912 -- 3920}, year = {2006}, language = {en} } @inproceedings{DeuflhardWeiser1998, author = {Deuflhard, Peter and Weiser, Martin}, title = {Global inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996.}, volume = {3}, booktitle = {Multigrid methods V. proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996.}, editor = {et al. Hackbusch, Wolfgang}, publisher = {Berlin: Springer}, pages = {71 -- 89}, year = {1998}, language = {en} } @book{DeuflhardWeiser2011, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3}, publisher = {de Gruyter, Berlin}, year = {2011}, language = {de} } @book{DeuflhardWeiser2012, author = {Deuflhard, Peter and Weiser, Martin}, title = {Adaptive numerical solution of PDEs}, publisher = {de Gruyter}, address = {Berlin}, year = {2012}, language = {en} } @article{DeuflhardWeiserZachow2006, author = {Deuflhard, Peter and Weiser, Martin and Zachow, Stefan}, title = {Mathematics in Facial Surgery}, series = {AMS Notices}, volume = {53}, journal = {AMS Notices}, number = {9}, pages = {1012 -- 1016}, year = {2006}, language = {en} } @incollection{ZachowWeiserHegeetal.2005, author = {Zachow, Stefan and Weiser, Martin and Hege, Hans-Christian and Deuflhard, Peter}, title = {Soft Tissue Prediction in Computer Assisted Maxillofacial Surgery Planning}, series = {Biomechanics Applied to Computer Assisted Surgery}, booktitle = {Biomechanics Applied to Computer Assisted Surgery}, editor = {Payan, Y.}, publisher = {Research Signpost}, pages = {277 -- 298}, year = {2005}, language = {en} } @incollection{ZachowWeiserDeuflhard2008, author = {Zachow, Stefan and Weiser, Martin and Deuflhard, Peter}, title = {Modellgest{\"u}tzte Operationsplanung in der Kopfchirurgie}, series = {Modellgest{\"u}tzte Therapie}, booktitle = {Modellgest{\"u}tzte Therapie}, editor = {Niederlag, Wolfgang and Lemke, Heinz and Meixensberger, J{\"u}rgen and Baumann, Michael}, publisher = {Health Academy}, pages = {140 -- 156}, year = {2008}, language = {en} } @article{PruefertTroeltzschWeiser2008, author = {Pr{\"u}fert, Uwe and Tr{\"o}ltzsch, Fredi and Weiser, Martin}, title = {The convergence of an interior point method for an elliptic control problem with mixed control-state constraints}, series = {Comput. Optim. Appl.}, volume = {39}, journal = {Comput. Optim. Appl.}, number = {2}, pages = {183 -- 218}, year = {2008}, language = {en} } @misc{DeuflhardKornhuberSanderetal., author = {Deuflhard, Peter and Kornhuber, Ralf and Sander, Oliver and Schiela, Anton and Weiser, Martin}, title = {Mathematics cures virtual patients}, series = {MATHEON-Mathematics for Key Technologies}, 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}, language = {en} } @article{MoualeuNgangueWeiserEhrigetal., 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}, series = {Communications in Nonlinear Science and Numerical Simulation}, volume = {20}, journal = {Communications in Nonlinear Science and Numerical Simulation}, number = {3}, doi = {10.1016/j.cnsns.2014.06.037}, pages = {986 -- 1003}, 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} } @article{MoldenhauerWeiserZachow, author = {Moldenhauer, Marian and Weiser, Martin and Zachow, Stefan}, title = {Adaptive Algorithms for Optimal Hip Implant Positioning}, series = {PAMM}, volume = {17}, journal = {PAMM}, number = {1}, doi = {10.1002/pamm.201710071}, pages = {203 -- 204}, abstract = {In an aging society where the number of joint replacements rises, it is important to also increase the longevity of implants. In particular hip implants have a lifetime of at most 15 years. This derives primarily from pain due to implant migration, wear, inflammation, and dislocation, which is affected by the positioning of the implant during the surgery. Current joint replacement practice uses 2D software tools and relies on the experience of surgeons. Especially the 2D tools fail to take the patients' natural range of motion as well as stress distribution in the 3D joint induced by different daily motions into account. Optimizing the hip joint implant position for all possible parametrized motions under the constraint of a contact problem is prohibitively expensive as there are too many motions and every position change demands a recalculation of the contact problem. For the reduction of the computational effort, we use adaptive refinement on the parameter domain coupled with the interpolation method of Kriging. A coarse initial grid is to be locally refined using goal-oriented error estimation, reducing locally high variances. This approach will be combined with multi-grid optimization such that numerical errors are reduced.}, language = {en} } @article{FischerGoetschelWeiser, author = {Fischer, Lisa and G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy data compression reduces communication time in hybrid time-parallel integrators}, series = {Comput. Vis. Sci.}, volume = {19}, journal = {Comput. Vis. Sci.}, number = {1}, doi = {10.1007/s00791-018-0293-2}, pages = {19 -- 30}, 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{GoetschelWeiserMaierhoferetal., author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina}, title = {Data Enhancement for Active Thermography}, series = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, journal = {E-book Proceedings, 11th International Conference on Quantitative Infrared Thermography, Naples}, editor = {Cardone, Gennaro}, 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{GoetschelWeiserSchiela, author = {G{\"o}tschel, Sebastian and Weiser, Martin and Schiela, Anton}, title = {Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox}, series = {Advances in DUNE}, journal = {Advances in DUNE}, editor = {Dedner, A. and Flemisch, B. and Kl{\"o}fkorn, R.}, publisher = {Springer}, pages = {101 -- 112}, 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{Weiser, author = {Weiser, Martin}, title = {Faster SDC convergence on non-equidistant grids by DIRK sweeps}, series = {BIT Numerical Mathematics}, volume = {55}, journal = {BIT Numerical Mathematics}, number = {4}, doi = {10.1007/s10543-014-0540-y}, pages = {1219 -- 1241}, 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{WeiserGoetschel, author = {Weiser, Martin and G{\"o}tschel, Sebastian}, title = {State Trajectory Compression for Optimal Control with Parabolic PDEs}, series = {SIAM J. Sci. Comput.}, volume = {34}, journal = {SIAM J. Sci. Comput.}, number = {1}, doi = {10.1137/11082172X}, pages = {A161 -- A184}, 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{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Direct LDDMM of Discrete Currents with Adaptive Finite Elements}, series = {Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability}, 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}, 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{SchielaWeiser, author = {Schiela, Anton and Weiser, Martin}, title = {Barrier methods for a control problem from hyperthermia treatment planning}, series = {Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009)}, 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}, 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., 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}, series = {Heat and Mass Transfer}, volume = {46}, journal = {Heat and Mass Transfer}, number = {11-12}, pages = {1419 -- 1428}, abstract = {Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.}, language = {en} } @misc{WeiserErdmannDeuflhard, author = {Weiser, Martin and Erdmann, Bodo and Deuflhard, Peter}, title = {On Efficiency and Accuracy in Cardioelectric Simulation}, series = {Progress in Industrial Mathematics at ECMI 2008}, 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}, 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., 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}, series = {Biomed. Engineer.}, volume = {55}, journal = {Biomed. Engineer.}, doi = {10.1515/BMT.2010.712}, pages = {99 -- 102}, language = {en} } @misc{WustWeihrauchWeiseretal., 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}, series = {World Congress on Medical Physics and Biomedical Engineering, September 2009, Munich, Germany}, 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}, language = {en} } @article{GoetschelWeiser, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {State Trajectory Compression in Optimal Control}, series = {PAMM}, volume = {10}, journal = {PAMM}, number = {1}, doi = {10.1002/pamm.201010282}, pages = {579 -- 580}, 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{Weiser, author = {Weiser, Martin}, title = {Delayed Residual Compensation for Bidomain Equations}, series = {AIP Conference Proceedings}, volume = {1281}, journal = {AIP Conference Proceedings}, doi = {10.1063/1.3498495}, pages = {419 -- 422}, 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} } @article{GuentherLameckerWeiser, author = {G{\"u}nther, Andreas and Lamecker, Hans and Weiser, Martin}, title = {Flexible Shape Matching with Finite Element Based LDDMM}, series = {International Journal of Computer Vision}, volume = {105}, journal = {International Journal of Computer Vision}, number = {2}, doi = {10.1007/s11263-012-0599-3}, pages = {128 -- 143}, 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} } @article{Weiser, author = {Weiser, Martin}, title = {On goal-oriented adaptivity for elliptic optimal control problems}, series = {Opt. Meth. Softw.}, volume = {28}, journal = {Opt. Meth. Softw.}, number = {13}, pages = {969 -- 992}, 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{DeuflhardSchielaWeiser, author = {Deuflhard, Peter and Schiela, Anton and Weiser, Martin}, title = {Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia}, series = {Acta Numerica}, volume = {21}, journal = {Acta Numerica}, pages = {307 -- 378}, 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} } @article{LubkollSchielaWeiser, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An optimal control problem in polyconvex hyperelasticity}, series = {SIAM J. Control Opt.}, volume = {52}, journal = {SIAM J. Control Opt.}, number = {3}, doi = {10.1137/120876629}, pages = {1403 -- 1422}, 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{LubkollSchielaWeiser, author = {Lubkoll, Lars and Schiela, Anton and Weiser, Martin}, title = {An affine covariant composite step method for optimization with PDEs as equality constraints}, series = {Optimization Methods and Software}, volume = {32}, journal = {Optimization Methods and Software}, number = {5}, doi = {10.1080/10556788.2016.1241783}, pages = {1132 -- 1161}, 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{NadobnyWeihrauchWeiseretal., 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}, series = {Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy}, journal = {Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy}, pages = {1010 -- 1013}, language = {en} } @article{PowellWeiser, author = {Powell, Gary and Weiser, Martin}, title = {Views, A new form of container adaptors}, series = {C/C++ Users Journal}, volume = {18}, journal = {C/C++ Users Journal}, number = {4}, pages = {40 -- 51}, 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} } @inproceedings{MuellerGoetschelWeiseretal., author = {M{\"u}ller, Jan and G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane}, title = {Thermografie mit optimierter Anregung f{\"u}r die quantitative Untersuchung von Delaminationen in kohlenstofffaserverst{\"a}rkten Kunststoffen}, series = {NDT.net Proc. DGZfP 2017}, booktitle = {NDT.net Proc. DGZfP 2017}, abstract = {Da kohlenstofffaserverst{\"a}rkte Kunststoffe (CFK) in anspruchsvollen sicherheitsrelevanten Einsatzgebieten wie im Automobilbau und in der Luftfahrt eingesetzt werden, besteht ein zunehmender Bedarf an zerst{\"o}rungsfreien Pr{\"u}fmethoden. Ziel ist die Gew{\"a}hrleistung der Sicherheit und Zuverl{\"a}ssigkeit der eingesetzten Bauteile. Aktive Thermografieverfahren erm{\"o}glichen die effiziente Pr{\"u}fung großer Fl{\"a}chen mit hoher Aufl{\"o}sung in wenigen Arbeitsschritten. Ein wichtiges Teilgebiet der Pr{\"u}fungen ist die Ortung und Charakterisierung von Delaminationen, die sowohl bereits in der Fertigung als auch w{\"a}hrend der Nutzung eines Bauteils auftreten k{\"o}nnen, und dessen strukturelle Integrit{\"a}t schw{\"a}chen. ;In diesem Beitrag werden CFK-Strukturen mit k{\"u}nstlichen und nat{\"u}rlichen Delaminationen mit Hilfe unterschiedlich zeitlich modulierter Strahlungsquellen experimentell untersucht. Verwendet werden dabei Anregungen mit Blitzlampen und mit frequenzmodulierten Halogenlampen. Mittels Filterfunktionen im Zeit- und Frequenzbereich wird das Kontrast-zu-Rausch-Verh{\"a}ltnis (CNR) der detektierten Fehlstellen optimiert. Verglichen werden anschließend die Nachweisempfindlichkeit, das CNR und die Ortsaufl{\"o}sung der zu charakterisierenden Delaminationen f{\"u}r die unterschiedlichen Anregungs- und Auswertungstechniken. Erg{\"a}nzt werden die Experimente durch numerische Simulationen des dreidimensionalen W{\"a}rmetransportes.}, language = {de} } @article{TierneyMiraReinholdetal., author = {Tierney, Nicholas J. and Mira, Antonietta and Reinhold, J. Jost and Weiser, Martin and Burkart, Roman and Benvenuti, Claudio and Auricchio, Angelo}, title = {Novel relocation methods for automatic external defibrillator improve out-of-hospital cardiac arrest coverage under limited resources}, series = {Resuscitation}, journal = {Resuscitation}, number = {125}, doi = {10.1016/j.resuscitation.2018.01.055}, pages = {83 -- 89}, abstract = {Background Mathematical optimisation models have recently been applied to identify ideal Automatic External Defibrillator (AED) locations that maximise coverage of Out of Hospital Cardiac Arrest (OHCA). However, these fixed location models cannot relocate existing AEDs in a flexible way, and have nearly exclusively been applied to urban regions. We developed a flexible location model for AEDs, compared its performance to existing fixed location and population models, and explored how these perform across urban and rural regions. Methods Optimisation techniques were applied to AED deployment and OHCA coverage was assessed. A total of 2802 geolocated OHCAs occurred in Canton Ticino, Switzerland, from January 1st 2005 to December 31st 2015. Results There were 719 AEDs in Canton Ticino. 635 (23\%) OHCA events occurred within 100m of an AED, with 306 (31\%) in urban, and 329 (18\%) in rural areas. Median distance from OHCA events to the nearest AED was 224m (168m urban vs. 269m rural). Flexible location models performed better than fixed location and population models, with the cost to deploy 20 new AEDs instead relocating 171 existing AEDs to new locations, improving OHCA coverage to 38\%, compared to 26\% using fixed models, and 24\% with the population based model. Conclusions Optimisation models for AEDs placement are superior to population models and should be strongly considered by communities when selecting areas for AED deployment. Compared to other models, flexible location models increase overall OHCA coverage, and decreases the distance to nearby AEDs, even in rural areas, while saving significant financial resources.}, language = {en} } @article{WeiserErdmannSchenkletal., 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}, series = {Heat and Mass Transfer}, volume = {54}, journal = {Heat and Mass Transfer}, number = {9}, publisher = {Springer}, doi = {10.1007/s00231-018-2324-4}, pages = {2815 -- 2826}, 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.}, language = {en} } @article{WeiserGhosh, author = {Weiser, Martin and Ghosh, Sunayana}, title = {Theoretically optimal inexact SDC methods}, series = {Communications in Applied Mathematics and Computational Science}, journal = {Communications in Applied Mathematics and Computational Science}, number = {13-1}, doi = {10.2140/camcos.2018.13.53}, pages = {53 -- 86}, abstract = {In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples.}, language = {en} } @inproceedings{GoetschelHoehneKolkoorietal., 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}, series = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, booktitle = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, language = {en} } @inproceedings{GoetschelMaierhoferMuelleretal., author = {G{\"o}tschel, Sebastian and Maierhofer, Christiane and M{\"u}ller, Jan and Rothbart, Nick and Weiser, Martin}, title = {Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites}, series = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, booktitle = {Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)}, language = {en} } @inproceedings{MuellerGoetschelMaierhoferetal., author = {M{\"u}ller, Jan and G{\"o}tschel, Sebastian and Maierhofer, Christiane and Weiser, Martin}, title = {Determining the material parameters for the reconstruction of defects in carbon fiber reinforced polymers from data measured by flash thermography}, series = {AIP Conference Proceedings}, volume = {1806}, booktitle = {AIP Conference Proceedings}, doi = {10.1063/1.4974671}, language = {en} } @article{WeiserSchiela2004, author = {Weiser, Martin and Schiela, Anton}, title = {Function space interior point methods for PDE constrained optimization}, series = {PAMM}, volume = {4}, journal = {PAMM}, number = {1}, pages = {43 -- 46}, year = {2004}, language = {en} } @article{VolkweinWeiser2002, author = {Volkwein, S. and Weiser, Martin}, title = {Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian SQP Methods}, series = {SIAM J. Control Optim.}, volume = {41}, journal = {SIAM J. Control Optim.}, number = {3}, pages = {875 -- 899}, year = {2002}, language = {en} } @techreport{VolkweinWeiser2004, author = {Volkwein, S. and Weiser, Martin}, title = {Optimality Conditions for a Constrained Parameter Identification Problem in Hyperthermia}, number = {305}, publisher = {University of Graz, SFB F003}, address = {Graz, Austria}, year = {2004}, language = {en} } @article{WeiserGaenzlerSchiela2007, author = {Weiser, Martin and G{\"a}nzler, Tobias and Schiela, Anton}, title = {A control reduced primal interior point method for a class of control constrained optimal control problems}, series = {Comput. Optim. Appl.}, volume = {41}, journal = {Comput. Optim. Appl.}, number = {1}, pages = {127 -- 145}, year = {2007}, language = {en} } @article{WeiserSchielaDeuflhard2005, author = {Weiser, Martin and Schiela, Anton and Deuflhard, Peter}, title = {Asymptotic Mesh Independence of Newton's Method Revisited}, series = {SIAM J. Num. Anal.}, volume = {42}, journal = {SIAM J. Num. Anal.}, number = {5}, pages = {1830 -- 1845}, year = {2005}, language = {en} } @article{Weiser2009, author = {Weiser, Martin}, title = {Optimization and Identification in Regional Hyperthermia}, series = {Int. J. Appl. Electromagn. and Mech.}, volume = {30}, journal = {Int. J. Appl. Electromagn. and Mech.}, pages = {265 -- 275}, year = {2009}, language = {en} } @article{Weiser2009, author = {Weiser, Martin}, title = {Pointwise Nonlinear Scaling for Reaction-Diffusion Equations}, series = {Appl. Num. Math.}, volume = {59}, journal = {Appl. Num. Math.}, number = {8}, pages = {1858 -- 1869}, year = {2009}, language = {en} } @article{WeiserDeuflhardErdmann2007, author = {Weiser, Martin and Deuflhard, Peter and Erdmann, Bodo}, title = {Affine conjugate adaptive Newton methods for nonlinear elastomechanics}, series = {Opt. Meth. Softw.}, volume = {22}, journal = {Opt. Meth. Softw.}, number = {3}, pages = {413 -- 431}, year = {2007}, language = {en} } @article{WeihrauchWustWeiseretal.2007, author = {Weihrauch, Mirko and Wust, Peter and Weiser, Martin and Nadobny, Johanna and Eisenhardt, Steffen and Budach, Volker and Gellermann, Johanna}, title = {Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system}, series = {Medical Physics}, volume = {34}, journal = {Medical Physics}, number = {12}, pages = {4717 -- 4725}, year = {2007}, language = {en} } @article{Weiser2005, author = {Weiser, Martin}, title = {Interior point methods in function space}, series = {SIAM J. Control Optimization}, volume = {44}, journal = {SIAM J. Control Optimization}, number = {5}, pages = {1766 -- 1786}, year = {2005}, language = {en} } @article{SchenklMuggenthalerHubigetal.2017, author = {Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Erdmann, Bodo and Weiser, Martin and Zachow, Stefan and Heinrich, Andreas and G{\"u}ttler, Felix Victor and Teichgr{\"a}ber, Ulf and Mall, Gita}, title = {Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis}, series = {International Journal of Legal Medicine}, volume = {131}, journal = {International Journal of Legal Medicine}, number = {3}, doi = {doi:10.1007/s00414-016-1523-0}, pages = {699 -- 712}, year = {2017}, abstract = {Temperature based death time estimation is based either on simple phenomenological models of corpse cooling or on detailed physical heat transfer models. The latter are much more complex, but allow a higher accuracy of death time estimation as in principle all relevant cooling mechanisms can be taken into account. Here, a complete work flow for finite element based cooling simulation models is presented. The following steps are demonstrated on CT-phantoms: • CT-scan • Segmentation of the CT images for thermodynamically relevant features of individual geometries • Conversion of the segmentation result into a Finite Element (FE) simulation model • Computation of the model cooling curve • Calculation of the cooling time For the first time in FE-based cooling time estimation the steps from the CT image over segmentation to FE model generation are semi-automatically performed. The cooling time calculation results are compared to cooling measurements performed on the phantoms under controlled conditions. In this context, the method is validated using different CTphantoms. Some of the CT phantoms thermodynamic material parameters had to be experimentally determined via independent experiments. Moreover the impact of geometry and material parameter uncertainties on the estimated cooling time is investigated by a sensitivity analysis.}, language = {en} } @book{Weiser, author = {Weiser, Martin}, title = {Inside Finite Elements}, publisher = {De Gruyter}, abstract = {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.}, language = {en} } @article{WeiserZachowDeuflhard2010, author = {Weiser, Martin and Zachow, Stefan and Deuflhard, Peter}, title = {Craniofacial Surgery Planning Based on Virtual Patient Models}, series = {it - Information Technology}, volume = {52}, journal = {it - Information Technology}, number = {5}, publisher = {Oldenbourg Verlagsgruppe}, doi = {10.1524/itit.2010.0600}, pages = {258 -- 263}, year = {2010}, language = {en} } @inproceedings{GoetschelTycowiczPolthieretal., author = {G{\"o}tschel, Sebastian and Tycowicz, Christoph von and Polthier, Konrad and Weiser, Martin}, title = {Reducing Memory Requirements in Scientific Computing and Optimal Control}, series = {Multiple Shooting and Time Domain Decomposition Methods}, booktitle = {Multiple Shooting and Time Domain Decomposition Methods}, editor = {Carraro, T. and Geiger, M. and Koerkel, S. and Rannacher, R.}, publisher = {Springer}, pages = {263 -- 287}, language = {en} } @article{GoetschelNagaiahKunischetal., author = {G{\"o}tschel, Sebastian and Nagaiah, Chamakuri and Kunisch, Karl and Weiser, Martin}, title = {Lossy Compression in Optimal Control of Cardiac Defibrillation}, series = {J. Sci. Comput.}, volume = {60}, journal = {J. Sci. Comput.}, number = {1}, doi = {10.1007/s10915-013-9785-x}, pages = {35 -- 59}, abstract = {This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.}, language = {en} } @article{GoetschelWeiser, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Lossy Compression for PDE-constrained Optimization: Adaptive Error Control}, series = {Comput. Optim. Appl.}, volume = {62}, journal = {Comput. Optim. Appl.}, number = {1}, publisher = {Springer}, pages = {131 -- 155}, abstract = {For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the ad-joint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results which are accurate enough, in many case very fine discretizations in time and space are necessary, which leads to a significant amount of data to be stored and transmitted to mass storage. Lossy compression methods were developed to overcome the storage problem by reducing the accuracy of the stored trajectories. The inexact data induces errors in the reduced gradient and reduced Hessian. In this paper, we analyze the influence of such a lossy trajectory compression method on Newton-CG methods for optimal control of parabolic PDEs and design an adaptive strategy for choosing appropriate quantization tolerances.}, language = {en} } @inproceedings{WeiserScacchi, author = {Weiser, Martin and Scacchi, Simone}, title = {Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation}, series = {G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014}, booktitle = {G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014}, publisher = {Springer}, doi = {10.1007/978-3-319-23413-7_42}, pages = {321 -- 328}, 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} } @article{GoetschelWeiserMaierhoferetal., author = {G{\"o}tschel, Sebastian and Weiser, Martin and Maierhofer, Christiane and Richter, Regina and R{\"o}llig, Mathias}, title = {Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography}, series = {Nondestructive Testing of Materials and Structures}, volume = {6}, journal = {Nondestructive Testing of Materials and Structures}, pages = {83 -- 89}, language = {en} } @inproceedings{KrauseWeiser, author = {Krause, Rolf and Weiser, Martin}, title = {Multilevel augmented Lagrangian solvers for overconstrained contact formulations}, series = {ESAIM: ProcS}, volume = {71}, booktitle = {ESAIM: ProcS}, doi = {10.1051/proc/202171175}, pages = {175 -- 184}, abstract = {Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.}, language = {en} } @book{DeuflhardWeiser, author = {Deuflhard, Peter and Weiser, Martin}, title = {Numerische Mathematik 3. Adaptive L{\"o}sung partieller Differentialgleichungen}, edition = {2}, publisher = {de Gruyter}, isbn = {978-3-11-069168-9}, doi = {10.1515/9783110689655}, pages = {456}, language = {de} } @article{WeiserFreytagErdmannetal., 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}, series = {Inverse Problems}, volume = {34}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/aae7a5}, pages = {125005}, 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} } @article{GoetschelWeiser, author = {G{\"o}tschel, Sebastian and Weiser, Martin}, title = {Compression Challenges in Large Scale Partial Differential Equation Solvers}, series = {Algorithms}, volume = {12}, journal = {Algorithms}, number = {9}, doi = {10.3390/a12090197}, pages = {197}, abstract = {Solvers for partial differential equations (PDEs) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that need to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to the relatively small arithmetic intensity, and increasingly 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 over the recent decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to the main memory. We illustrate concepts for particular methods, with examples, and give references to alternatives.}, language = {en} } @article{GoetschelSchielaWeiser, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 - a Flexible Finite Element Toolbox}, series = {Computers and Mathematics with Applications}, volume = {81}, journal = {Computers and Mathematics with Applications}, doi = {10.1016/j.camwa.2020.02.011}, pages = {444 -- 458}, 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 \textsc{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} } @article{AlhaddadFoerstnerGrothetal., author = {Alhaddad, Samer and F{\"o}rstner, Jens and Groth, Stefan and Gr{\"u}newald, Daniel and Grynko, Yevgen and Hannig, Frank and Kenter, Tobias and Pfreundt, Franz-Josef and Plessl, Christian and Schotte, Merlind and Steinke, Thomas and Teich, J{\"u}rgen and Weiser, Martin and Wende, Florian}, title = {HighPerMeshes - A Domain-Specific Language for Numerical Algorithms on Unstructured Grids}, series = {Euro-Par 2020: Parallel Processing Workshops.}, journal = {Euro-Par 2020: Parallel Processing Workshops.}, publisher = {Springer}, doi = {10.1007/978-3-030-71593-9_15}, pages = {185 -- 196}, abstract = {Solving partial differential equations on unstructured grids is a cornerstone of engineering and scientific computing. Nowadays, heterogeneous parallel platforms with CPUs, GPUs, and FPGAs enable energy-efficient and computationally demanding simulations. We developed the HighPerMeshes C++-embedded Domain-Specific Language (DSL) for bridging the abstraction gap between the mathematical and algorithmic formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different parallel programming and runtime models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPer-Meshes DSL, and demonstrate its usage with three examples, a Poisson and monodomain problem, respectively, solved by the continuous finite element method, and the discontinuous Galerkin method for Maxwell's equation. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters is presented. Finally, the achievable performance and scalability are demonstrated for a typical example problem on a multi-core CPU cluster.}, language = {en} } @article{CheginiKopanicakovaKrauseetal., author = {Chegini, Fatemeh and Kopanicakova, Alena and Krause, Rolf and Weiser, Martin}, title = {Efficient Identification of Scars using Heterogeneous Model Hierarchies}, series = {EP Europace}, volume = {23}, journal = {EP Europace}, doi = {10.1093/europace/euaa402}, pages = {i113 -- i122}, abstract = {Aims. Detection and quantification of myocardial scars are helpful both for diagnosis of heart diseases and for building personalized simulation models. Scar tissue is generally charac­terized by a different conduction of electrical excitation. We aim at estimating conductivity-related parameters from endocardial mapping data, in particular the conductivity tensor. Solving this inverse problem requires computationally expensive monodomain simulations on fine discretizations. Therefore, we aim at accelerating the estimation using a multilevel method combining electrophysiology models of different complexity, namely the mono­domain and the eikonal model. Methods. Distributed parameter estimation is performed by minimizing the misfit between simulated and measured electrical activity on the endocardial surface, subject to the mono­domain model and regularization, leading to a constrained optimization problem. We formulate this optimization problem, including the modeling of scar tissue and different regularizations, and design an efficient iterative solver. We consider monodomain grid hierarchies and monodomain-eikonal model hierarchies in a recursive multilevel trust-region method. Results. From several numerical examples, both the efficiency of the method and the estimation quality, depending on the data, are investigated. The multilevel solver is significantly faster than a comparable single level solver. Endocardial mapping data of realistic density appears to be just sufficient to provide quantitatively reasonable estimates of location, size, and shape of scars close to the endocardial surface. Conclusion. In several situations, scar reconstruction based on eikonal and monodomain models differ significantly, suggesting the use of the more accurate but more expensive monodomain model for this purpose. Still, eikonal models can be utilized to accelerate the computations considerably, enabling the use of complex electrophysiology models for estimating myocardial scars from endocardial mapping data.}, language = {en} } @article{CardereraPokuttaSchuetteetal., author = {Carderera, Alejandro and Pokutta, Sebastian and Sch{\"u}tte, Christof and Weiser, Martin}, title = {CINDy: Conditional gradient-based Identification of Non-linear Dynamics - Noise-robust recovery}, series = {Journal of Computational and Applied Mathematics}, journal = {Journal of Computational and Applied Mathematics}, abstract = {Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.}, language = {en} } @inproceedings{GanderKrauseWeiseretal., author = {Gander, Lia and Krause, Rolf and Weiser, Martin and Costabal, Francisco and Pezzuto, Simone}, title = {On the Accuracy of Eikonal Approximations in Cardiac Electrophysiology in the Presence of Fibrosis}, series = {Functional Imaging and Modeling of the Heart. FIMH 2023.}, volume = {13958}, booktitle = {Functional Imaging and Modeling of the Heart. FIMH 2023.}, publisher = {Springer, Cham}, doi = {10.1007/978-3-031-35302-4_14}, abstract = {Fibrotic tissue is one of the main risk factors for cardiac arrhythmias. It is therefore a key component in computational studies. In this work, we compare the monodomain equation to two eikonal models for cardiac electrophysiology in the presence of fibrosis. We show that discontinuities in the conductivity field, due to the presence of fibrosis, introduce a delay in the activation times. The monodomain equation and eikonal-diffusion model correctly capture these delays, contrarily to the classical eikonal equation. Importantly, a coarse space discretization of the monodomain equation amplifies these delays, even after accounting for numerical error in conduction velocity. The numerical discretization may also introduce artificial conduction blocks and hence increase propagation complexity. Therefore, some care is required when comparing eikonal models to the discretized monodomain equation.}, language = {en} } @article{BorndoerferDaneckerWeiser2020, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {A Discrete-Continuous Algorithm for Free Flight Planning}, series = {Algorithms}, volume = {14}, journal = {Algorithms}, number = {1}, publisher = {MDPI}, issn = {1438-0064}, doi = {10.3390/a14010004}, pages = {4}, 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} } @article{OzelKulkarniHasanetal., author = {Ozel, Mehmet Neset and Kulkarni, Abhishek and Hasan, Amr and Brummer, Josephine and Moldenhauer, Marian and Daumann, Ilsa-Maria and Wolfenberg, Heike and Dercksen, Vincent J. and Kiral, Ferdi Ridvan and Weiser, Martin and Prohaska, Steffen and von Kleist, Max and Hiesinger, Peter Robin}, title = {Serial synapse formation through filopodial competition for synaptic seeding factors}, series = {Developmental Cell}, volume = {50}, journal = {Developmental Cell}, number = {4}, doi = {10.1016/j.devcel.2019.06.014}, pages = {447 -- 461}, abstract = {Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses.}, language = {en} } @article{RannebergWeiserWeihrauchetal., author = {Ranneberg, Maximilian and Weiser, Martin and Weihrauch, Mirko and Budach, Volker and Gellermann, Johanna and Wust, Peter}, title = {Regularized Antenna Profile Adaptation in Online Hyperthermia Treatment}, series = {Medical Physics}, volume = {37}, journal = {Medical Physics}, doi = {10.1118/1.3488896}, pages = {5382 -- 5394}, language = {en} } @article{SchneckWeiserWende, author = {Schneck, Jakob and Weiser, Martin and Wende, Florian}, title = {Impact of mixed precision and storage layout on additive Schwarz smoothers}, series = {Numerical Linear Algebra with Applications}, volume = {28}, journal = {Numerical Linear Algebra with Applications}, number = {4}, doi = {10.1002/nla.2366}, abstract = {The growing discrepancy between CPU computing power and memory bandwidth drives more and more numerical algorithms into a bandwidth-bound regime. One example is the overlapping Schwarz smoother, a highly effective building block for iterative multigrid solution of elliptic equations with higher order finite elements. Two options of reducing the required memory bandwidth are sparsity exploiting storage layouts and representing matrix entries with reduced precision in floating point or fixed point format. We investigate the impact of several options on storage demand and contraction rate, both analytically in the context of subspace correction methods and numerically at an example of solid mechanics. Both perspectives agree on the favourite scheme: fixed point representation of Cholesky factors in nested dissection storage.}, language = {en} } @article{SchielaStoeckleinWeiser, author = {Schiela, Anton and St{\"o}cklein, Matthias and Weiser, Martin}, title = {A primal dual projection algorithm for efficient constraint preconditioning}, series = {SIAM Journal on Scientific Computing}, volume = {43}, journal = {SIAM Journal on Scientific Computing}, number = {6}, doi = {10.1137/20M1380739}, pages = {A4095 -- A4120}, abstract = {We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and analysed as a gradient method on a quotient space, the given problem can be solved by computing sulutions for a sequence of constrained surrogate problems, projections onto the feasible subspaces, and Lagrange multiplier updates. As a major application we consider a class of optimization problems with PDEs, where PDP can be applied together with a projected cg method using a block triangular constraint preconditioner. Numerical experiments show reliable and competitive performance for an optimal control problem in elasticity.}, language = {en} } @inproceedings{CheginiFroehlyHuynhetal., author = {Chegini, Fatemeh and Froehly, Algiane and Huynh, Ngoc Mai Monica and Pavarino, Luca and Potse, Mark and Scacchi, Simone and Weiser, Martin}, title = {Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution}, series = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, abstract = {The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes.}, language = {en} } @inproceedings{SteyerCheginiStaryetal., author = {Steyer, Joshua and Chegini, Fatemeh and Star{\´y}, Tomas and Potse, Mark and Weiser, Martin and Loewe, Axel}, title = {Electrograms in a Cardiac Cell-by-Cell Model}, abstract = {Cardiac electrograms are an important tool to study the spread of excitation waves inside the heart, which in turn underlie muscle contraction. Electrograms can be used to analyse the dynamics of these waves, e.g. in fibrotic tissue. In computational models, these analyses can be done with greater detail than during minimally invasive in vivo procedures. Whilst homogenised models have been used to study electrogram genesis, such analyses have not yet been done in cellularly resolved models. Such high resolution may be required to develop a thorough understanding of the mechanisms behind abnormal excitation patterns leading to arrhythmias. In this study, we derived electrograms from an excitation propagation simulation in the Extracellular, Membrane, Intracellular (EMI) model, which represents these three domains explicitly in the mesh. We studied the effects of the microstructural excitation dynamics on electrogram genesis and morphology. We found that electrograms are sensitive to the myocyte alignment and connectivity, which translates into micro-fractionations in the electrograms.}, language = {en} } @article{BartelsFisikopoulosWeiser, author = {Bartels, Tinko and Fisikopoulos, Vissarion and Weiser, Martin}, title = {Fast Floating-Point Filters for Robust Predicates}, series = {BIT Numerical Mathematics}, volume = {63}, journal = {BIT Numerical Mathematics}, doi = {10.1007/s10543-023-00975-x}, abstract = {Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information systems and computer-aided design. With floating-point arithmetic, these geometric predicates can incur round-off errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetic for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We combine and extend different approaches to filtering, branch reduction, and overflow avoidance that have previously been proposed. We show examples of how this approach produces correct results for data sets that could lead to incorrect predicate results with naive implementations. Our benchmark results demonstrate that our implementation surpasses state-of-the-art implementations.}, language = {en} } @incollection{DeuflhardWeiser1997, author = {Deuflhard, Peter and Weiser, Martin}, title = {Local inexact Newton multilevel FEM for nonlinear elliptic problems}, series = {Computational science for the 21st century}, booktitle = {Computational science for the 21st century}, editor = {et al. Bristeau, M.-O.}, publisher = {Chichester: John Wiley \& Sons.}, pages = {129 -- 138}, year = {1997}, language = {en} } @article{NiemannUramWolfetal., author = {Niemann, Jan-Hendrik and Uram, Samuel and Wolf, Sarah and Conrad, Natasa Djurdjevac and Weiser, Martin}, title = {Multilevel Optimization for Policy Design with Agent-Based Epidemic Models}, series = {Computational Science}, volume = {77}, journal = {Computational Science}, doi = {10.1016/j.jocs.2024.102242}, pages = {102242}, abstract = {Epidemiological models can not only be used to forecast the course of a pandemic like COVID-19, but also to propose and design non-pharmaceutical interventions such as school and work closing. In general, the design of optimal policies leads to nonlinear optimization problems that can be solved by numerical algorithms. Epidemiological models come in different complexities, ranging from systems of simple ordinary differential equations (ODEs) to complex agent-based models (ABMs). The former allow a fast and straightforward optimization, but are limited in accuracy, detail, and parameterization, while the latter can resolve spreading processes in detail, but are extremely expensive to optimize. We consider policy optimization in a prototypical situation modeled as both ODE and ABM, review numerical optimization approaches, and propose a heterogeneous multilevel approach based on combining a fine-resolution ABM and a coarse ODE model. Numerical experiments, in particular with respect to convergence speed, are given for illustrative examples.}, language = {en} } @article{SemlerWeiser, author = {Semler, Phillip and Weiser, Martin}, title = {Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems}, series = {Inverse Problems}, volume = {39}, journal = {Inverse Problems}, number = {12}, doi = {10.1088/1361-6420/ad0028}, pages = {125003}, abstract = {In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures.}, language = {en} }