arXiv subjects

Alexander Popp

Publications and source records attributed to Alexander Popp.

At least 19 recordsLinked to original sources

arXiv2026

Mechanical Modeling of Braided Neurovascular Flow Diverters using a Beam-to-Beam and Beam-to-Surface Contact Formulation

Braided neurovascular flow diverters are widely used for the endovascular treatment of intracranial aneurysms, where their mechanical response and final deployed configuration are governed by the interaction of many slender, interwoven wires. Accurate numerical modeling of these devices is essential for analyzing their structural behavior during deformation occurring in compression or deployment. This work presents a structural-mechanics-based modeling framework and finite element formulation for the numerical simulation of braided flow diverters. The individual wires are modeled using geometrically exact Simo--Reissner beam theory, allowing a consistent description of large rotations and curved reference configurations. Mechanical interactions between individual wires are described by a beam-to-beam contact formulation, while the interaction with surrounding tubular structures, such as microcatheters, is captured by a beam-to-surface contact formulation. A flexible parametric description of interwoven braided flow diverter geometries is introduced, enabling systematic control of geometric design parameters such as wire count, braiding angle, device length, and radial interweaving pattern. The proposed framework is assessed by means of three representative validation cases from the literature. A tensile test is considered to investigate the length--diameter relation and axial force response of the device, while a radial compression test is used to study the pressure--diameter behavior. Finally, a stepwise compression example is used to evaluate geometry-sensitive quantities, including local wire distance, pitch angle, porosity, and metal coverage ratio. Rooted in structural mechanics and contact mechanics, these examples provide a systematical validation setting for the proposed modeling framework and its application to the mechanical analysis of braided flow diverters.

cs.CE↗

arXiv2026

Contact-resolved deployment of the Contour Neurovascular System in patient-specific intracranial aneurysms

While intrasaccular flow disruptors are widely used to treat wide-neck intracranial aneurysms, state-of-the-art patient-specific computational models routinely neglect the deployment mechanics by prescribing a pre-seated geometry. This shortcut oversimplifies the true physics and misrepresents the Contour Neurovascular System (CNS), whose critical biomechanical features, such as neck coverage, wall apposition, and migration resistance, are highly path-dependent. To resolve this limitation, we present a contact-resolved finite-element framework that explicitly computes the structural mechanics of implant deployment within patient-specific vascular environments. The device is discretized as a dual-layer interwoven Nitinol braid using geometrically exact beams, while the vascular wall is represented as a deformable hyperelastic shell. Non-linear frictional contact formulations govern complex wire-wire and wire-wall interactions under a staged release protocol. Evaluating three anatomical phenotypes reveals that the final equilibrium morphology is highly sensitive to tangential slip resistance and vertical release depth. Frictionless assumptions permit excessive post-contact sliding, whereas near-stick conditions enhance anchoring but restrict local compliance. Crucially, conventional geometric fast placement fails to capture these critical contact interactions and wall-supported mechanical equilibrium. This deployment-resolved framework establishes a biomechanically grounded foundation for downstream hemodynamics, fluid-structure interaction, and mechanobiological thrombus-formation modeling.

physics.comp-ph↗

arXiv2026

High-Fidelity Numerical Modeling for the Mechanical Characterization of a Full-Scale Test Bridge

Bridges are vital components of transportation networks, serving as critical lifelines that ensure the safe and efficient movement of people, goods, and emergency services. With aging infrastructures, increasing traffic volumes and loads, and growing impact of extreme weather events driven by climate change, the development of reliable structural health monitoring (SHM) strategies has become of utmost importance. A key challenge in this domain is the scarcity of data on well-characterized damage states. To address this, a monitoring campaign was recently conducted on a full-scale, two-span test bridge specifically designed and built at the University of the Bundeswehr Munich to investigate damage scenarios related to specific structural deficiencies of the deck and to foundations settlement, the latter being connected to failure mechanisms typical in the context of floodings, when scour, i.e., washing out of the foundations, might happen. The test bridge is a crucial intermediate step between laboratory-scale experiments and real-world monitoring. In this study, a high-fidelity, physics-based numerical model of the same structure is presented as a complementary tool. The model enables accurate performances assessment and provides a detailed reference to interpret measured responses under varying environmental conditions and artificial damage scenarios. Experimental data collected under operational conditions were used to refine the model's mechanical characterization through Bayesian updating. The goal is to develop a functional digital twin of the test bridge, acting as a dynamic, data-driven shadow of the physical structure, to support informed maintenance decisions, extend service life, and enhance safety in future studies applied to real-world infrastructures.

cs.CE↗

arXiv2026

Physics-Informed Sensitivity Analysis for Enhanced Structural Health Assessment: Test-Case for a Mixed Steel-Concrete Bridge

Bridges are vital components of transportation systems, that serve as essential links ensuring the safe and efficient movement of people, goods, and emergency responders, especially during crises. With aging infrastructures, increasing traffic volumes and loads, and the intensifying impacts of extreme weather events due to climate change, the development of effective physics-informed structural health monitoring (SHM) frameworks has become critically important, more so when combined with sensitivity analysis (SA), which identifies the most influential structural parameters in the bridge's response. To support this, a high-fidelity, physics-based numerical model of a full-scale, two-span, mixed steel-concrete test bridge has been developed. This model serves as a virtual replica of a real structure located at the University of the Bundeswehr Munich. The numerical model is used as a complementary tool to improve prognostic capabilities and quantify uncertainty. A SA study is conducted to evaluate the structure's response under various mechanical conditions. Assessing these operational variations' effects on structural behavior forms part of an integrated, systematic evaluation framework aimed at combining SHM and SA.

cs.CE↗

arXiv2026

Sparsity-Driven Source Localization in Tomographic Sensing Applications

Hyperspectral standoff detection systems such as Focal Plane Array (FPA) Fourier Transform Infrared (FTIR) spectrometers provide high spatial resolution in detecting airborne chemical contaminants that are invisible to the human eye but potentially hazardous. When two such systems are operated simultaneously with a suitable opening angle, they enable tomographic reconstruction of contaminant plumes with improved spatial and temporal accuracy. This work presents a mathematical model of these measurement capabilities and an algorithm to identify, localize, and quantify contaminant release sources. The objective is to develop a a tool that reconstructs release locations and predict the future plume evolution from standoff measurement data, thereby supporting early warning and situational awareness in hazardous material release scenarios. The transport of contaminants is modeled by an advection-diffusion equation, and the corresponding inverse problem for source identification is formulated accordingly. Owing to the severe ill-posedness and underdetermination of the problem, a sparsity-promoting regularization approach is employed together with a high-performance optimization algorithm. To incorporate the tomographic measurement data into the discrete formulation, a level-set description of a threshold concentration is used, allowing the measurements to be represented independently of the computational mesh and avoiding costly remeshing procedures.

math.NA↗

arXiv2026

Modified augmented Lagrangian preconditioning for mixed-dimensional beam-solid coupling

This paper presents modified augmented Lagrangian block preconditioners for the mixed-dimensional coupling of three-dimensional solid bodies with embedded one-dimensional torsion-free Kirchhoff-Love beams using Lagrange multipliers for constraint enforcement. The finite element discretization of this mixed formulation leads to an indefinite saddle-point system. An augmented Lagrangian formulation is employed to regularize the linear system while maintaining exact enforcement of the coupling constraints. Starting from the corresponding ideal augmented Lagrangian block preconditioner, more practical block-triangular variants are derived in which the solid, beam, and Schur complement blocks can be treated independently. In addition, different variants of Schur complement approximations are introduced. Numerical experiments demonstrate robustness with respect to model parameters, near mesh-independent iteration counts, and favorable strong and weak scalability. These results indicate the suitability of the proposed approach for large-scale simulations of mixed-dimensional models in solid and structural mechanics, as demonstrated by an engineering example involving a composite sandwich plate.

cs.CE↗

arXiv2026

Towards Interpretable Damage Detection based on Aerodynamic Pressure Measurements

The increasing flexibility of modern large wind turbine blades necessitates cost-efficient and reliable structural monitoring solutions. For this purpose, we propose to use aerodynamic pressure measurements obtained via Aerosense, a novel, non-intrusive and economical sensing system. In former work [Franz et al., 2025], we investigated the potential of aerodynamic pressure measurements for structural damage detection on elastic and aerodynamically loaded structures. An experimental campaign was conducted on a NACA 633418 airfoil mounted on a vertically vibrating cantilever beam within an open wind tunnel. Structural damage was introduced progressively through controlled saw cuts near the beam support. Aerodynamic pressure distributions were recorded under varying inflow conditions and structural states. Based on this data set, we developed a convolutional neural network to detect structural damage and classify its severity using only aerodynamic pressure signals. The results demonstrate that pressure measurements can effectively enable real-time detection and quantification of damage in elastic, beam-like structures subjected to mildly turbulent flow and varying operational conditions. Recognizing the limitations of pure black-box classification, in this study, we further incorporate physics-based insights and explainable machine learning methods to interpret how structural damage influences both the dynamic response and the aerodynamic pressure field. This leads to an enhanced damage detection pipeline, aiming to improve transparency, robustness, and physical consistency in data-driven monitoring of elastic, aerodynamically loaded structures.

eess.SP↗

arXiv2026

A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories

Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical formulations are involved in terms of underlying beam theory, interpolation schemes, and rotation parametrization. In this work, a versatile formulation-independent beam-to-beam point coupling approach is proposed within the framework of the geometrically exact beam theory discretized by the finite element method. The coupling constraints are expressed solely in terms of cross-section kinematics, namely centroid positions and orientations. Suitable generalized deformation measures for positional and rotational coupling are introduced, allowing for general coupling configurations, including relative rotations and non-coincident cross-section centroids in the reference configuration. The contribution of the coupling conditions to the weak form of the balance equations is derived in a variationally consistent manner and can be incorporated directly into the weak form of existing beam finite element models. Constraint enforcement is formulated using a Lagrange multiplier method and a penalty regularization. The proposed approach satisfies key properties such as objectivity, symmetry, and consistency with an stress-free reference configuration. Numerical examples demonstrate the robustness and flexibility of the method for coupling beams with different formulations and discretizations, even when the interaction points are located at arbitrary positions within beam elements.

cs.CE↗

arXiv2026

Rapid Identification of Moving Contaminant Sources Through Physics-Based Modelling

In an act of sabotage or terrorism, hazardous material might be released deliberately into the atmosphere to threaten individuals, e.g., those operating critical infrastructure. Hazardous materials in such a scenario include toxic industrial chemicals (TICs), which are often invisible to the human eye, making it difficult to detect and respond to releases in a timely manner. This contribution considers the scenario of an airborne hazardous release requiring rapid and reliable assessment, with a chemical, biological, radiological, and nuclear (CBRN) sensor system providing scarce and local measurements. We present a novel algorithm that couples these data with an advection-diffusion model to detect, localize, and quantify a moving and time-varying contaminant source. Unlike many existing methods, the approach identifies sources with unknown occurrence time and trajectory by incorporating spatial sparsity as prior information. The feasibility of the approach is demonstrated in a two-dimensional computational domain. To further increase the technology readiness level, we additionally propose a calibration methodology for the required three-dimensional flow models based on wind tunnel experiments. Finally, a strategy for coupling the framework with real-time sensor data within a digital twin environment is outlined to enable predictive decision support in emergency scenarios.

math.NA↗

arXiv2026

An Embedded Mesh Approach for Isogeometric Boundary Layers in Contact Mechanics

This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact interface and the bulk volume, allowing local requirements--such as element type and mesh resolution--to be addressed efficiently. Exploiting the boundary representation of CAD models, the contact interface of each body is discretized using a NURBS-based boundary layer mesh. This provides a smooth geometric description of the contact surface and enhanced inter-element continuity. The bulk domain is discretized using a structured Cartesian grid. To couple the resulting non-matching discretizations, an embedded mesh approach based on a mortar-type constraint formulation is employed. The paper describes in detail the proposed discretization workflow for generating both the isogeometric boundary layer and the structured Cartesian grid, and presents several strategies for constructing NURBS-based boundary layer meshes. Finally, a set of numerical examples is provided to validate the proposed approach.

cs.CE↗

arXiv2026

Intrusive and Non-Intrusive Model Order Reduction for Airborne Contaminant Transport: Comparative Analysis and Uncertainty Quantification

Numerical simulations of contaminant dispersion after a gas leakage incident on a chemical plant can provide valuable insights for both emergency response and preparedness. Simulation approaches combine incompressible Navier-Stokes (INS) equations with advection-diffusion (AD) processes to model wind and concentration field. However, the computational cost of such high-fidelity simulations increases rapidly for complex geometries like urban environments, making them unfeasible in time-critical or multi-query "what-if" scenarios. Therefore, this study focuses on the application of model order reduction (MOR) techniques enabling fast yet accurate predictions. To this end, a thorough comparison of intrusive and non-intrusive MOR methods is performed for the computationally more demanding parametric INS problem with varying wind velocities. Based on these insights, a non-intrusive reduced-order model (ROM) is constructed accounting for both wind velocity and direction. The study is conducted on a two-dimensional domain derived from real-world building footprints, preserving key features for analyzing passive transport across urban areas. The resulting ROM enables faster than real-time predictions of spatio-temporal contaminant dispersion from an instantaneous source under varying wind conditions. This capability allows assessing wind measurement uncertainties by a Monte Carlo analysis. To demonstrate the practical applicability, an interactive dashboard provides intuitive access to simulation results.

cs.CE↗

arXiv2026

Experimental and Numerical Study of the Transient Response of a Cantilever Beam with a Piezoelectric Disc Sensor

Online and real-time sensing and monitoring of the health state of complex structures, such as aircraft and critical components of power stations, are essential aspects of research in dynamics. Several types of sensors are used to capture dynamic responses and monitor changes during the operation of critical parts of complex systems. Piezoelectric (PZ) materials belong to a class of electroactive materials that convert mechanical deformation into an electrical response. For example, PZ ceramics or PVDF foils are employed for online sensing of the time history of mechanical deformation. This paper focuses on the dynamical response of a cantilever beam structure equipped with a glued PZ sensor and combines experimental and modelling approaches to achieve accurate and reliable results. The time history of the normal velocity at a point on the beam surface was recorded with a laser vibrometer during transient vibrations of the beam, triggered by the sudden removal of a mass load at the beam's free end. Simultaneously, the output voltage of the PZ sensor was measured with an electronic device. An elastodynamic model of a cantilever beam coupled with a piezoelectric sensor is introduced, along with its discretization using the finite element method. The mathematical model includes additional terms that enforce a floating-potential boundary condition to maintain a constant charge on one of the sensor's electrodes and is presented in an extended form suitable for sensitivity analysis or parameter identification. The model implementation is validated using a numerical example corresponding to the experimental setup. The computed results show good agreement with the experimental data. Furthermore, values of the Rayleigh damping parameters were identified based on the experimental measurements.

cs.CE↗

arXiv2026

Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic materials

This paper introduces a material-aware strength-of-connection measure for smoothed aggregation algebraic multigrid methods, aimed at improving robustness for scalar partial differential equations with heterogeneous and anisotropic material properties. Classical strength-of-connection measures typically rely only on matrix entries or geometric distances, which often fail to capture weak couplings across material interfaces or align with anisotropy directions, ultimately leading to poor convergence. The proposed approach directly incorporates material tensor information into the coarsening process, enabling a reliable detection of weak connections and ensuring that coarse levels preserve the true structure of the underlying problem. As a result, smooth error components are represented properly and sharp coefficient jumps or directional anisotropies are handled consistently. A wide range of academic tests and real-world applications, including thermally activated batteries and solar cells, demonstrate that the proposed method maintains robustness across material contrasts, anisotropies, and mesh variations. Scalability and parallel performance of the algebraic multigrid method highlight the suitability for large-scale, high-performance computing environments.

cs.CE↗

arXiv2025

Sparse Source Identification in Transient Advection-Diffusion Problems with a Primal-Dual-Active-Point Strategy

This work presents a mathematical model to enable rapid prediction of airborne contaminant transport based on scarce sensor measurements. The method is designed for applications in critical infrastructure protection (CIP), such as evacuation planning following contaminant release. In such scenarios, timely and reliable decision-making is essential, despite limited observation data. To identify contaminant sources, we formulate an inverse problem governed by an advection-diffusion equation. Given the problem's underdetermined nature, we further employ a variational regularization ansatz and model the unknown contaminant sources as distribution over the spatial domain. To efficiently solve the arising inverse problem, we employ a problem-specific variant of the Primal-Dual-Active-Point (PDAP) algorithm which efficiently approximates sparse minimizers of the inverse problem by alternating between greedy location updates and source intensity optimization. The approach is demonstrated on two- and three-dimensional test cases involving both instantaneous and continuous contaminant sources and outperforms state-of-the-art techniques with $L^2$-regularization. Its effectiveness is further illustrated in complex domains with real-world building geometries imported from OpenStreetMap.

math.NA↗

arXiv2025

Influence of coronary plaque morphology on local mechanical states and associated in-stent restenosis

In-stent restenosis (ISR) after percutaneous coronary intervention is a multi-factorial process. Specific morphological lesion characteristics were observed to contribute to the occurrence of ISR. Local mechanical factors, such as stresses and strains, are known to influence tissue adaptation after stent implantation. However, the influence of morphological features on those local mechanical states and, hence, on the occurrence of ISR remains understudied. This work explores how local mechanical quantities relate to ISR by evaluating the stress distributions in the artery wall during and after stent implantation for morphology-informed lesion examples. We perform computational simulations of the stenting procedure with physics-based patient-specific coronary artery models. Different morphologies are assessed using the spatial plaque composition information from high-resolution coronary computed tomography angiography data. In the sample cases, elevated local tensile stresses were consistently found at sites corresponding to ISR. We found that specific morphological characteristics like circumferential or asymmetric block calcifications result in higher stresses in the surrounding tissue. These findings show that for the observed connection between plaque morphology and ISR, the local mechanical state may represent a relevant link. This study provides a mechanistic, illustrative insight for the examined cases. Future work with larger cohorts and systematic follow-up can establish statistically robust associations.

cs.CE↗

arXiv2025

Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management

This paper presents a novel framework for goal-oriented optimal static sensor placement and dynamic sensor steering in PDE-constrained inverse problems, utilizing a Bayesian approach accelerated by low-rank approximations. The framework is applied to airborne contaminant tracking, extending recent dynamic sensor steering methods to complex geometries for computational efficiency. A C-optimal design criterion is employed to strategically place sensors, minimizing uncertainty in predictions. Numerical experiments validate the approach's effectiveness for source identification and monitoring, highlighting its potential for real-time decision-making in crisis management scenarios.

math.NA↗

arXiv2025

Data-Driven Surrogate Modeling Techniques to Predict the Effective Contact Area of Rough Surface Contact Problems

The effective contact area in rough surface contact plays a critical role in multi-physics phenomena such as wear, sealing, and thermal or electrical conduction. Although accurate numerical methods, like the Boundary Element Method (BEM), are available to compute this quantity, their high computational cost limits their applicability in multi-query contexts, such as uncertainty quantification, parameter identification, and multi-scale algorithms, where many repeated evaluations are required. This study proposes a surrogate modeling framework for predicting the effective contact area using fast-to-evaluate data-driven techniques. Various machine learning algorithms are trained on a precomputed dataset, where the inputs are the imposed load and statistical roughness parameters, and the output is the corresponding effective contact area. All models undergo hyperparameter optimization to enable fair comparisons in terms of predictive accuracy and computational efficiency, evaluated using established quantitative metrics. Among the models, the Kernel Ridge Regressor demonstrates the best trade-off between accuracy and efficiency, achieving high predictive accuracy, low prediction time, and minimal training overhead-making it a strong candidate for general-purpose surrogate modeling. The Gaussian Process Regressor provides an attractive alternative when uncertainty quantification is required, although it incurs additional computational cost due to variance estimation. The generalization capability of the Kernel Ridge model is validated on an unseen simulation scenario, confirming its ability to transfer to new configurations. Database generation constitutes the dominant cost in the surrogate modeling process. Nevertheless, the approach proves practical and efficient for multi-query tasks, even when accounting for this initial expense.

cs.CE↗

arXiv2024

Physics-Informed Neural Networks for Solving Contact Problems in Three Dimensions

This paper explores the application of physics-informed neural networks (PINNs) to tackle forward problems in 3D contact mechanics, focusing on small deformation elasticity. We utilize a mixed-variable formulation, enhanced with output transformations, to enforce Dirichlet and Neumann boundary conditions as hard constraints. The inherent inequality constraints in contact mechanics, particularly the Karush-Kuhn-Tucker (KKT) conditions, are addressed as soft constraints by integrating them into the network's loss function. To enforce the KKT conditions, we leverage the nonlinear complementarity problem (NCP) approach, specifically using the Fischer-Burmeister function, which is known for its advantageous properties in optimization. We investigate two benchmark examples of PINNs in 3D contact mechanics: a single contact patch test and the Hertzian contact problem.

cs.CE↗