@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{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization}, series = {Journal of Optimization Theory and Applications}, volume = {198}, journal = {Journal of Optimization Theory and Applications}, doi = {10.1007/s10957-023-02264-7}, pages = {830 -- 856}, abstract = {Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators.}, language = {en} } @article{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, series = {Operations Research Forum}, volume = {4}, journal = {Operations Research Forum}, doi = {10.1007/s43069-023-00238-z}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91846}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @misc{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Newton's Method for Global Free Flight Trajectory Optimization}, doi = {10.12752/8987}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-89876}, abstract = {Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.}, language = {en} } @article{HuynhCheginiPavarinoetal., author = {Huynh, Ngoc and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone}, title = {Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model}, series = {SIAM Journal on Scientific Computing}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {6}, pages = {A2836 -- A2857}, abstract = {A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.}, language = {en} } @article{SubramaniamHubigMuggenthaleretal., author = {Subramaniam, Jayant S. and Hubig, Michael and Muggenthaler, Holger and Schenkl, Sebastian and Ullrich, Julia and Pourtier, Gr{\´e}groire and Weiser, Martin and Mall, Gita}, title = {Sensitivity of temperature-based time since death estimation on measurement location}, series = {International Journal of Legal Medicine}, volume = {137}, journal = {International Journal of Legal Medicine}, doi = {10.1007/s00414-023-03040-y}, pages = {1815 -- 1837}, abstract = {Rectal temperature measurement (RTM) from crime scenes is an important parameter for temperature-based time of death estimation (TDE). Various influential variables exist in TDE methods like the uncertainty in thermal and environmental parameters. Although RTM depends in particular on the location of measurement position, this relationship has never been investigated separately. The presented study fills this gap using Finite Element (FE) simulations of body cooling. A manually meshed coarse human FE model and an FE geometry model developed from the CT scan of a male corpse are used for TDE sensitivity analysis. The coarse model is considered with and without a support structure of moist soil. As there is no clear definition of ideal rectal temperature measurement location for TDE, possible variations in RTM location (RTML) are considered based on anatomy and forensic practice. The maximum variation of TDE caused by RTML changes is investigated via FE simulation. Moreover, the influence of ambient temperature, of FE model change and of the models positioning on a wet soil underground are also discussed. As a general outcome, we notice that maximum TDE deviations of up to ca. 2-3 h due to RTML deviations have to be expected. The direction of maximum influence of RTML change on TDE generally was on the line caudal to cranial.}, language = {en} } @misc{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-91309}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @inproceedings{BorndoerferDaneckerWeiser, author = {Bornd{\"o}rfer, Ralf and Danecker, Fabian and Weiser, Martin}, title = {Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization}, series = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, volume = {115}, booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)}, doi = {10.4230/OASIcs.ATMOS.2023.3}, pages = {3:1 -- 3:6}, abstract = {The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.}, language = {en} } @article{UllrichWeiserSubramaniametal., author = {Ullrich, Julia and Weiser, Martin and Subramaniam, Jayant and Schenkl, Sebastian and Muggenthaler, Holger and Hubig, Michael and Mall, Gita}, title = {The impact of anatomy variation on temperature based time of death estimation}, series = {International Journal of Legal Medicine}, volume = {137}, journal = {International Journal of Legal Medicine}, doi = {10.1007/s00414-023-03026-w}, pages = {1615 -- 1627}, abstract = {Temperature-based time of death estimation (TTDE) using simulation methods such as the finite element (FE) method promises higher accuracy and broader applicability in nonstandard cooling scenarios than established phenomenological methods. Their accuracy depends crucially on the simulation model to capture the actual situation. The model fidelity in turn hinges on the representation of the corpse's anatomy in form of computational meshes as well as on the thermodynamic parameters. While inaccuracies in anatomy representation due to coarse mesh resolution are known to have a minor impact on the estimated time of death, the sensitivity with respect to larger differences in the anatomy has so far not been studied. We assess this sensitivity by comparing four independently generated and vastly different anatomical models in terms of the estimated time of death in an identical cooling scenario. In order to isolate the impact of shape variation, the models are scaled to a reference size, and the possible impact of measurement location variation is excluded explicitly, which gives a lower bound on the impact of anatomy on the estimated time of death.}, 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} }