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The combined use of data from different sources can be critical in emergencies, where accurate models are needed to make real-time decisions, but high-fidelity representations and detailed information are simply unavailable. This study presents a data assimilation framework based on an ensemble Kalman filter that sequentially exploits and improves an advection-diffusion model in a case study concerning an airborne contaminant dispersion problem over a complex two-dimensional domain. An autonomous aerial drone is used to sequentially observe the actual contaminant concentration in a small fraction of the domain, orders of magnitude smaller than the total domain area. Such observations are synchronized with the data assimilation framework, iteratively adjusting the simulation. The path of the drone is sequentially optimized by balancing exploration and exploitation according to the available knowledge at each decision time. Starting from an erroneous initial model based on approximated assumptions that represent the limited initial knowledge available during emergency scenarios, results show how the proposed framework sequentially improves its belief about the dispersion dynamics, thus providing a reliable contaminant concentration map.

A digital twin framework for rapid predictions of atmospheric contaminant dispersion is developed to support informed decision making in emergency situations. In an offline preparation phase, the geometry of a built environment is discretized with a finite element (FEM) mesh and a reduced-order model (ROM) of the steady-state incompressible Navier-Stokes equations is constructed for various wind conditions. Subsequently, the ROM provides a fast wind field estimate based on the current wind speed during the online phase. To support crisis management, several methodological building blocks are combined. Automatic FEM meshing of built environments and numerical flow solver capabilities enable fast forward-simulations of contaminant dispersion using the advection-diffusion equation as transport model. Further methods are integrated in the framework to address inverse problems such as contaminant source localization based on sparse concentration measurements. Additionally, the contaminant dispersion model is coupled with a continuum-based pedestrian crowd model to derive fast and safe evacuation routes for people seeking protection during contaminant dispersion emergencies. The interplay of these methods is demonstrated in two critical infrastructure protection (CIP) test cases. Based on simulated real world interaction (measurements, communication), this article demonstrates a full Measurement-Inversion-Prediction-Steering (MIPS) cycle including a Bayesian formulation of the inverse problem.

Coronary angioplasty with stent implantation is the most frequently used interventional treatment for coronary artery disease. However, reocclusion within the stent, referred to as in-stent restenosis, occurs in up to 10% of lesions. It is widely accepted that mechanical loads on the vessel wall strongly affect adaptive and maladaptive mechanisms. Yet, the role of procedural and lesion-specific influence on restenosis risk remains understudied. Computational modeling of the stenting procedure can provide new mechanistic insights, such as local stresses, that play a significant role in tissue growth and remodeling. Previous simulation studies often featured simplified artery and stent geometries and cannot be applied to real-world examples. Realistic simulations were computationally expensive since they featured fully resolved stenting device models. The aim of this work is to develop and present a mixed-dimensional formulation to simulate the patient-specific stenting procedure with a reduced-dimensional beam model for the stent and 3D models for the artery. In addition to presenting the numerical approach, we apply it to realistic cases to study the intervention's mechanical effect on the artery and correlate the findings with potential high-risk locations for in-stent restenosis. We found that high artery wall stresses develop during the coronary intervention in severely stenosed areas and at the stent boundaries. Herewith, we lay the groundwork for further studies towards preventing in-stent restenosis after coronary angioplasty.

Urban populations continue to grow, highlighting the critical need to safeguard civilians against potential disruptions, such as dangerous gas contaminant dispersion. The digital twin (DT) framework offers promise in analyzing and predicting such events. This study presents a computational framework for modelling airborne contaminant dispersion in built environments. Leveraging automatic generation of computational domains and solution processes, the proposed framework solves the underlying physical model equations with the finite element method (FEM) for numerical solutions. Model order reduction (MOR) methods are investigated to enhance computational efficiency without compromising accuracy. The study outlines the automatic model generation process, the details of the employed model, and the future perspectives for the realization of a DT. Throughout this research, the aim is to develop a reliable predictive model combining physics and data in a hybrid DT to provide informed real-time support within evacuation scenarios.

In this study, we investigate the potential of fast-to-evaluate surrogate modeling techniques for developing a hybrid digital twin of a steel-reinforced concrete beam, serving as a representative example of a civil engineering structure. As surrogates, two distinct models are developed utilizing physics-informed neural networks, which integrate experimental data with given governing laws of physics. The experimental data (sensor data) is obtained from a previously conducted four-point bending test. The first surrogate model predicts strains at fixed locations along the center line of the beam for various time instances. This time-dependent surrogate model is inspired by the motion of a harmonic oscillator. For this study, we further compare the physics-based approach with a purely data-driven method, revealing the significance of physical laws for the extrapolation capabilities of models in scenarios with limited access to experimental data. Furthermore, we identify the natural frequency of the system by utilizing the physics-based model as an inverse solver. For the second surrogate model, we then focus on a fixed instance in time and combine the sensor data with the equations of linear elasticity to predict the strain distribution within the beam. This example reveals the importance of balancing different loss components through the selection of suitable loss weights.

This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized mortar-type approach for embedding geometrically exact beams into solid continua. Due to the lack of block diagonal dominance of the arising 2 x 2 block system, an approximate block factorization preconditioner is used. It exploits the sparsity structure of the beam sub-block to construct a sparse approximate inverse, which is then not only used to explicitly form an approximation of the Schur complement, but also acts as a smoother within the prediction step of the arising SIMPLE-type preconditioner. The correction step utilizes an algebraic multigrid method. Although, for now, the beam sub-block is tackled by a one-level method only, the multi-level nature of the computationally demanding correction step delivers a scalable preconditioner in practice. In numerical test cases, the influence of different algorithmic parameters on the quality of the sparse approximate inverse is studied and the weak scaling behavior of the proposed preconditioner on up to 1000 MPI ranks is demonstrated, before the proposed preconditioner is finally applied for the analysis of steel-reinforced concrete structures in civil engineering.

Predicting the long-term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient-specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the post-surgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long-term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the post-surgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier-Stokes equations and patient-specific geometries. To probe the suitability of homogenized models, we also investigate poro-elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced-order models of the vascular system. The present study demonstrates our capabilities to predict the post-surgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step.

The present article proposes a partitioned Dirichlet-Neumann algorithm, that allows to address unique challenges arising from a novel mixed-dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar-type finite element discretization. The fibers are modeled via one-dimensional (1D) partial differential equations based on geometrically exact nonlinear beam theory, while the flow is described by the three-dimensional (3D) incompressible Navier-Stokes equations. The arising truly mixed-dimensional 1D-3D coupling scheme constitutes a novel approximate model and numerical strategy, that naturally necessitates specifically tailored solution schemes to ensure an accurate and efficient computational treatment. In particular, we present a strongly coupled partitioned solution algorithm based on a Quasi-Newton method for applications involving fibers with high slenderness ratios that usually present a challenge with regard to the well-known added mass effect. The influence of all employed algorithmic and numerical parameters, namely the applied acceleration technique, the employed constraint regularization parameter as well as shape functions, on efficiency and results of the solution procedure is studied through appropriate examples. Finally, the convergence of the two-way coupled mixed-dimensional problem solution under uniform mesh refinement is demonstrated, a comparison to a 3D reference solution is performed, and the method's capabilities in capturing flow phenomena at large geometric scale separation is illustrated by the example of a submersed vegetation canopy.

The present article proposes a novel computational method for coupling 1D fibers with the 2D surface of a 3D solid. The fibers are modeled as 1D Cosserat continua (beams) with six local degrees of freedom, three positional and three rotational ones. A kinematically consistent 1D-2D coupling scheme for this problem type is proposed considering the positional and rotational degrees of freedom along the beams. The positional degrees of freedom are coupled by enforcing a constant normal distance between a point on the beam centerline and a corresponding point on the solid surface. This strategy requires a consistent description of the solid surface normal vector field to guarantee fundamental mechanical properties such as conservation of angular momentum. Coupling of the rotational degrees of freedom of the beams and a suitable rotation tensor representative for the local orientation within a Boltzmann continuum has been considered in a previous contribution. In the present work, this coupling approach will be extended by constructing rotation tensors that are representative for local surface orientations. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method. To showcase its applicability to multi-physics systems of practical relevance, the fluid-structure interaction example of a vascular stent is presented.

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling conditions at high accuracy, but come with considerable numerical effort and cost for the evaluation of the mortar integrals to compute the coupling operators. In this paper, we identify bottlenecks in parallel data layout and domain decomposition that hinder an efficient evaluation of the mortar integrals. We then propose a set of computational strategies to restore optimal parallel communication and scalability for the core kernels devoted to the evaluation of mortar terms. We exemplarily study the proposed algorithmic components in the context of three-dimensional large-deformation contact mechanics, both for cases with fixed and dynamically varying interface topology, yet these concepts can naturally and easily be transferred to other mortar applications, e.g. classical meshtying problems. To restore parallel scalability, we employ overlapping domain decompositions of the interface discretization independent from the underlying volumes and then tackle parallel communication for the mortar evaluation by a geometrically motivated reduction of ghosting data. Using three-dimensional contact examples, we demonstrate strong and weak scalability of the proposed algorithms up to 480 parallel processes as well as study and discuss improvements in parallel communication related to mortar finite element methods. For the first time, dynamic load balancing is applied to mortar contact problems with evolving contact zones, such that the computational work is well balanced among all parallel processors independent of the current state of the simulation.

Contact and related phenomena, such as friction, wear or elastohydrodynamic lubrication, remain as one of the most challenging problem classes in nonlinear solid and structural mechanics. In the context of their computational treatment with finite element methods (FEM) or isogeometric analysis (IGA), the inherent non-smoothness of contact conditions, the design of robust discretization approaches as well as the implementation of efficient solution schemes seem to provide a never ending source of hard nuts to crack. This is particularly true for the case of beam-to-solid interaction with its mixed-dimensional 1D-3D contact models. Therefore, this contribution gives an overview of current steps being taken, starting from state-of-the-art beam-to-beam (1D) and solid-to-solid (3D) contact algorithms, towards a truly general 1D-3D beam-to-solid contact formulation., Comment: 10 pages, 4 figures

This article proposes a mortar type finite element formulation for consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into 3D solid volumes. A consistent 1D-3D coupling scheme for this problem type is proposed, which enforces both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions in the 3D solid. The rotation tensor defined by the polar decomposition of the deformation gradient is demonstrated to represent these material directions in a L2-optimal manner. Subsequently, objective rotational coupling constraints between beam and solid are formulated and enforced in a variationally consistent framework. Eventually, finite element discretization of all primary fields results in an embedded mortar formulation for rotational and translational constraint enforcement. Based on carefully chosen numerical test cases, the proposed scheme is demonstrated to exhibit a consistent spatial convergence behavior and to offer the up-scaling potential for studying real-life engineering applications such as fiber-reinforced composite materials., Comment: 32 pages, 28 figures

This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-dimensional background fluid mesh, referred to as fluid-beam interaction (FBI) in analogy to the well-established notion of FSI. Here, the fluid is described by the incompressible isothermal Navier-Stokes equations for Newtonian fluids. In particular, we present algorithmic aspects regarding the solution of the resulting one-way coupling schemes and, through selected numerical examples, analyze their spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric analysis is directly based on the spline parametrization and nowadays used for the calculation of higher-order partial differential equations. The computational, or more general, the engineering analysis necessitates suitable coupling techniques between the different patches. Mortar methods have been successfully applied for coupling of patches and for contact mechanics in recent years to resolve the arising issues within the interface. We present here current achievements in the design of mortar technologies in isogeometric analysis within the Priority Program SPP 1748, Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis.

In this paper, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. While the idea of extending multigrid methods to saddle point systems can already be found, e.g., in the context of Stokes and Oseen equations in literature, the main contributions of this work are (i) the development and open-source implementation of an interface aggregation strategy specifically suited for generating Lagrange multiplier aggregates that are required for coupling structural equilibrium equations with contact constraints and (ii) a review of saddle point smoothers in the context of constrained interface problems. The new interface aggregation strategy perfectly fits into an aggregation-based multigrid framework and can easily be combined with segregated transfer operators, which allow to preserve the saddle point structure on the coarse levels. Further analysis provides insight into saddle point smoothers applied to contact problems, while numerical experiments illustrate the robustness of the new method. We have implemented the proposed algorithm within the MueLu package of the open-source Trilinos project. Numerical examples demonstrate the robustness of the proposed method in complex dynamic contact problems as well as its scalability up to 23.9 million unknowns on 480 MPI ranks.

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to capture for the reinforcements, while still being able to account for complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test., Comment: This is a pre-print of an article published in Computational Mechanics (2019). The final authenticated version is available online at: https://link.springer.com/article/10.1007/s00466-019-01791-3

In the authors' previous works, novel finite element formulations for the contact interaction of slender beams have been proposed. In their recent article "Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid Beam Contact - Analysis for the Non-Frictional Case", Konyukhov et al. refer extensively to the aforementioned works by the authors. However, many of these statements turn out to be scientifically incorrect and not only question the quality and correctness of the authors' previous works in a way that is neither objective nor justified but also might cause quite some confusion to researchers in this field. Hence, the authors find it necessary to comment on these statements, disprove them if incorrect, and demonstrate the correctness of the derivations made in their previous works.

Simulation approaches for fluid-structure-contact interaction, especially if requested to be consistent even down to the real contact scenarios, belong to the most challenging and still unsolved problems in computational mechanics. The main challenges are twofold - one is to have a correct physical model for this scenario, and the other one is to have a numerical method that is capable of working and being consistent down to a zero gap. And when analyzing such challenging setups of fluid-structure interaction that include contact of submersed solid components it gets obvious that the influence of surface roughness effects is essential for a physical consistent modeling of such configurations. To capture this system behavior, we present a continuum mechanical model which is able to include the effects of the surface microstructure in a fluid-structure-contact interaction framework. An averaged representation for the mixture of fluid and solid on the rough surfaces, which is of major interest for the macroscopic response of such a system, is introduced therein. The inherent coupling of the macroscopic fluid flow and the flow inside the rough surfaces, the stress exchange of all contacting solid bodies involved, and the interaction between fluid and solid is included in the construction of the model. Although the physical model is not restricted to finite element based methods, a numerical approach with its core based on the Cut Finite Element Method (CutFEM), enabling topological changes of the fluid domain to solve the presented model numerically, is introduced. Such a CutFEM based approach is able to deal with the numerical challenges mentioned above. Different test cases give a perspective towards the potential capabilities of the presented physical model and numerical approach., Comment: 33 pages, 23 figures

A new construction of biorthogonal splines for isogeometric mortar methods is proposed. The biorthogonal basis has a local support and, at the same time, optimal approximation properties, which yield optimal results with mortar methods. We first present the univariate construction, which has an inherent crosspoint modification. The multivariate construction is then based on a tensor product for weighted integrals, whereby the important properties are inherited from the univariate case. Numerical results including large deformations confirm the optimality of the newly constructed biorthogonal basis., Comment: biorthogonal basis, finite deformation, isogeometric analysis, mortar methods, multi-patch geometries