TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin A1 - Schiela, Anton ED - Dedner, A. ED - Flemisch, B. ED - Klöfkorn, R. T1 - Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox T2 - Advances in DUNE N2 - This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study. Y1 - 2012 SP - 101 EP - 112 PB - Springer ER - TY - JOUR A1 - Weiser, Martin T1 - Faster SDC convergence on non-equidistant grids by DIRK sweeps JF - BIT Numerical Mathematics N2 - Spectral deferred correction methods for solving stiff ODEs are known to converge rapidly towards the collocation limit solution on equidistant grids, but show a much less favourable contraction on non-equidistant grids such as Radau-IIa points. We interprete SDC methods as fixed point iterations for the collocation system and propose new DIRK-type sweeps for stiff problems based on purely linear algebraic considerations. Good convergence is recovered also on non-equidistant grids. The properties of different variants are explored on a couple of numerical examples. Y1 - 2015 U6 - https://doi.org/10.1007/s10543-014-0540-y VL - 55 IS - 4 SP - 1219 EP - 1241 ER - TY - JOUR A1 - Weiser, Martin A1 - Götschel, Sebastian T1 - State Trajectory Compression for Optimal Control with Parabolic PDEs JF - SIAM J. Sci. Comput. N2 - In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient. Y1 - 2012 U6 - https://doi.org/10.1137/11082172X VL - 34 IS - 1 SP - A161 EP - A184 ER - TY - GEN A1 - Nadobny, Johanna A1 - Weihrauch, Mirko A1 - Weiser, Martin A1 - Gellermann, Johanna A1 - Wlodarczyk, Waldemar A1 - Budach, Volker A1 - Wust, Peter T1 - Advances in the Planning and Control of the MR-guided Regional Hyperthermia Applications T2 - Proc. Int. Conf. Electromagnetics in Advanced Applications, ICEAA 2007, Torino, Italy Y1 - 2007 SP - 1010 EP - 1013 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - State Trajectory Compression in Optimal Control JF - PAMM N2 - In optimal control problems with nonlinear time-dependent 3D PDEs, the computation of the reduced gradient by adjoint methods requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. Since the state enters into the adjoint equation, the storage of a 4D discretization is necessary. We propose a lossy compression algorithm using a cheap predictor for the state data, with additional entropy coding of prediction errors. Analytical and numerical results indicate that compression factors around 30 can be obtained without exceeding the FE discretization error. Y1 - 2010 U6 - https://doi.org/10.1002/pamm.201010282 VL - 10 IS - 1 SP - 579 EP - 580 ER - TY - GEN A1 - Weiser, Martin T1 - Delayed Residual Compensation for Bidomain Equations T2 - AIP Conference Proceedings N2 - The biodomain model of cardioelectric excitation consists of a reaction‐diffusion equation, an elliptic algebraic constraint, and a set of pointwise ODEs. Fast reaction enforces small time steps, such that for common mesh sizes the reaction‐diffusion equation is easily solved implicitly due to a dominating mass matrix. In contrast, the elliptic constraint does not benefit from small time steps and requires a comparably expensive solution. We propose a delayed residual compensation that improves the solution of the elliptic constraint and thus alleviates the need for long iteration times. Y1 - 2010 U6 - https://doi.org/10.1063/1.3498495 VL - 1281 SP - 419 EP - 422 ER - TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Deuflhard, Peter ED - Wilson, E. ED - Fitt, A. ED - Ockendon, H. ED - Norbury, J. T1 - On Efficiency and Accuracy in Cardioelectric Simulation T2 - Progress in Industrial Mathematics at ECMI 2008 N2 - Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy. Y1 - 2010 SP - 371 EP - 376 PB - Springer ER - TY - JOUR A1 - Wilhelms, Mathias A1 - Seemann, Gunnar A1 - Weiser, Martin A1 - Dössel, Olaf T1 - Benchmarking Solvers of the Monodomain Equation in Cardiac Electrophysiological Modeling JF - Biomed. Engineer. Y1 - 2010 U6 - https://doi.org/10.1515/BMT.2010.712 VL - 55 SP - 99 EP - 102 ER - TY - GEN A1 - Wust, Peter A1 - Weihrauch, Mirko A1 - Weiser, Martin A1 - Gellermann, Johanna A1 - Eisenhardt, Steffen A1 - Chobrok, Thorsten A1 - Budach, Volker ED - Dössel, O. ED - Schlegel, W. ED - Magjarevic, R. T1 - Optimization of clinical radiofrequency hyperthermia by use of MR-thermography in a hybrid system T2 - World Congress on Medical Physics and Biomedical Engineering, September 2009, Munich, Germany Y1 - 2010 SP - 174 EP - 175 PB - Springer ER - TY - JOUR A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An optimal control problem in polyconvex hyperelasticity JF - SIAM J. Control Opt. N2 - We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented. Y1 - 2014 U6 - https://doi.org/10.1137/120876629 VL - 52 IS - 3 SP - 1403 EP - 1422 ER - TY - JOUR A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin T1 - Flexible Shape Matching with Finite Element Based LDDMM JF - International Journal of Computer Vision N2 - We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes. Y1 - 2013 U6 - https://doi.org/10.1007/s11263-012-0599-3 VL - 105 IS - 2 SP - 128 EP - 143 ER - TY - GEN A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin ED - Pennec, X. ED - Joshi, S. ED - Nielsen, M. T1 - Direct LDDMM of Discrete Currents with Adaptive Finite Elements T2 - Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability N2 - We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes. Y1 - 2011 SP - 1 EP - 14 ER - TY - GEN A1 - Schiela, Anton A1 - Weiser, Martin ED - Diehl, M. ED - Glineur, F. ED - Jarlebring, E. ED - Michiels, W. T1 - Barrier methods for a control problem from hyperthermia treatment planning T2 - Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009) N2 - We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem. Y1 - 2010 SP - 419 EP - 428 PB - Springer ER - TY - JOUR A1 - Weiser, Martin A1 - Röllig, Mathias A1 - Arndt, Ralf A1 - Erdmann, Bodo T1 - Development and test of a numerical model for pulse thermography in civil engineering JF - Heat and Mass Transfer N2 - Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens. Y1 - 2010 VL - 46 IS - 11-12 SP - 1419 EP - 1428 ER - TY - JOUR A1 - Ranneberg, Maximilian A1 - Weiser, Martin A1 - Weihrauch, Mirko A1 - Budach, Volker A1 - Gellermann, Johanna A1 - Wust, Peter T1 - Regularized Antenna Profile Adaptation in Online Hyperthermia Treatment JF - Medical Physics Y1 - 2010 U6 - https://doi.org/10.1118/1.3488896 VL - 37 SP - 5382 EP - 5394 ER - TY - JOUR A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An affine covariant composite step method for optimization with PDEs as equality constraints JF - Optimization Methods and Software N2 - We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2016.1241783 VL - 32 IS - 5 SP - 1132 EP - 1161 ER - TY - GEN A1 - Götschel, Sebastian A1 - Maierhofer, Christiane A1 - Müller, Jan P. A1 - Rothbart, Nick A1 - Weiser, Martin T1 - Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites N2 - Carbon-fiber reinforced composites are becoming more and more important in the production of light-weight structures, e.g., in the automotive and aerospace industry. Thermography is often used for non-destructive testing of these products, especially to detect delaminations between different layers of the composite. In this presentation, we aim at methods for defect reconstruction from thermographic measurements of such carbon-fiber reinforced composites. The reconstruction results shall not only allow to locate defects, but also give a quantitative characterization of the defect properties. We discuss the simulation of the measurement process using finite element methods, as well as the experimental validation on flat bottom holes. Especially in pulse thermography, thin boundary layers with steep temperature gradients occurring at the heated surface need to be resolved. Here we use the combination of a 1D analytical solution combined with numerical solution of the remaining defect equation. We use the simulations to identify material parameters from the measurements. Finally, fast heuristics for reconstructing defect geometries are applied to the acquired data, and compared for their accuracy and utility in detecting different defects like back surface defects or delaminations. T3 - ZIB-Report - 16-13 KW - thermography KW - inverse problems KW - parameter identification KW - geometry identification KW - nondestructive testing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58374 UR - https://www.wcndt2016.com/portals/wcndt/bb/Th4C4.pdf SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Höhne, Christian A1 - Kolkoori, Sanjeevareddy A1 - Mitzscherling, Steffen A1 - Prager, Jens A1 - Weiser, Martin T1 - Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing N2 - The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave propagation through the material, in particular travel times between two points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points. In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the eikonal equation. The implementation of such a two point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools. As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value problem allows a straightforward derivation of the ray path from a given transducer position to any pixel in the reconstruction area and reduces the computational cost considerably. T3 - ZIB-Report - 16-14 KW - ray tracing KW - ODE boundary value problems KW - ultrasonics KW - nondestructive testing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58386 UR - https://www.wcndt2016.com/portals/wcndt/bb/Fr1H4.pdf SN - 1438-0064 ER - TY - BOOK A1 - Weiser, Martin T1 - Inside Finite Elements N2 - All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms.Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave. Y1 - 2016 PB - De Gruyter ER - TY - GEN A1 - Volkwein, Stefan A1 - Weiser, Martin T1 - Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods N2 - An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solves. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation. T3 - ZIB-Report - 00-56 KW - nonlinear programming KW - multiplier methods KW - affine invariant norms KW - Burgers' equation Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6243 ER - TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter T1 - The Central Path towards the Numerical Solution of Optimal Control Problems N2 - A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem. T3 - ZIB-Report - 01-12 KW - optimal control KW - interior point methods KW - affine invariance Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6380 ER - TY - GEN A1 - Weiser, Martin T1 - Linear convergence of an interior point method for linear control constrained optimal control problems N2 - The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a recent paper of Weiser and Deuflhard, where convergence rates have not been derived. The choice of free parameters, i.e. the corrector accuracy and the number of corrector steps, is discussed. T3 - ZIB-Report - 02-13 KW - linear optimal control KW - infinite dimensional KW - interior point methods KW - inexact Newton methods Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6809 ER - TY - GEN A1 - Weiser, Martin T1 - Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations N2 - Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples. T3 - ZIB-Report - 07-45 KW - reaction-diffusion equations KW - travelling waves KW - nonlinear scaling KW - discretization error Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10493 SN - 1438-0064 ER - TY - GEN A1 - Schenk, Olaf A1 - Wächter, Andreas A1 - Weiser, Martin T1 - Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization N2 - Fast nonlinear programming methods following the all-at-once approach usually employ Newton's method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is only guaranteed to be a descent direction if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints, otherwise some modifications to Newton's method are necessary. This condition can be verified using the signs of the KKT's eigenvalues (inertia), which are usually available from direct solvers for the arising linear saddle point problems. Iterative solvers are mandatory for very large-scale problems, but in general do not provide the inertia. Here we present a preconditioner based on a multilevel incomplete $LBL^T$ factorization, from which an approximation of the inertia can be obtained. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale 3D PDE-constrained optimal control problems, as well as 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with $150^3$ state variables and $150^2$ control variables, both subject to bound constraints. T3 - ZIB-Report - 07-32 KW - nonconvex constrained optimization KW - interior-point method KW - inertia KW - multilevel incomplete factorization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10314 SN - 1438-0064 ER - TY - GEN A1 - Griesse, Roland A1 - Weiser, Martin T1 - On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control N2 - This paper is concerned with the sensitivities of function space oriented interior point approximations in parameter dependent problems. For an abstract setting that covers control constrained optimal control problems, the convergence of interior point sensitivities to the sensitivities of the optimal solution is shown. Error bounds for $L_q$ norms are derived and illustrated with numerical examples. T3 - ZIB-Report - 05-44 KW - interior point methods KW - parametric sensitivity KW - optimal control Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8773 ER - TY - GEN A1 - Weiser, Martin A1 - Hubig, Michael A1 - Shanmugam Subramaniam, Jayant T1 - Reconstructing Ambient Temperature Changes in Death Time Estimation with a Bayesian Double-Exponential Approach T2 - Zenodo N2 - Code and data for the reconstruction of ambient temperature drop in time of death estimation We provide Octave code and temperature measurement data for - empirircally estimating thermal sensor likelihood - estimating time and amplitude of a single sudden ambient temperature drop from temperature measurement data in two thermally different compartments. Y1 - 2025 U6 - https://doi.org/10.5281/zenodo.17702240 ER - TY - GEN A1 - Villani, Paolo A1 - Weiser, Martin T1 - Adaptive Gaussian process regression for inverse problems. ALGORITMY 2024 N2 - This submission contains the code used for the proceedings paper for ALGORITMY 2024, concerning surrogate model-based inverse problems. Version 2 modified plot appearances and fixed some minor typos. Y1 - 2024 ER - TY - CHAP A1 - Semler, Phillip A1 - Weiser, Martin ED - Fackeldey, Konstantin ED - Kannan, Aswin ED - Pokutta, Sebastian ED - Sharma, Kartikey ED - Walter, Daniel ED - Walther, Andrea ED - Weiser, Martin T1 - Adaptive gradient-enhanced Gaussian process surrogates for inverse problems T2 - Mathematical Optimization for Machine Learning: Proceedings of the MATH+ Thematic Einstein Semester 2023 N2 - Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational budget. We address not only the choice of evaluation points but also of required simulation accuracy, both of values and gradients of the forward model. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs as well as a clear benefit of including gradient information into the surrogate training. Y1 - 2025 U6 - https://doi.org/10.1515/9783111376776-005 SP - 59 EP - 78 PB - De Gruyter ER - TY - CHAP A1 - Villani, Paolo A1 - Unger, Jörg F. A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Bayesian inverse problems T2 - Proceedings of the Conference Algoritmy 2024 N2 - We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems. Y1 - 2024 SP - 214 EP - 224 ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - A Bayesian Framework for Simulation-based Digital Twins of Bridges JF - EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability N2 - Simulation-based digital twins have emerged as a powerful tool for evaluating the mechanical response of bridges. As virtual representations of physical systems, digital twins can provide a wealth of information that complements traditional inspection and monitoring data. By incorporating virtual sensors and predictive maintenance strategies, they have the potential to improve our understanding of the behavior and performance of bridges over time. However, as bridges age and undergo regular loading and extreme events, their structural characteristics change, often differing from the predictions of their initial design. Digital twins must be continuously adapted to reflect these changes. In this article, we present a Bayesian framework for updating simulation-based digital twins in the context of bridges. Our approach integrates information from measurements to account for inaccuracies in the simulation model and quantify uncertainties. Through its implementation and assessment, this work demonstrates the potential for digital twins to provide a reliable and up-to-date representation of bridge behavior, helping to inform decision-making for maintenance and management. Y1 - 2023 U6 - https://doi.org/10.1002/cepa.2177 VL - 6 IS - 5 SP - 734 EP - 740 ER - TY - CHAP A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - Evaluation of Model Bias Identification Approaches Based on Bayesian Inference and Applications to Digital Twins T2 - 5th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering N2 - In recent years, the use of simulation-based digital twins for monitoring and assessment of complex mechanical systems has greatly expanded. Their potential to increase the information obtained from limited data makes them an invaluable tool for a broad range of real-world applications. Nonetheless, there usually exists a discrepancy between the predicted response and the measurements of the system once built. One of the main contributors to this difference in addition to miscalibrated model parameters is the model error. Quantifying this socalled model bias (as well as proper values for the model parameters) is critical for the reliable performance of digital twins. Model bias identification is ultimately an inverse problem where information from measurements is used to update the original model. Bayesian formulations can tackle this task. Including the model bias as a parameter to be inferred enables the use of a Bayesian framework to obtain a probability distribution that represents the uncertainty between the measurements and the model. Simultaneously, this procedure can be combined with a classic parameter updating scheme to account for the trainable parameters in the original model. This study evaluates the effectiveness of different model bias identification approaches based on Bayesian inference methods. This includes more classical approaches such as direct parameter estimation using MCMC in a Bayesian setup, as well as more recent proposals such as stat-FEM or orthogonal Gaussian Processes. Their potential use in digital twins, generalization capabilities, and computational cost is extensively analyzed. Y1 - 2023 UR - https://2023.uncecomp.org/proceedings/pdf/19795.pdf SP - 1 EP - 15 ER - TY - JOUR A1 - Maier, Kristina A1 - Weiser, Martin A1 - Conrad, Tim T1 - Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology JF - Proceedings of the Royal Society A N2 - This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of PDEs and the computational efficiency of ODEs, the model enables rapid evaluation of public health interventions. Applied to synthetic environments and real-world scenarios in Lombardy, Italy, and Berlin, Germany, the model highlights how interactions between PDE and ODE regions affect infection dynamics, especially in high-density areas. Key findings reveal that the placement of model boundaries in densely populated regions can lead to inaccuracies in infection spread, suggesting that boundaries should be positioned in areas of lower population density to better reflect transmission dynamics. Additionally, regions with low population density hinder infection flow, indicating a need for incorporating, e.g., jumps in the model to enhance its predictive capabilities. Results indicate that the hybrid model achieves a balance between computational speed and accuracy, making it a valuable tool for policymakers in real-time decision-making and scenario analysis in epidemiology and potentially in other fields requiring similar modeling approaches. Y1 - 2025 U6 - https://doi.org/10.1098/rspa.2024.0421 VL - 481 IS - 2306 PB - Royal Society ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Faidon-Stelios A1 - Unger, Jörg F. T1 - Model bias identification for Bayesian calibration of stochastic digital twins of bridges JF - Applied Stochastic Models in Business and Industry N2 - Simulation-based digital twins must provide accurate, robust and reliable digital representations of their physical counterparts. Quantifying the uncertainty in their predictions plays, therefore, a key role in making better-informed decisions that impact the actual system. The update of the simulation model based on data must be then carefully implemented. When applied to complex standing structures such as bridges, discrepancies between the computational model and the real system appear as model bias, which hinders the trustworthiness of the digital twin and increases its uncertainty. Classical Bayesian updating approaches aiming to infer the model parameters often fail at compensating for such model bias, leading to overconfident and unreliable predictions. In this paper, two alternative model bias identification approaches are evaluated in the context of their applicability to digital twins of bridges. A modularized version of Kennedy and O'Hagan's approach and another one based on Orthogonal Gaussian Processes are compared with the classical Bayesian inference framework in a set of representative benchmarks. Additionally, two novel extensions are proposed for such models: the inclusion of noise-aware kernels and the introduction of additional variables not present in the computational model through the bias term. The integration of such approaches in the digital twin corrects the predictions, quantifies their uncertainty, estimates noise from unknown physical sources of error and provides further insight into the system by including additional pre-existing information without modifying the computational model. Y1 - 2024 U6 - https://doi.org/10.1002/asmb.2897 VL - 41 IS - 3 ER - TY - JOUR A1 - Göbel, Fritz A1 - Huynh, Ngoc Mai Monica A1 - Chegini, Fatemeh A1 - Pavarino, Luca A1 - Weiser, Martin A1 - Scacchi, Simone A1 - Anzt, Hartwig T1 - A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions JF - SIAM J. Sci. Comput. N2 - We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments. Y1 - 2025 ER - TY - JOUR A1 - Andrés Arcones, Daniel A1 - Weiser, Martin A1 - Koutsourelakis, Phaedon-Stelios A1 - Unger, Jörg F. T1 - Bias Identification Approaches for Model Updating of Simulation-based Digital Twins of Bridges JF - Structural Health Monitoring in the Light of Climate Impact and Data Science. Research and Review Journal of Nondestructive Testing N2 - Simulation-based digital twins of bridges have the potential not only to serve as monitoring devices of the current state of the structure but also to generate new knowledge through physical predictions that allow for better-informed decisionmaking. For an accurate representation of the bridge, the underlying models must be tuned to reproduce the real system. Nevertheless, the necessary assumptions and simplifications in these models irremediably introduce discrepancies between measurements and model response. We will show that quantifying the extent of the uncertainties introduced through the models that lead to such discrepancies provides a better understanding of the real system, enhances the model updating process, and creates more robust and trustworthy digital twins. The inclusion of an explicit bias term will be applied to a representative demonstrator case based on the thermal response of the Nibelungenbrücke of Worms. The findings from this work are englobed in the initiative SPP 100+, whose main aim is the extension of the service life of structures, especially through the implementation of digital twins. Y1 - 2024 U6 - https://doi.org/10.58286/30524 VL - 2 IS - 2 ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Kopanicakova, Alena A1 - Weiser, Martin A1 - Krause, Rolf T1 - Quantitative Analysis of Nonlinear MultifidelityOptimization for Inverse Electrophysiology T2 - Domain Decomposition Methods in Science and Engineering XXVI N2 - The electric conductivity of cardiac tissue determines excitation propagation and is important for quantifying ischemia and scar tissue and for building personalized models. Estimating conductivity distributions from endocardial mapping data is a challenging inverse problem due to the computational complexity of the monodomain equation, which describes the cardiac excitation. For computing a maximum posterior estimate, we investigate different optimization approaches based on adjoint gradient computation: steepest descent, limited memory BFGS, and recursive multilevel trust region methods, which are using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration. Y1 - 2022 SP - 65 EP - 76 PB - Springer 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, F.J. A1 - Plessl, Christian A1 - Schotte, Merlind A1 - Steinke, Thomas A1 - Teich, J. A1 - Weiser, Martin A1 - Wende, Florian T1 - The HighPerMeshes Framework for Numerical Algorithms on Unstructured Grids JF - Concurrency and Computation: Practice and Experience N2 - Solving PDEs on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HPM C++-embedded DSL that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HPM 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 HPM DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HPM code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems. Y1 - 2022 U6 - https://doi.org/10.1002/cpe.6616 VL - 34 IS - 14 ER - TY - GEN A1 - Weiser, Martin A1 - Chegini, Fatemeh T1 - Higher-order time integration using spectral deferred correction method (SDC) in a cell by cell discretization of cardiac excitation N2 - This C++ code implements a cell-by-cell model of cardiac excitation using a piecewise-continuous finite element discretization and spectral deferred correction time stepping. The code is based on the Kaskade 7 finite element toolbox and forms a prototype for the µCarp code to be implemented in the Microcard project. Y1 - 2022 U6 - https://doi.org/10.35097/716 ER - TY - JOUR A1 - Niemann, Jan-Hendrik A1 - Uram, Samuel A1 - Wolf, Sarah A1 - Conrad, Natasa Djurdjevac A1 - Weiser, Martin T1 - Multilevel Optimization for Policy Design with Agent-Based Epidemic Models JF - Computational Science N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1016/j.jocs.2024.102242 VL - 77 SP - 102242 ER - TY - CHAP A1 - Gander, Lia A1 - Krause, Rolf A1 - Weiser, Martin A1 - Costabal, Francisco A1 - Pezzuto, Simone T1 - On the Accuracy of Eikonal Approximations in Cardiac Electrophysiology in the Presence of Fibrosis T2 - Functional Imaging and Modeling of the Heart. FIMH 2023. N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/978-3-031-35302-4_14 VL - 13958 PB - Springer, Cham ER - TY - JOUR A1 - Subramaniam, Jayant S. A1 - Hubig, Michael A1 - Muggenthaler, Holger A1 - Schenkl, Sebastian A1 - Ullrich, Julia A1 - Pourtier, Grégroire A1 - Weiser, Martin A1 - Mall, Gita T1 - Sensitivity of temperature-based time since death estimation on measurement location JF - International Journal of Legal Medicine N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/s00414-023-03040-y VL - 137 SP - 1815 EP - 1837 ER - TY - JOUR A1 - Semler, Phillip A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems JF - Inverse Problems N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1088/1361-6420/ad0028 VL - 39 IS - 12 SP - 125003 ER - TY - JOUR A1 - Ullrich, Julia A1 - Weiser, Martin A1 - Subramaniam, Jayant A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita T1 - The impact of anatomy variation on temperature based time of death estimation JF - International Journal of Legal Medicine N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1007/s00414-023-03026-w VL - 137 SP - 1615 EP - 1627 ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Steinke, Thomas A1 - Weiser, Martin T1 - Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods N2 - The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples. Y1 - 2022 ER - TY - JOUR A1 - Huynh, Ngoc A1 - Chegini, Fatemeh A1 - Pavarino, Luca A1 - Weiser, Martin A1 - Scacchi, Simone T1 - Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model JF - SIAM Journal on Scientific Computing N2 - 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. Y1 - 2023 VL - 45 IS - 6 SP - A2836 EP - A2857 ER - TY - JOUR A1 - Carderera, Alejandro A1 - Pokutta, Sebastian A1 - Schütte, Christof A1 - Weiser, Martin T1 - An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise JF - Journal of Computational and Applied Mathematics N2 - 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. Y1 - 2021 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 - 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 - Schiela, Anton A1 - Stöcklein, Matthias A1 - Weiser, Martin T1 - A primal dual projection algorithm for efficient constraint preconditioning JF - SIAM Journal on Scientific Computing N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1137/20M1380739 VL - 43 IS - 6 SP - A4095 EP - A4120 ER - TY - CHAP A1 - Steyer, Joshua A1 - Chegini, Fatemeh A1 - Potse, Mark A1 - Loewe, Axel A1 - Weiser, Martin T1 - Continuity of Microscopic Cardiac Conduction in a Computational Cell-by-Cell Model T2 - 2023 Computing in Cardiology Conference (CinC) N2 - Conduction velocity in cardiac tissue is a crucial electrophysiological parameter for arrhythmia vulnerability. Pathologically reduced conduction velocity facilitates arrhythmogenesis because such conduction velocities decrease the wavelength with which re-entry may occur. Computational studies on CV and how it changes regionally in models at spatial scales multiple times larger than actual cardiac cells exist. However, microscopic conduction within cells and between them have been studied less in simulations. In this work, we study the relation of microscopic conduction patterns and clinically observable macroscopic conduction using an extracellular-membrane-intracellular model which represents cardiac tissue with these subdomains at subcellular resolution. By considering cell arrangement and non-uniform gap junction distribution, it yields anisotropic excitation propagation. This novel kind of model can for example be used to understand how discontinuous conduction on the microscopic level affects fractionation of electrograms in healthy and fibrotic tissue. Along the membrane of a cell, we observed a continuously propagating activation wavefront. When transitioning from one cell to the neighbouring one, jumps in local activation times occurred, which led to lower global conduction velocities than locally within each cell. Y1 - 2023 U6 - https://doi.org/10.22489/CinC.2023.385 SN - 2325-887X VL - 50 PB - Computing in Cardiology ER - TY - CHAP A1 - Chegini, Fatemeh A1 - Froehly, Algiane A1 - Huynh, Ngoc Mai Monica A1 - Pavarino, Luca A1 - Potse, Mark A1 - Scacchi, Simone A1 - Weiser, Martin T1 - Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution T2 - 10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023 N2 - 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. Y1 - 2023 UR - https://www.scipedia.com/public/2023f U6 - https://doi.org/10.23967/c.coupled.2023.004 ER -