arXiv subjects

Martin Schneider

Publications and source records attributed to Martin Schneider.

At least 19 recordsLinked to original sources

arXiv2026

Lens-Aware Differentiable Beamforming for In Vivo Distributed Aberration Correction with Curvilinear Transducers

This work extends ultrasound autofocusing via common midpoint phase error optimization to support curvilinear array geometries. Iterative model-based aberration correction via local sound speed estimation is performed by accounting for refraction caused by the transducer lens by using a differentiable bent-ray tracing approach. Model validation is performed in silico, using calibrated sound speed phantoms, and on in vivo human liver images. This work represents the first large-scale in vivo validation of our distributed aberration-correction method on 321 acquisitions from 81 high-BMI human liver subjects. In acquired images with anechoic regions, average contrast and CNR improved by $1.42 \pm 1.63$ dB (+18.4%), and $0.09 \pm 0.14$ (+10.3%), respectively. An average improvement was also observed across multiple image quality metrics: speckle brightness (+20.1%), coherence factor (+13.1%), lag-one coherence (+2.6%), common-midpoint correlation coefficient (+0.7%), and common-midpoint phase error (-9.1%, lower is better). All metric improvements were statistically significant. Additionally, a significant qualitative improvement in target structure and visibility was observed. These results demonstrate the potential for future clinical distributed aberration correction techniques using ultrasound autofocusing.

physics.med-ph↗

arXiv2026

Enhancing event reconstruction for $\gamma$-ray particle detector arrays using transformers

Gamma-ray astronomy from hundreds of GeV to PeV is confined to ground-based experiments that detect air showers induced by $\gamma$-rays entering Earth's atmosphere. While particle detector arrays feature huge detection areas, accurately reconstructing the primary particle properties is difficult due to the sparse sampling of the air shower and its intrinsic fluctuations. In this work, using simulations of a future water-Cherenkov array, we investigate two end-to-end deep learning approaches based on the transformer architecture with different computational complexities that utilize calibrated raw data. We benchmark both methods against well-established methods in the field in terms of $\gamma$-hadron separation, angular, core, and energy reconstruction. Our results show significant improvements across the whole energy range, particularly at low and intermediate energies. This work is the first to consistently demonstrate improved performance in both event reconstruction and $\gamma$-hadron separation using a single architecture.

astro-ph.IM↗

arXiv2025

Modelling Interfacial Dynamics Using Hydrodynamic Density Functional Theory: Dynamic Contact Angles and the Role of Local Viscosity

Hydrodynamic density functional theory (DFT) is applied to analyse dynamic contact angles of droplets in order to assess its predictive capability regarding wetting phenomena at the microscopic scale and to evaluate its feasibility for multiscale modelling. Hydrodynamic DFT incorporates the influence of fluid-fluid and solid-fluid interfaces into a hydrodynamic theory by including a thermodynamic model based on classical DFT for the chemical potential of inhomogeneous fluids. It simplifies to the isothermal Navier-Stokes equations far away from interfaces, thus connecting microscopic molecular modelling and continuum fluid dynamics. In this work we use a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and the viscosity is obtained from generalised entropy scaling, a one-parameter model which takes microscopic information of the fluid and solid phase into account. Deterministic (noise-free) density and velocity profiles reveal wetting phenomena including different advancing and receding contact angles, the transition from equilibrium to steady state and the rolling motion of droplets. Compared to a viscosity model based on bulk values, generalised entropy scaling provides more accurate results, which stresses the importance of including microscopic information in the local viscosity model. Hydrodynamic DFT is transferable as it captures the influence of different external forces, wetting strengths and (molecular) solid roughness. For all results good quantitative agreement with non-equilibrium molecular dynamics simulations is found, which emphasises that hydrodynamic DFT is able to predict wetting phenomena at the microscopic scale.

physics.flu-dyn↗

arXiv2025

Improvement of fully-implicit two-phase pore-network models by employing generalized flux functions with additional throat variables

In fully-implicit two-phase pore-network models, developing a well-converged scheme remains a major challenge, primarily due to the discontinuities in the phase conductivities. This paper addresses these numerical issues by proposing a generalized flux function that establishes a continuous flux expression for two-phase flows by introducing an additional throat variable $Θ$. Two approaches for expressing this additional throat variable are introduced: the first applies regularization strategies, while the second constructs an additional residual constraint equation. It is shown that this approach significantly improves accuracy and ensures the temporal convergence, as demonstrated through various numerical examples.

math.NA↗

arXiv2025

Application of Graph Networks to a wide-field Water-Cherenkov-based Gamma-Ray Observatory

With their wide field of view and high duty cycle, water-Cherenkov-based observatories are integral to studying the very high-energy gamma-ray sky. For gamma-ray observations, precise event reconstruction and highly effective background rejection are crucial and have been continuously improving in recent years. In this work, we investigate the application of graph neural networks (GNNs) to background rejection and energy reconstruction and benchmark their performance against state-of-the-art methods. In our simulation study, we find that GNNs outperform hand-designed classification algorithms and observables in background rejection and find an improved energy resolution compared to template-based methods.

astro-ph.IM↗

arXiv2024

Analysis, Design, and Fabrication of a High-Gain Low-Profile Metasurface Antenna Using Direct Feeding of Sievenpiper s HIS

HISs have recently shown the ability to support leaky waves, and to excite plasmonic and HIS resonance frequency modes for use as an antenna. In this paper, we analyzed, designed, and fabricated a TMA by directly feeding edge-located HIS cells through a microstrip feeding network. In contrast to other metasurface antennas that necessitate an external antenna to excite metasurfaces, our approach is inspired by the TMA design methodology that directly feeds the HIS cells rather than using it as a reflector. We developed a circuit model for the proposed structure and compared the results with those obtained from full-wave simulations. In addition, our further objective was to simplify the structure based on the working principle of the proposed antenna. This objective was achieved by converting square patches into parallel strip lines, leading to an aperture efficiency of 0.77. This simplification also creates additional space to explore various resonant patterns on the top surface and the feeding network on the bottom surface of the TMA. Full-wave simulation results indicate that, despite the compact dimensions of the proposed array with 64 electrically small patch resonators (1.84λ*1.84λ*0.032λ, whereλis the free space wavelength at 6.0 GHz), it achieves a realized gain, HPBW of about 15.1 dBi and 28° respectively at 6 GHz. Finally, we constructed a prototype and conducted measurements to validate the design. Measured results demonstrate good agreement with simulation ones with a gain of about 13.5 (+-0.5) dBi and a HPBW of 27° at 6 GHz. The proposed TMA is scaled to fit within the required dimensions for smart handheld devices at higher frequencies, while maintaining high gain capability. The design s scalability, single-feed, and compact footprint make it optimal for diverse wireless communication systems, such as car to car communications.

physics.app-ph↗

arXiv2024

Data-Driven Closure Parametrizations with Metrics: Dispersive Transport

This work presents a data-driven framework for multi-scale parametrization of velocity-dependent dispersive transport in porous media. Pore-scale flow and transport simulations are conducted on periodic pore geometries, and volume-averaging is used to isolate dispersive transport, producing parameters for the dispersive closure term at the Representative Elementary Volume (REV) scale. After validation on unit cells with symmetric and asymmetric geometries, a convolutional neural network (CNN) is trained to predict dispersivity directly from pore-geometry images. Descriptive metrics are also introduced to better understand the parameter space and are used to build a neural network that predicts dispersivity based solely on these metrics. While the models predict longitudinal dispersivity well, transversal dispersivity remains difficult to capture, likely requiring more advanced models to fully describe pore-scale transversal dynamics.

math.NA↗

arXiv2024

A fully-implicit solving approach to an adaptive multi-scale model -- coupling a vertical-equilibrium and full-dimensional model for compressible, multi-phase flow in porous media

Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the dynamics of a system. While conventional full-dimensional models have the ability to represent dynamics, they come at the cost of high computational effort. We aim to combine the efficiency of the vertical equilibrium model and the accuracy of the full-dimensional model by coupling the two models adaptively in a unified framework and solving the emerging system of equations in a monolithic, fully-implicit approach. The model domains are coupled via mass-conserving fluxes while the model adaptivity is ruled by adaption criteria. Overall, the adaptive model shows an excellent behaviour both in terms of accuracy as well as efficiency, especially for elongated geometries of storage systems with large aspect ratios.

physics.flu-dyn↗

arXiv2023

A DuMux Framework for Data-Driven Multi-Scale Parametrizations

Presented in this work is a framework for the data-driven determination of multi-scale porous media parametrizations. Simulations of flow and transport in a porous medium at the REV scale, although efficient, require well defined parameters that represent pore-scale phenomena to maintain their accuracy. Determining the optimal parameters for this often require expensive pore-scale calculations. This work outlines a series of four steps where these parameters can be calculated from pore scale data, their solutions generalized with a convolutional neural network, and their content better understood with descriptive pore metrics.

math.NA↗

arXiv2023

A new numerical mesoscopic scale one-domain approach solver for free fluid/porous medium interaction

A new numerical continuum \textit{one-domain} approach (ODA) solver is presented for the simulation of the transfer processes between a free fluid and a porous medium. The solver is developed in the \textit{mesoscopic} scale framework, where a continuous variation of the physical parameters of the porous medium (e.g., porosity and permeability) is assumed. The Navier-Stokes-Brinkman equations are solved along with the continuity equation, under the hypothesis of incompressible fluid. The porous medium is assumed to be fully saturated and can potentially be anisotropic. The domain is discretized with unstructured meshes allowing local refinements. A fractional time step procedure is applied, where one predictor and two corrector steps are solved within each time iteration. The predictor step is solved in the framework of a marching in space and time procedure, with some important numerical advantages. The two corrector steps require the solution of large linear systems, whose matrices are sparse, symmetric and positive definite, with $\mathcal{M}$-matrix property over Delaunay-meshes. A fast and efficient solution is obtained using a preconditioned conjugate gradient method. The discretization adopted for the two corrector steps can be regarded as a Two-Point-Flux-Approximation (TPFA) scheme, which, unlike the standard TPFA schemes, does not require the grid mesh to be $\mathbf{K}$-orthogonal, (with $\mathbf{K}$ the anisotropy tensor). As demonstrated with the provided test cases, the proposed scheme correctly retains the anisotropy effects within the porous medium. Furthermore, it overcomes the restrictions of existing mesoscopic scale one-domain approachs proposed in the literature.

math.NA↗

arXiv2023

Stable and locally mass- and momentum-conservative control-volume finite-element schemes for the Stokes problem

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy employs a non-overlapping partitioning into control volumes. The second represents a new idea by splitting into two sets of control volumes, the first set yielding a partition of the domain and the second containing the remaining overlapping control volumes required for stability. The third represents a hybrid approach where finite volumes are combined with finite elements based on a hierarchical splitting of the ansatz space. All approaches are based on typical finite element function spaces but yield locally mass and momentum conservative discretization schemes that can be interpreted as finite volume schemes. We apply all strategies to the inf-sub stable MINI finite-element pair. Various test cases, including convergence tests and the numerical observation of the boundedness of the number of preconditioned Krylov solver iterations, as well as more complex scenarios of flow around obstacles or through a three-dimensional vessel bifurcation, demonstrate the stability and robustness of the schemes.

math.NA↗

arXiv2022

A Surrogate-Assisted Uncertainty-Aware Bayesian Validation Framework and its Application to Coupling Free Flow and Porous-Medium Flow

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid--porous interface. These models include a porous-medium model using Darcy's law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems' behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model's predictive capabilities, and make a probabilistic model comparison.

stat.AP↗

arXiv2021

Coupling staggered-grid and vertex-centered finite-volume methods for coupled porous-medium free-flow problems

In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a vertex-centered finite volume method is used in the porous-medium flow domain. The latter allows for the use of unstructured grids in the porous-medium subdomain, and the presented method is capable of handling non-matching grids at the interface. In addition, the accurate evaluation of coupling terms and of additional nonlinear velocity-dependent terms in the porous medium is ensured by the use of basis functions and by having degrees of freedom naturally located at the interface. The available advantages of this coupling method are investigated in a series of tests: a convergence test for various grid types, an evaluation of the implementation of coupling conditions, and an example using the velocity dependent Forchheimer term in the porous-medium subdomain.

math.NA↗

arXiv2021

Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake

We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical applications such as in the modeling of root-water uptake, heat exchangers, or geothermal wells. The nonlinearity appears in form of solution-dependent parameters such as pressure-dependent permeability or temperature-dependent thermal conductivity. We derive and analyse a numerical scheme based on distributing the bulk-network coupling source term by a smoothing kernel with local support. By the use of local analytical solutions, interface unknowns and fluxes at the bulk-network interface can be accurately reconstructed from coarsely resolved numerical solutions in the bulk domain. Numerical examples give confidence in the robustness of the method and show the results in comparison to previously published methods. The new method outperforms these existing methods in accuracy and efficiency. In a root water uptake scenario, we accurately estimate the transpiration rate using only a few thousand 3D mesh cells and a structured cube grid whereas other state-of-the-art numerical schemes require millions of cells and local grid refinement to reach comparable accuracy.

cs.CE↗

arXiv2020

Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media

Flow in fractured porous media is of high relevance in a variety of geotechnical applications, given the fact that they ubiquitously occur in nature and that they can have a substantial impact on the hydraulic properties of rock. As a response to this, an active field of research has developed over the past decades, focussing on the development of mathematical models and numerical methods to describe and simulate the flow processes in fractured rock. In this work, we present a comparison of different finite volume-based numerical schemes for the simulation of flow in fractured porous media by means of numerical experiments. Two novel vertex-centered approaches are presented and compared to well-established numerical schemes in terms of convergence behaviour and their performance on benchmark studies taken from the literature. The new schemes show to produce results that are in good agreement with those of established methods while being computationally less expensive on unstructured simplex grids.

math.NA↗

arXiv2019

DuMu$^\text{x}$ 3 -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling

We present version 3 of the open-source simulator for flow and transport processes in porous media DuMu$^\text{x}$. DuMu$^\text{x}$ is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMu$^\text{x}$, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

cs.CE↗

arXiv2019

A new and consistent well model for one-phase flow in anisotropic porous media using a distributed source model

A new well model for one-phase flow in anisotropic porous media is introduced, where the mass exchange between well and a porous medium is modeled by spatially distributed source terms over a small neighborhood region. To this end, we first present a compact derivation of the exact analytical solution for an arbitrarily oriented, infinite well cylinder in an infinite porous medium with anisotropic permeability tensor in R3 , for constant well pressure and a given injection rate, using a conformal map. The analytical solution motivates the choice of a kernel function to distribute the sources. The presented model is independent from the discretization method and the choice of computational grids. In numerical experiments, the new well model is shown to be consistent and robust with respect to rotation of the well axis, rotation of the permeability tensor, and different anisotropy ratios. Finally, a comparison with a Peaceman-type well model suggests that the new scheme leads to an increased accuracy for injection (and production) rates for arbitrarily-oriented pressure-controlled wells.

cs.CE↗

arXiv2019

Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources

We present a new method for modeling tissue perfusion on the capillary scale. The microvasculature is represented by a network of one-dimensional vessel segments embedded in the extra-vascular space. Vascular and extra-vascular space exchange fluid over the vessel walls. This exchange is modeled by distributed sources using smooth kernel functions for the extra-vascular domain. It is shown that the proposed method may significantly improve the approximation of the exchange flux, in comparison with existing methods for mixed-dimension embedded problems. Furthermore, the method exhibits better convergence rates of the relevant quantities due to the increased regularity of the extra-vascular pressure solution. Numerical experiments with a vascular network from the rat cortex show that the error in the approximation of the exchange flux for coarse grid resolution may be decreased by a factor of $3$. This may open the way for computing on larger network domains, where a fine grid resolution cannot be achieved in practical simulations due to constraints in computational resources, for example in the context of uncertainty quantification.

physics.comp-ph↗