TY - JOUR A1 - Weiser, Martin T1 - Optimization and Identification in Regional Hyperthermia JF - Int. J. Appl. Electromagn. and Mech. Y1 - 2009 VL - 30 SP - 265 EP - 275 ER - TY - JOUR A1 - Weiser, Martin T1 - Pointwise Nonlinear Scaling for Reaction-Diffusion Equations JF - Appl. Num. Math. Y1 - 2009 VL - 59 IS - 8 SP - 1858 EP - 1869 ER - TY - JOUR A1 - Weiser, Martin A1 - Deuflhard, Peter A1 - Erdmann, Bodo T1 - Affine conjugate adaptive Newton methods for nonlinear elastomechanics JF - Opt. Meth. Softw. Y1 - 2007 VL - 22 IS - 3 SP - 413 EP - 431 ER - TY - JOUR A1 - Weihrauch, Mirko A1 - Wust, Peter A1 - Weiser, Martin A1 - Nadobny, Johanna A1 - Eisenhardt, Steffen A1 - Budach, Volker A1 - Gellermann, Johanna T1 - Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR-HT system JF - Medical Physics Y1 - 2007 VL - 34 IS - 12 SP - 4717 EP - 4725 ER - TY - JOUR A1 - Weiser, Martin T1 - Interior point methods in function space JF - SIAM J. Control Optimization Y1 - 2005 VL - 44 IS - 5 SP - 1766 EP - 1786 ER - TY - JOUR A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Erdmann, Bodo A1 - Weiser, Martin A1 - Zachow, Stefan A1 - Heinrich, Andreas A1 - Güttler, Felix Victor A1 - Teichgräber, Ulf A1 - Mall, Gita T1 - Automatic CT-based finite element model generation for temperature-based death time estimation: feasibility study and sensitivity analysis JF - International Journal of Legal Medicine N2 - 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. KW - temperature based death time estimation KW - finite element method KW - CT segmentation KW - sensitivity analysis Y1 - 2017 U6 - https://doi.org/doi:10.1007/s00414-016-1523-0 VL - 131 IS - 3 SP - 699 EP - 712 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 - 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 - Götschel, Sebastian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad A1 - Weiser, Martin ED - Carraro, T. ED - Geiger, M. ED - Koerkel, S. ED - Rannacher, R. T1 - Reducing Memory Requirements in Scientific Computing and Optimal Control T2 - Multiple Shooting and Time Domain Decomposition Methods Y1 - 2015 SP - 263 EP - 287 PB - Springer ER - TY - JOUR A1 - Götschel, Sebastian A1 - Nagaiah, Chamakuri A1 - Kunisch, Karl A1 - Weiser, Martin T1 - Lossy Compression in Optimal Control of Cardiac Defibrillation JF - J. Sci. Comput. N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1007/s10915-013-9785-x VL - 60 IS - 1 SP - 35 EP - 59 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy Compression for PDE-constrained Optimization: Adaptive Error Control JF - Comput. Optim. Appl. N2 - 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. Y1 - 2015 VL - 62 IS - 1 SP - 131 EP - 155 PB - Springer 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 - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Maierhofer, Christiane A1 - Richter, Regina A1 - Röllig, Mathias T1 - Fast Defect Shape Reconstruction Based on the Travel Time in Pulse Thermography JF - Nondestructive Testing of Materials and Structures Y1 - 2013 VL - 6 SP - 83 EP - 89 ER - TY - CHAP A1 - Krause, Rolf A1 - Weiser, Martin T1 - Multilevel augmented Lagrangian solvers for overconstrained contact formulations T2 - ESAIM: ProcS N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1051/proc/202171175 VL - 71 SP - 175 EP - 184 ER - TY - BOOK A1 - Deuflhard, Peter A1 - Weiser, Martin T1 - Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen Y1 - 2020 SN - 978-3-11-069168-9 U6 - https://doi.org/10.1515/9783110689655 PB - de Gruyter ET - 2 ER - TY - JOUR A1 - Weiser, Martin A1 - Freytag, Yvonne A1 - Erdmann, Bodo A1 - Hubig, Michael A1 - Mall, Gita T1 - Optimal Design of Experiments for Estimating the Time of Death in Forensic Medicine JF - Inverse Problems N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1088/1361-6420/aae7a5 VL - 34 IS - 12 SP - 125005 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Compression Challenges in Large Scale Partial Differential Equation Solvers JF - Algorithms N2 - 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. Y1 - 2019 U6 - https://doi.org/10.3390/a12090197 VL - 12 IS - 9 SP - 197 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Schiela, Anton A1 - Weiser, Martin T1 - Kaskade 7 - a Flexible Finite Element Toolbox JF - Computers and Mathematics with Applications N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1016/j.camwa.2020.02.011 VL - 81 SP - 444 EP - 458 ER - TY - JOUR A1 - Alhaddad, Samer A1 - Förstner, Jens A1 - Groth, Stefan A1 - Grünewald, Daniel A1 - Grynko, Yevgen A1 - Hannig, Frank A1 - Kenter, Tobias A1 - Pfreundt, Franz-Josef A1 - Plessl, Christian A1 - Schotte, Merlind A1 - Steinke, Thomas A1 - Teich, Jürgen A1 - Weiser, Martin A1 - Wende, Florian T1 - HighPerMeshes - A Domain-Specific Language for Numerical Algorithms on Unstructured Grids JF - Euro-Par 2020: Parallel Processing Workshops. N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1007/978-3-030-71593-9_15 SP - 185 EP - 196 PB - Springer ER - TY - JOUR A1 - Chegini, Fatemeh A1 - Kopanicakova, Alena A1 - Krause, Rolf A1 - Weiser, Martin T1 - Efficient Identification of Scars using Heterogeneous Model Hierarchies JF - EP Europace N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1093/europace/euaa402 VL - 23 SP - i113 EP - i122 ER -