@article{GoetschelSchielaWeiser2021, author = {G{\"o}tschel, Sebastian and Schiela, Anton and Weiser, Martin}, title = {Kaskade 7 - a Flexible Finite Element Toolbox}, volume = {81}, journal = {Computers and Mathematics with Applications}, doi = {10.1016/j.camwa.2020.02.011}, pages = {444 -- 458}, year = {2021}, 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.2021, 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}, journal = {Euro-Par 2020: Parallel Processing Workshops.}, publisher = {Springer}, doi = {10.1007/978-3-030-71593-9_15}, pages = {185 -- 196}, year = {2021}, 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{SchneckWeiserWende2021, author = {Schneck, Jakob and Weiser, Martin and Wende, Florian}, title = {Impact of mixed precision and storage layout on additive Schwarz smoothers}, volume = {28}, journal = {Numerical Linear Algebra with Applications}, number = {4}, doi = {10.1002/nla.2366}, year = {2021}, 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{AndresArconesWeiserKoutsourelakisetal.2023, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {A Bayesian Framework for Simulation-based Digital Twins of Bridges}, volume = {6}, journal = {EUROSTRUCT 2023:European Association on Quality Control of Bridges and Structures: Digital Transformation in Sustainability}, number = {5}, doi = {10.1002/cepa.2177}, pages = {734 -- 740}, year = {2023}, abstract = {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.}, language = {en} } @article{MaierWeiserConrad2025, author = {Maier, Kristina and Weiser, Martin and Conrad, Tim}, title = {Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology}, volume = {481}, journal = {Proceedings of the Royal Society A}, number = {2306}, publisher = {Royal Society}, arxiv = {http://arxiv.org/abs/2405.12938}, doi = {10.1098/rspa.2024.0421}, year = {2025}, abstract = {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.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2024, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Faidon-Stelios and Unger, J{\"o}rg F.}, title = {Model bias identification for Bayesian calibration of stochastic digital twins of bridges}, volume = {41}, journal = {Applied Stochastic Models in Business and Industry}, number = {3}, doi = {10.1002/asmb.2897}, year = {2024}, abstract = {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.}, language = {en} } @article{BecksLippoldWinkleretal.2024, author = {Becks, Henrik and Lippold, Lukas and Winkler, Paul and Rohrer, Maximilian and Leusmann, Thorsten and Anton, David and Sprenger, Bjarne and K{\"a}hler, Philipp and Rudenko, Iryna and Andr{\´e}s Arcones, Daniel and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F. and Weiser, Martin and Petryna, Yuri and Schnellenbach-Held, Martina and Lowke, Dirk and Wessels, Henning and Lenzen, Armin and Zabel, Volkmar and K{\"o}nke, Carsten and Claßen, Martin and Hegger, Josef}, title = {Neuartige Konzepte f{\"u}r die Zustands{\"u}berwachung und -analyse von Br{\"u}ckenbauwerken - Einblicke in das Forschungsvorhaben SPP100+}, volume = {99}, journal = {Bauingenieur}, number = {10}, doi = {10.37544/0005-6650-2024-10-63}, pages = {327 -- 338}, year = {2024}, abstract = {Die Br{\"u}ckeninfrastruktur in Deutschland und Europa steht aufgrund steigender Verkehrslasten und alternder Bauwerke vor erheblichen Herausforderungen. Das DFG-Schwerpunktprogramm 2388 „Hundert plus - Verl{\"a}ngerung der Lebensdauer komplexer Baustrukturen durch intelligente Digitalisierung" (SPP100+) strebt an, durch digitale Innovationen und pr{\"a}diktive Instandhaltungsstrategien die Nutzungsdauer bestehender Br{\"u}ckenbauwerke zu verl{\"a}ngern. Der vorliegende Beitrag fokussiert sich auf das SPP100+ zugeh{\"o}rige Cluster „Monitoring und Simulation", das sieben Teilprojekte umfasst. Die Projekte entwickeln fortschrittliche Methoden zur {\"U}berwachung und Zustandsbewertung von Br{\"u}cken mittels Digitaler Zwillinge, hochaufl{\"o}sender Sensortechnik und numerischer Simulationen. Innovative Ans{\"a}tze wie nichtlineare Modellanpassungen, stochastische Methoden und k{\"u}nstliche Intelligenz erm{\"o}glichen eine pr{\"a}zise und fr{\"u}hzeitige Identifizierung potenzieller Sch{\"a}den. Die Kombination aus kontinuierlichem Bauwerksmonitoring und effizienter Datenauswertung ist entscheidend f{\"u}r die langfristige Sicherheit und Langlebigkeit bestehender Br{\"u}cken und tr{\"a}gt dar{\"u}ber hinaus zur Ressourcenschonung bei.}, language = {de} } @article{GoebelHuynhCheginietal.2025, author = {G{\"o}bel, Fritz and Huynh, Ngoc Mai Monica and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone and Anzt, Hartwig}, title = {A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions}, journal = {SIAM J. Sci. Comput.}, arxiv = {http://arxiv.org/abs/2502.07722}, year = {2025}, abstract = {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.}, language = {en} } @article{SubramaniamHubigSchenkletal.2025, author = {Subramaniam, Jayant Shanmugam and Hubig, Michael and Schenkl, Sebastian and Muggenthaler, Holger and Springer, Steffen and Weiser, Martin and Sudau, Jakob and Shah, Faisal and Mall, Gita}, title = {Reconstructing Ambient Temperature in Forensic Death Time Estimation}, year = {2025}, abstract = {In medicolegal practice, time since death is estimated to assess alibi for homicide cases. Ambient temperature TA has a strong impact on cooling and therefore on temperature based time since death estimation (TTDE). At many crimescenes the ambient temperature TA1 is lowered instantaneously from a start value TA0 to a value TA1 at a certain time t0 during investigations due to human intervention such as window or door opening or body transport. Usually TA0 and t0 are unknown to the investigators. In this paper we focus on reconstruction of the unknown parameters TA0 and t0. Our approach is inspired by TTDE literature remarks of detecting said changes by measuring temperatures in closed compartments as e.g. cupboards or neighboring rooms of the crime scene, where TA0 could have been 'preserved' after t0. We aim to estimate t0 and TA0 from temperature measurements TZ(t) in closed compartments Z at times t > t0. We got results even under the most trivial assumption of Newtonian cooling for boxes filled with air, with heaps of clothes or even with books in two different experimental scenarios. Two different parameter estimators, (t0^, TA0^) using a single quadruple temperature measurement in two boxes and (t0*, TA0*) on the basis of weighted averaging the results of a series of N quadruple measurements during cooling of the two boxes respectively, were tested. Our results were partially appropriate for TTDE input. For example a sudden decline at time t0 from TA0 = 22.5°C to TA1 = 14°C of the ambient temperature in a climate chamber could be reconstructed at t = t0 + 95min with relative deviations ρt0^ = 27\% and ρTA0^ = 19\% of the estimators relative to t - t0 and TA0 - TA1 respectively, only based on N = 1 quadruple measurement with a span of Δt = 50min. In case of N = 200 quadruple measurements starting at t = t0 + 95min and ending at t = t0 + 295min we found for weighted mean estimators distinctively reduced relative deviations ρt0^ = 5\% and ρTA0^ = 11\% with the same quadruple span Δt = 50min. Further research is necessary to guarantee applicability in routine case work. We will investigate more elaborate cooling models, estimation algorithms and evaluation localization.}, language = {en} } @article{AndresArconesWeiserKoutsourelakisetal.2024, author = {Andr{\´e}s Arcones, Daniel and Weiser, Martin and Koutsourelakis, Phaedon-Stelios and Unger, J{\"o}rg F.}, title = {Bias Identification Approaches for Model Updating of Simulation-based Digital Twins of Bridges}, volume = {2}, journal = {Structural Health Monitoring in the Light of Climate Impact and Data Science. Research and Review Journal of Nondestructive Testing}, number = {2}, doi = {10.58286/30524}, year = {2024}, abstract = {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 Nibelungenbr{\"u}cke 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.}, language = {en} }