Mesh Edges Research Articles

An interface tracking method with triangle edge cuts

This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.

Patch Decomposition for Efficient Mesh Contours Extraction

AbstractObject‐space occluding contours of triangular meshes (a.k.a. mesh contours) are at the core of many methods in computer graphics and computational geometry. A number of hierarchical data‐structures have been proposed to accelerate their computation on the CPU, but they do not map well to the GPU for real‐time applications, such as video games. We show that a simple, flat data‐structure composed of patches bounded by a normal cone and a bounding sphere may reach this goal, provided it is constructed to maximize the probability for a patch to be culled over all viewpoints. We derive a heuristic metric to efficiently estimate this probability, and present a greedy, bottom‐up algorithm that constructs patches by grouping mesh edges according to this metric. In addition, we propose an effective way of computing their bounding sphere. We demonstrate through extensive experiments that this data‐structure achieves similar performance as the state‐of‐the‐art on the CPU but is also perfectly adapted to the GPU, leading to up to ×5 speedups.

GeoSparseNet: A Multi-Source Geometry-Aware CNN for Urban Scene Analysis

The convolutional neural networks (CNNs) functioning on geometric learning for the urban large-scale 3D meshes are indispensable because of their substantial, complex, and deformed shape constitutions. To address this issue, we proposed a novel Geometry-Aware Multi-Source Sparse-Attention CNN (GeoSparseNet) for the urban large-scale triangular mesh classification task. GeoSparseNet leverages the non-uniformity of 3D meshes to depict both broad flat areas and finely detailed features by adopting the multi-scale convolutional kernels. By operating on the mesh edges to prepare for subsequent convolutions, our method exploits the inherent geodesic connections by utilizing the Large Kernel Attention (LKA) based Pooling and Unpooling layers to maintain the shape topology for accurate classification predictions. Learning which edges in a mesh face to collapse, GeoSparseNet establishes a task-oriented process where the network highlights and enhances crucial features while eliminating unnecessary ones. Compared to previous methods, our innovative approach outperforms them significantly by directly processing extensive 3D mesh data, resulting in more discerning feature maps. We achieved an accuracy rate of 87.5% when testing on an urban large-scale model dataset of the Australian city of Adelaide.

Graph Neural Networks to Simulate Flexible Pavement Responses Using Three-Dimensional Finite Element Analysis Data

The significant computational costs and efforts required for accurate three-dimensional (3D) finite element (FE) pavement response calculations necessitate an expedited approach. This study proposes a graph neural network (GNN)-based simulator for the modeling of 3D pavement structural responses under tire loading. The GNN model was trained using 240 simulations of 3D pavement FE data of flexible pavement structures. The simulator represented the state of pavement structure meshes in FE analysis at any given timestep as a graph, with FE nodes encoded as graph nodes and mesh edges as graph edges. The dynamic behaviors of pavement FEs were computed via learned message-passing between two graphs within two continuous timesteps. The one-step mean squared error (MSE) and rollout MSE were used as evaluation metrics for the GNN model. The results showed that, given an initial state of FE responses, the model could perform accurate one-step predictions, extending to trajectory predictions with one-step MSE as low as [Formula: see text] and rollout MSE around [Formula: see text]. The prediction framework is efficient; it requires a week of model training but only a mere 5 min of prediction for each single case. This a contrast to traditional 3D FE analyses that can span hours to weeks for a single case. The hyperparameters, including the number of message-passing steps M and the number of historical timesteps C, were established as 10 and 1, respectively, based on model performance and computation time. It was also observed that data normalization before training could significantly reduce model simulation noise.

Internet of Things (IoT) Data Communication Challenges, and Solutions

IoT has become an integral part of our lives, and data communication is one of the most important aspects of IoT. IoT devices can exchange data with each other via secure communication channels. This study aimed to review the IoT data communication challenges and solutions This paper attempts to address the key challenges and solutions for effective IoT data communication, starting by exploring the current challenges of IoT data communication related to scalability, reliability, and security, potential solutions to these challenges, such as using a mesh network, centralized servers, and edge computing. In addition, the paper discusses the importance of proper authentication and authorization techniques to ensure secure communication between IoT devices. The potential of IoT data communication is vast and has the power to fundamentally transform our society. It is an exciting time to be involved in this field, and the future looks promising for the advancement of IoT data communication.

A velocity-based moving mesh virtual element method

We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving boundaries which are free to move. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary Lagrangian-Eulerian solution transfer on general polygonal meshes. The approach extends the linear finite element method to polygonal mesh structures, achieving the same degree of accuracy. In the context of moving meshes, a major advantage of the virtual element approach is the ease with which nodes can be inserted on mesh edges. Demonstrations of node insertion techniques are presented to show that moving polygonal meshes can be simply adapted for situations where a boundary encounters a solid object or another moving boundary, without reduction in degree of accuracy.

Versatile Curve Design by Level Set with Quadratic Convergence.

Many 3D mesh processing tasks revolve around generating and manipulating curves on surface meshes. While it is intuitive to explicitly model these curves using mesh edges or parametric curves in the ambient space, these methods often suffer from numerical instability or inaccuracy due to the projection operation. Another natural strategy is to adapt spline based tools, these methods are quite fast but are hard to be extended to more versatile constraints and need heavy manual interactions. In this paper, we present an efficient and versatile approach to curve design based on an implicit representation known as the level set. While previous works have explored the use of the level set to generate curves with minimal length, they typically have limitations in accommodating additional conditions for rich and robust control. To address these challenges, we formulate curve editing with constraints like smoothness, interpolation, tangent control, etc., via a level set based variational problem by constraining the values or derivatives of the level set function. However, the widely used gradient flow strategy converges very slowly for this complicated variational problem compared to the classical geodesic one. Thus, we propose to solve it via Newton's method enhanced by local Hessian correction and a trust-region strategy. As a result, our method not only enables versatile control, but also excels in terms of performance due to nearly quadratic convergence and almost linear complexity in each iteration via narrow band acceleration. In practice, these advantages effectively benefit various applications, such as interactive curve manipulation, boundary smoothing for surface segmentation and path planning with obstacles as demonstrated.

The interior penalty virtual element method for the fourth-order elliptic hemivariational inequality

We develop an interior penalty virtual element method (IPVEM) for solving a Kirchhoff plate contact problem, which can be described by a fourth-order elliptic hemivariational inequality (HVI). The virtual element space in IPVEM is constructed by modifying the H2-conforming virtual element space, and the number of degrees of freedom is greatly reduced. To force the C1 continuity, the interior penalty scheme is adopted, that is, we introduce a penalty term for the jump of normal derivatives on mesh edges and two additional terms to guarantee the consistency and symmetry of the scheme. With certain assumptions, the well-posedness of the discrete problem is proved. Furthermore, a priori error estimation is established for the IPVEM for the fourth-order elliptic HVI, and we show that the lowest-order VEM achieves optimal convergence order. Finally, some numerical examples are presented to support the theoretical results.

A high-accuracy framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches in which the interface is only given by a smeared zone. For multi-domain problems, the accuracy of the coupling conditions is, however, of utmost importance. Here, interface-tracking methods are preferred, since the interface is resolved on mesh edges up to discretisation errors, but it does not depend on the length scale parameter of some smeared zone. The key objective of this work is to construct a robust framework that computes first a crack path via the phase-field method (interface-capturing) and then does an interface-tracking reconstruction. We then discuss several approaches to reconstruct the Eulerian description of the open crack domain. This includes unfitted approaches where a level-set of the crack interface is constructed and an approach where the geometry is re-meshed. Using this reconstructed domain, we can compute the fluid–structure interaction problem between the fluid in the crack and the interacting solid. With the explicit mesh reconstruction of the two domains, we can then use an interface-tracking Arbitrary-Lagrangian–Eulerian (ALE) discretisation approach for the resulting fluid–structure interaction (FSI) problem. Our algorithmic procedure is realised in one final numerical algorithm and one implementation. We substantiate our approach using several numerical examples based on Sneddon’s benchmark and corresponding extensions to Stokes fluid-filled regimes.

Joint optimization of distortion and cut location for mesh parameterization using an Ambrosio-Tortorelli functional

UV mapping is a classical problem in computer graphics aiming at computing a planar parameterization of the input mesh with the lowest possible distortion while minimizing the seams length. Recent works propose optimization methods for solving these two joint problems at the same time with variational models, but they tend to be slower than other cutting methods. We present a new variational approach for this problem inspired by the Ambrosio-Tortorelli functional, which is easier to optimize than already existing methods. This functional has widely been used in image and geometry processing for anisotropic denoising and segmentation applications. The key feature of this functional is to model both regions where smoothing is applied, and the loci of discontinuities corresponding to the cuts. Our approach relies on this principle to model both the low distortion objective of the UV map, and the minimization of the seams length (sequences of mesh edges). Our method significantly reduces the distortion in a faster way than state-of-the art methods, with comparable seam quality. We also demonstrate the versatility of the approach when external constraints on the parameterization are provided (packing constraints, seam visibility).

Trilinear Immersed-Finite-Element Method for Three-Dimensional Anisotropic Interface Problems in Plasma Thrusters

Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. These advantages lead to much higher efficiency when solving complex anisotropic interface problems in practice. In addition, the proposed method can be easily incorporated into other typical methods based on Cartesian meshes, such as the particle-in-cell method for plasma simulation. Numerical experiments are provided to verify the optimal accuracy, high efficiency, and reliability of the proposed method for solving complex interface problems, as well as its applicability to practical plasma thruster problems.

V09-07 HOW TO USE A MESH SLING SAFELY AFTER THE POST-VESICOVAGINAL FISTULA REPAIR REPAIR PATIENT WITH STRESS URINARY INCONTINENCE

You have accessJournal of UrologyCME1 Apr 2023V09-07 HOW TO USE A MESH SLING SAFELY AFTER THE POST-VESICOVAGINAL FISTULA REPAIR REPAIR PATIENT WITH STRESS URINARY INCONTINENCE Micheal Breen Tamatave, Madagascar, Ly Hoang Roberts, and Larry Sirls Micheal Breen Tamatave, MadagascarMicheal Breen Tamatave, Madagascar More articles by this author , Ly Hoang RobertsLy Hoang Roberts More articles by this author , and Larry SirlsLarry Sirls More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000003317.07AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Patients with complicated obstetric fistulas may have stress urinary incontinence (SUI) after vesicovaginal fistula repair (VVF), especially if the urethra in involved. Various techniques to treat post-VVF SUI have low success rates or is technically challenging due to thin and scarred peri-urethral tissue. We describe a technique to place a midurethral mesh sling outside of the pre-existing vaginal mucosa. METHODS: With the patient in dorsal lithotomy under spinal anesthesia, a foley catheter is placed into the bladder and the labial majora is retracted for adequate exposure. A rectangular area of the same size as the mesh sling (3x1cm) at the midurethra is marked. A number 15 scalpel is used to incise the vaginal mucosa at the marked lines, and Metzenbaum scissors are used to dissect and mobilize the edges. The dissection is then carried out laterally to be behind the inferior pubic bone. This is done on both sides. The island of vaginal mucosa is then superficially scored using low power bovie cauterization to allow for mesh adhesion and tissue ingrowth. The mesh is sutured to the island of skin using a 3-0 Chromic or vicryl suture at the mesh edges in 4 areas. 0- prolen sutures are then placed on each lateral edge of the mesh in a running stitch. The Metzenbaum scissors are then used to enter into the endopelvic fascia behind the pubic bone to develop the retropubic space. Next, a suprapubic incision is made 1cm cranial to the pubic bone down to the rectus fascia. The Stamey needle is passed in a top-down approach approximately 2cm from midline and end delivered into the vaginal incision. To check for bladder perforation, a metal catheter is placed into the bladder and swept laterally to evaluate for any metallic noise indicative of contact. The prolene suture is passed up to the suprapubic incision and the same is done contralaterally. Bladder is backfilled with sterile saline with methylene blue by gravity and foley removed. Sutures are tied together midline with the sling tension adjusted while patient performs a Valsalva. Suprapubic incision is then closed in multiple layers. The vaginal incision is closed with mobilization of the proximal vaginal mucosa and reapproximation to the distal edge. For larger incisions, a Singapore flap can be done for adequate coverage. RESULTS: Successful managment of SUI. CONCLUSIONS: For challenging cases of SUI after a post-VVF repair, this technique can be an option. Further investigation is needed for clinical outcomes. Source of Funding: None © 2023 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 209Issue Supplement 4April 2023Page: e839 Advertisement Copyright & Permissions© 2023 by American Urological Association Education and Research, Inc.MetricsAuthor Information Micheal Breen Tamatave, Madagascar More articles by this author Ly Hoang Roberts More articles by this author Larry Sirls More articles by this author Expand All Advertisement PDF downloadLoading ...

A Rational Approach to Meshing Cerebral Venous Geometries for High-Fidelity Computational Fluid Dynamics.

Computational fluid dynamics (CFD) of cerebral venous flows has become popular owing to the possibility of using local hemodynamics and hemoacoustics to help diagnose and plan treatments for venous diseases of the brain. Lumen geometries in low-pressure cerebral veins are different from those in cerebral arteries, often exhibiting fenestrations and flattened or triangular cross section, in addition to constrictions and expansions. These can challenge conventional size-based volume meshing strategies, and the ability to resolve nonlaminar flows. Here we present a novel strategy leveraging estimation of length scales that could be present if flow were to become transitional or turbulent. Starting from the lumen geometry and flow rate boundary conditions, centerlines are used to determine local hydraulic diameters and cross-sectional mean velocities, from which flow length scales are approximated using conventional definitions of local Kolmogorov and Taylor microscales. By inspection of these scales, a user specifies minimum and maximum mesh edge lengths, which are then distributed along the model in proportion to the approximated local Taylor length scales. We demonstrate in three representative cases that this strategy avoids some of the pitfalls of conventional size-based strategies. An exemplary CFD mesh-refinement study shows convergence of high-frequency flow instabilities even starting from relatively coarse edge lengths near the lower bounds of the approximated Taylor length scales. Rational consideration of the length scales in a possibly nonlaminar flow may thus provide a useful and replicable baseline for denovo meshing of complicated or unfamiliar venous lumen geometries.

Ionization wave propagation of a surface dielectric barrier discharge with a flexible-structure plasma sheet

Plasma sources based on flexible substrates are receiving attention due to their unique adaptability to irregular surfaces and large range of plasma coverage, which endows them with irreplaceable advantages in the fields of material processing and biomedical treatment. Numerous studies have been carried out focusing on the application effects of these flexible plasma sources, while their surface discharge characteristics and mechanisms still lack revelation. In this work, a flexible plasma sheet with a surface dielectric barrier discharge structure is realized via a printed circuit board, and its multiple surface ionization wave (SIW) propagation on curved gas–solid interfaces is studied via experiments and 2D fluid simulation models. Qualitative agreement is achieved between the experiments and simulations. It is found that a positive and a negative discharge are generated at the rising and falling edges of the excitation pulse, respectively. In the positive discharge, SIWs originate at the grounded mesh edge and then propagate to the center in a petal-like pattern, which is shaped by the space electric field. Controlled by electron collision reactions, the development of the excited states of N2 and O2 molecules is similar to that of electrons. In the negative discharge, electrons dissipate and no SIW is generated. The evolution of heavy particles shows differences in this period, which is attributed to the disparate rate coefficients of their consumption reactions. Further study shows that when the plasma sheet changes from convex to concave, the electron density and electron temperature above its surface increase, but the petal patterns of the SIW propagation have no variation. The electron density, electron temperature, and electron impact ionization source will rise as a result of the increasing pulse amplitude or the decreasing duration of the pulse rising edge.

Viaduct and Bridge Structural Analysis and Inspection through an App for Immersive Remote Learning

Until now, in the design phase of infrastructures there has been a general tendency to “economize” the resources allocated to them. This modus operandi did not consider the installation of monitoring and control systems as an integral part of the infrastructure itself, not considering the high post-intervention costs. This work aims to show how the integration of immersive technologies, including Virtual/Augmented/Mixed Reality, combined with geomatics, survey and structural monitoring techniques can ensure a better visualization and understanding of the different contexts in which the managing bodies are required to guarantee maintenance interventions. In particular, the potential of an application, developed by the authors in Unity 3D, to help the managing institution is described. The app permits the user to explore infrastructures under inspection in a virtual environment. This makes all the information related to the infrastructure available and accessible through the 3D analysis (which is manageable in the app after a mesh edge reduction phase) exploiting the full potential of Mixed/Virtual Reality. The main ability of our application derives from the chance to easily use and integrate different techniques (3D models, information models for construction, VR/AR) allowing for the choice of different 3D models testing and performing their simplification and dimensional reduction. This makes the loading phase of the application faster and the user experience easier and better. The experimentation of the proposed methodology was conducted on a viaduct located in Reggio Calabria.

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Ax=b. Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. We add vectors from the nullspace to improve the initial solution, maintaining Ax=b. Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. Hex meshes with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. With this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

Geodesic Tracks: Computing Discrete Geodesics With Track-Based Steiner Point Propagation.

This article presents a simple yet effective method for computing geodesic distances on triangle meshes. Unlike the popular window propagation methods that partition mesh edges into intervals of varying lengths, our method places evenly-spaced, source-independent Steiner points on edges. Given a source vertex, our method constructs a Steiner-point graph that partitions the surface into mutually exclusive tracks, called geodesic tracks. Inside each triangle, the tracks form sub-regions in which the change of distance field is approximately linear. Our method does not require any pre-computation, and can effectively balance speed and accuracy. Experimental results show that with 5 Steiner points on each edge, the mean relative error is less than 0.3 % for common 3D models used in the graphics community. We propose a set of effective filtering rules to eliminate a large amount of useless broadcast events. For a 1000K-face model, our method runs 10 times faster than the conventional Steiner point method that examines a complete graph of Steiner points in each triangle. We also observe that using more Steiner points increases the accuracy at only a small extra computational cost. Our method works well for meshes with poor triangulation and non-manifold configuration, which often poses challenges to the existing PDE methods. We show that geodesic tracks, as a new data structure that encodes rich information of discrete geodesics, support accurate geodesic path and isoline tracing, and efficient distance query. Our method can be easily extended to meshes with non-constant density functions and/or anisotropic metrics.

Fast evaluation of smooth distance constraints on co-dimensional geometry

We present a new method for computing a smooth minimum distance function based on the LogSumExp function for point clouds, edge meshes, triangle meshes, and combinations of all three. We derive blending weights and a modified Barnes-Hut acceleration approach that ensure our method approximates the true distance, and is conservative (points outside the zero isosurface are guaranteed to be outside the surface) and efficient to evaluate for all the above data types. This, in combination with its ability to smooth sparsely sampled and noisy data, like point clouds, shortens the gap between data acquisition and simulation, and thereby enables new applications such as direct, co-dimensional rigid body simulation using unprocessed lidar data.

Low divergent MeV-class proton beam with micrometer source size driven by a few-cycle laser pulse

Spatial characterization of 0.5 MeV proton beam, driven by 12 fs, 35 mJ, 1019 W/cm2 intense laser-foil interaction is presented. The accelerated proton beam has been applied to obtain a high-resolution, point-projection static radiograph of a fine mesh using a CR-39 plate. The reconstruction of mesh edge blurring and particle ray tracing suggests that these protons have an effective source size (FWHM) of just 3.3 ± 0.3 µm. Furthermore, the spatial distribution of the proton beam recorded on the CR-39 showed that the divergence of these particles is less than 5-degree (FWHM). The low divergence and small source size of the proton beam resulted in an ultralow transverse emittance of 0.00032 π-mm-mrad, which is several orders of magnitude smaller than that of a conventional accelerator beam.