Mesh Connectivity Research Articles

A new mesh deformation method using quaternion and displacement normal propagation for high quality and high efficiency

Mesh deformation technology is widely used in aerodynamic applications like unsteady flow, aeroelasticity, and aerodynamic shape optimization because of its low computational costs and consistent mesh connectivity. In order to raise deformed mesh quality and improve efficiency, a new mesh deformation method based on quaternion and displacement normal propagation (named QN method) is introduced in this paper. The boundary points propagate their displacements composed of translational vectors and quaternions to corresponding volume points along the normal direction under the control of the damping function, which preserves the mesh shape and guarantees the quality near boundaries, including orthogonality and normal size. It can also prevent the volume points from being interfered by other less relevant boundary points, so dealing with complex displacement fields effectively. In addition, it avoids complicated matrix and interpolation operations, thus saving lots of computational costs. For mesh with complex topology, a hybrid method combining the QN method and the radial basis function method (RBF method) is investigated to broaden application scenarios, which are applied to the mesh with normal correspondence inside the boundary layer and the mesh outside, respectively. Benefitting from effective handling for the near-wall elements by the QN method, the RBF interpolation part in the hybrid method requires minor support points to carry out valid large deformation, improving the deformation efficiency greatly compared to the individual RBF method. Five typical test cases with different deformation modes and mesh characteristics are implemented, showing better performance of the proposed method in deformed mesh quality and deformation efficiency.

Distributed virtual selective-forwarding units and SDN-assisted edge computing for optimization of multi-party WebRTC videoconferencing

Network service providers (NSP) have growing interest in placing network intelligence and services at network edges by deploying software-defined network (SDN) and network function virtualization infrastructure. In multi-party WebRTC videoconferencing using scalable video coding, a selective forwarding unit (SFU) provides connectivity between peers with heterogeneous bandwidth and terminals. An important question is where in the network to place the SFU service in order to minimize end-to-end delay between all pairs of peers. Clearly, there is no single optimal place for a cloud SFU for all possible peer locations. We propose placing virtual SFUs at network edges leveraging NSP edge datacenters to optimize end-to-end delay and usage of overall network resources. The main advantage of the distributed edge-SFU framework is that each peer video stream travels the shortest path to reach other peers similar to mesh connection model, whereas each peer uploads a single stream to its edge-SFU avoiding the upload bottleneck. While the proposed distributed edge-SFU framework applies to both best-effort and managed service models, this paper proposes a premium managed, edge-integrated multi-party WebRTC service architecture with bandwidth and delay guarantees within access networks by SDN-assisted slicing of edge networks. The performance of the proposed distributed edge-SFU service architecture is demonstrated by means of experimental results.

Triangular matrix-based lossless compression algorithm for 3D mesh connectivity

Triangular matrix-based lossless compression algorithm for 3D mesh connectivity

Hardwood and softwood timber - natural stone composite connections

This paper describes fabrication and testing to ultimate of timber-stone composite (TSC) connections using unreinforced limestone slabs fastened to hardwood or softwood stubs by screws at 45° or 90° to the interface, bonded-in meshes or interface bonding. The stone’s tensile strength prevented crack-formation during drilling or grooving of holes to accommodate the screws and meshes. Connections failed by splitting of the stone along the connectors (meshes, 90° screws in hardwood), pullout of 45° screws from softwood (S45), shear-flexure yield fracture of 90° screws in softwood (S90), longitudinal shear failure of softwood adjacent to interface adhesive, and tensile yield fracture of 45° screws in hardwood (H45). In descending order the glued, H45 and mesh connections were the strongest while the glued, meshed and 45° screw connections exhibited the highest slip stiffnesses, with the S90/S45 connections showing the most ductility. Likely influences of randomness in the stone’s tensile strength and in observed bond variabilities from fabrication of the mesh connections are discussed. The TSC connections performed well against timber-concrete composite connections. Stiffness predictions incorporating screw axial and lateral contributions are excellent for H45 and S90, but need improvement for S45 and H90. Strength predictions work well for all screw connections. These TSC connections can significantly reduce consumption of the natural materials stone and timber in low-carbon composite floor systems.

Point2MM: Learning medial mesh from point clouds

Medial mesh is the most commonly used representation of medial axis transform (MAT) which is a high-fidelity compact representation of 3D shape. Existing learning methods of extracting medial mesh from point clouds either have strict requirements of supervising training data, or are incapable of learning the complete form of medial mesh, leading to large reconstruction error. We introduce Point2MM, an unsupervised method for learning a complete medial mesh from point clouds. Our key idea is to use the envelop geometry of medial primitives – spheres, cones, and slabs – to capture the intrinsic geometry of shape, and the connectivity of medial mesh to capture the topology of shape. We firstly predict initial medial spheres by learning the geometric transformation of point clouds, then construct an initial connectivity of the medial spheres by learning the probability of medial cones and medial slabs with a novel unsupervised formulation. Finally we propose an iterative strategy for fine-tuning medial primitives. Extensive evaluations and comparisons show our method has superior accuracy and robustness in learning medial mesh from point clouds. In addition, the excessive training time is also a concern for our research, and it is a limitation where we need to make improvements in our future work.

Modeling with discrete equivalence classes of planar quads

We propose a novel method to model shapes using a small set of discrete equivalence classes of planar quads. Unlike previous modular modeling methods that only optimize vertex positions of an input quad mesh without modifying the mesh connectivity, we first generate a quadrilateral mesh considering the equivalence requirement and then optimize the geometry to be modular. Our meshing approach is field-driven, and the key is to transform the requirements of the quad mesh into those of the field. Specifically, the frame field is required to belong to a small set of discrete equivalence classes while being smooth, integrable, and nearly conjugate. After alternately optimizing the requirements to obtain the desired field, we use it to generate a quad mesh, which is further improved to be modeled with a small set of template planar quads. We demonstrate the practicability and effectiveness of our algorithm over various examples.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization.

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Design and Implementation of Evaluation Method for Spraying Coverage Region of Plant Protection UAV

Plant protection UAVs are becoming the preferred plant protection method for agricultural pest control. At present, the evaluation of droplet distribution in aerial spraying is collected and evaluated after the completion of prevention and control operations, and there is a lack of real-time evaluation methods. Based on the flight parameter during the UAV plant protection process, real-time estimation of droplet distribution is the key to solving this problem and further improving the effectiveness of aerial spraying. This study proposes a merging algorithm for arbitrary polygonal regions, meshing the boundaries of the region, divide the mesh segments based on the overlapping meshes between the two regions, and connect the valid mesh connection segments of the two regions according to certain rules to obtain the intersection, union, and residual operation results between the regions. Afterwards, software based on this algorithm was developed and applied to generate spraying coverage regions, leakage spray regions, and repeated spray regions. The experimental results on theoretical and irregular routes show that the algorithm can accurately generate droplet distribution regions. The error of the calculation results with a mesh scale of 0.05 m is within 7‰, and the operating speed is above 30 Hz, meeting the real-time requirements. The smaller the mesh scale is, the higher the accuracy of the calculation results is, but the slower the calculation speed. Therefore, in practical applications, it is necessary to choose an appropriate mesh scale based on hardware computing power and accuracy level requirements. This study solves the problem of cumulative calculation of droplet distribution during the operation of plant protection UAVs, providing a basis for objectively evaluating the operation quality of plant protection UAVs and optimizing the setting of operation parameters.

Three-field partitioned analysis of fluid–structure interaction problems with a consistent interface model

This paper proposes a new Fluid–Structure Interaction computational framework. The coupling between the solid and an incompressible fluid is formulated by means of the method of localized Lagrange multipliers (LLM). Instead of applying a direct coupling between the fluid and the structure, which is the traditional approach, LLM introduces an intermediate surface with its own degrees of freedom that is connected to the fluid and structure sides using independent fields of localized Lagrange multipliers. This approach allows the connection of non-matching meshes with mortar or classical localized methods and provides consistent dynamic equations of motion for the interface that can be integrated in parallel. Interface multipliers are later eliminated and the interface motion is used to update the fluid and structure states. This way, dedicated stand-alone software modules for the fluid and the structure are connected to a third interface system treating their interaction, thus preserving the modularity of the single-discipline software modules. Different numerical examples are solved with the proposed methodology to prove its efficiency and accuracy by running a series of classical dynamic FSI benchmark problems.

Exploiting spatial symmetries for solving Poisson's equation

This paper presents a strategy to accelerate virtually any Poisson solver by taking advantage of s spatial reflection symmetries. More precisely, we have proved the existence of an inexpensive block diagonalisation that transforms the original Poisson equation into a set of 2s fully decoupled subsystems then solved concurrently. This block diagonalisation is identical regardless of the mesh connectivity (structured or unstructured) and the geometric complexity of the problem, therefore applying to a wide range of academic and industrial configurations. In fact, it simplifies the task of discretising complex geometries since it only requires meshing a portion of the domain that is then mirrored implicitly by the symmetries' hyperplanes. Thus, the resulting meshes naturally inherit the exploited symmetries, and their memory footprint becomes 2s times smaller. Thanks to the subsystems' better spectral properties, iterative solvers converge significantly faster. Additionally, imposing an adequate grid points' ordering allows reducing the operators' footprint and replacing the standard sparse matrix-vector products with the sparse matrix-matrix product, a higher arithmetic intensity kernel. As a result, matrix multiplications are accelerated, and massive simulations become more affordable. Finally, we include numerical experiments based on a turbulent flow simulation and making state-of-the-art solvers exploit a varying number of symmetries. On the one hand, algebraic multigrid and preconditioned Krylov subspace methods require up to 23% and 72% fewer iterations, resulting in up to 1.7x and 5.6x overall speedups, respectively. On the other, sparse direct solvers' memory footprint, setup and solution costs are reduced by up to 48%, 58% and 46%, respectively.

Preoperative Prediction of Optimal Femoral Implant Size by Regularized Regression on 3D Femoral Bone Shape

Preoperative determination of implant size for total knee arthroplasty surgery has numerous clinical and logistical benefits. Currently, surgeons use X-ray-based templating to estimate implant size, but this method has low accuracy. Our study aims to improve accuracy by developing a machine learning approach that predicts the required implant size based on a 3D femoral bone mesh, the key factor in determining the correct implant size. A linear regression framework imposing group sparsity on the 3D bone mesh vertex coordinates was proposed based on a dataset of 446 MRI scans. The group sparse regression method was further regularized based on the connectivity of the bone mesh to enforce neighbouring vertices to have similar importance to the model. Our hypergraph regularized group lasso had an accuracy of 70.1% in predicting femoral implant size while the initial implant size prediction provided by the instrumentation manufacturer to the surgeon has an accuracy of 23.1%. Furthermore, our method was capable of predicting the implant size up to one size smaller or larger with an accuracy of 99.1%, thereby surpassing other state-of-the-art methods. The hypergraph regularized group lasso was able to obtain a significantly higher accuracy compared to the implant size prediction provided by the instrumentation manufacturer.

Variable node higher-order XFEM for fracture modeling in orthotropic material

A novel computational approach presented in this work to improve the accuracy and efficiency of fracture modeling in an orthotropic material medium. Extended finite element method (XFEM) with higher-order enrichment functions was employed at the different scale mesh topology. The approach combined variable node element concepts for different scale mesh connections and higher-order XFEM for accuracy and completeness of discontinuity domain. The proposed computational methodology was employed with in-house developed MATLAB code. Further, stochastic fracture studies were discussed for reliability of the cracked structures. Few numerical examples with multiple geometrical discontinuities were simulated to check the computational efficiency and accuracy.

A Task-Parallel Approach for Localized Topological Data Structures.

Unstructured meshes are characterized by data points irregularly distributed in the Euclidian space. Due to the irregular nature of these data, computing connectivity information between the mesh elements requires much more time and memory than on uniformly distributed data. To lower storage costs, dynamic data structures have been proposed. These data structures compute connectivity information on the fly and discard them when no longer needed. However, on-the-fly computation slows down algorithms and results in a negative impact on the time performance. To address this issue, we propose a new task-parallel approach to proactively compute mesh connectivity. Unlike previous approaches implementing data-parallel models, where all threads run the same type of instructions, our task-parallel approach allows threads to run different functions. Specifically, some threads run the algorithm of choice while other threads compute connectivity information before they are actually needed. The approach was implemented in the new Accelerated Clustered TOPOlogical (ACTOPO) data structure, which can support any processing algorithm requiring mesh connectivity information. Our experiments show that ACTOPO combines the benefits of state-of-the-art memory-efficient (TTK CompactTriangulation) and time-efficient (TTK ExplicitTriangulation) topological data structures. It occupies a similar amount of memory as TTK CompactTriangulation while providing up to 5x speedup. Moreover, it achieves comparable time performance as TTK ExplicitTriangulation while using only half of the memory space.

A partially mesh-free scheme for representing anisotropic spatial variations along field lines: Conservation, quadrature, and the delta property

A method for representing highly anisotropic fields is presented, based on a partially meshfree Galerkin formulation. A mapping function is used to provide information about the local direction of the anisotropy, with one of the global coordinates chosen to parameterize the ‘parallel’ position along the mapping in a one-to-one manner. Standard unstructured finite element meshes are used on planes of constant parallel coordinate to represent the necessary small-scale variations perpendicular to the mapping direction, with large spacings then possible between these planes because of the large-scale variations along the mapping. This greatly reduces the number of degrees of freedom required to represent fields in this space and the associated computational cost of simulations involving such fields. No mesh connectivity is defined between planes, and field aligned basis functions are constructed using the mapping function to extend the standard finite element basis into the full domain. Integration of the basis has been addressed with reference to methods developed for fully meshfree methods, and the scheme (as well as other similar element-free Galerkin schemes) is shown to be locally conservative under certain conditions. Robust convergence of several test problems is demonstrated.

XURLLC in 6G with meshed RAN

5G Ultra-Reliable Low Latency Communications Technology (URLLC) will not be able to provide extremely reliable low latency services to the complex networks in 6G. Moreover, URLLC that began with 5G has to be refined and improved in 6G to provide xURLCC (extreme URLCC) with sub-millisecond latency, for supporting diverse mission-critical applications. This paper aims to highlight the importance of peer-to-peer mesh connectivity for services that require xURLLC. Deploying mesh connectivity among RAN nodes would add significant value to the current 5G New Radio (5G NR) enabling 6G to increase flexibility and reliability of the networks while reducing the inherent latency introduced by the core network. To provide a mesh connectivity in RAN, the nodes should be able to communicate with each other directly and be independent from the mobile core network so that data can be directly exchanged between base stations (gNBs) whereas certain aspects of signalling procedure including data session establishment will be managed by RAN itself. In this paper, we introduce several architectural choices for a mesh network topology that could potentially be crucial to a number of applications. In addition, three possible options to create mesh connectivity in RAN are provided, and their pros and cons are discussed in detail.

Identification of vortices in quantum fluids: Finite element algorithms and programs

We present finite-element numerical algorithms for the identification of vortices in quantum fluids described by a macroscopic complex wave function. Their implementation using the free software FreeFem++ is distributed with this paper as a post-processing toolbox that can be used to analyse numerical or experimental data. Applications for Bose-Einstein condensates (BEC) and superfluid helium flows are presented. Programs are tested and validated using either numerical data obtained by solving the Gross-Pitaevskii equation or experimental images of rotating BEC. Vortex positions are computed as topological defects (zeros) of the wave function when numerical data are used. For experimental images, we compute vortex positions as local minima of the atomic density, extracted after a simple image processing. Once vortex centers are identified, we use a fit with a Gaussian to precisely estimate vortex radius. For vortex lattices, the lattice parameter (inter-vortex distance) is also computed. The post-processing toolbox offers a complete description of vortex configurations in superfluids. Tests for two-dimensional (giant vortex in rotating BEC, Abrikosov vortex lattice in experimental BEC) and three-dimensional (vortex rings, Kelvin waves and quantum turbulence fields in superfluid helium) configurations show the robustness of the software. The communication with programs providing the numerical or experimental wave function field is simple and intuitive. The post-processing toolbox can be also applied for the identification of vortices in superconductors. Program summaryProgram Title: FFEM_postproc_data_2D, FFEM_postproc_data_3D and FFEM_postproc_imageCPC Library link to program files:https://doi.org/10.17632/bhrtdbkxmy.1Licensing provisions: Apache 2.0Programming language: FreeFem++ (v 4.12) free software (www.freefem.org)Nature of problem: The software is scoped to the identification of quantized vortices in 2D or 3D configurations described by a complex wave function. Either simulation data obtained through numerical resolution of the Gross-Pitaevskii equation or 2D experimental images of Bose-Einstein condensates (BEC) can be used as input data. Examples of vortex identification in rotating BECs and superfluid helium are illustrated in the paper.Solution method: We model the complex wave function using P1 (piece-wise linear) Galerkin triangular (in 2D) and tetrahedral (in 3D) finite elements. For simulation data, the zeros of the wave function are directly computed and the circulation of the velocity on triangles sides is assessed. Vortices are obtained when a zero is found in a triangle with non-zero circulation. In 3D, the algorithm is applied on tetrahedron faces and the zero points are linked using mesh connectivity to form vortex lines. For experimental images, vortices are identified as local minima of the atomic density and extracted using the image contrast.Additional comments including restrictions and unusual features: Running time is from seconds to minutes depending on the mesh resolution of the simulation/experimental data.

Declarative Specification for Unstructured Mesh Editing Algorithms

We introduce a novel approach to describe mesh generation, mesh adaptation, and geometric modeling algorithms relying on changing mesh connectivity using a high-level abstraction. The main motivation is to enable easy customization and development of these algorithms via a declarative specification consisting of a set of per-element invariants, operation scheduling, and attribute transfer for each editing operation. We demonstrate that widely used algorithms editing surfaces and volumes can be compactly expressed with our abstraction, and their implementation within our framework is simple, automatically parallelizable on shared-memory architectures, and with guaranteed satisfaction of the prescribed invariants. These algorithms are readable and easy to customize for specific use cases. We introduce a software library implementing this abstraction and providing automatic shared-memory parallelization.

Priority‐based encoding of triangle mesh connectivity for a known geometry

AbstractIn certain practical situations, the connectivity of a triangle mesh needs to be transmitted or stored given a fixed set of 3D vertices that is known at both ends of the transaction (encoder/decoder). This task is different from a typical mesh compression scenario, in which the connectivity and geometry (vertex positions) are encoded either simultaneously or in reversed order (connectivity first), usually exploiting the freedom in vertex/triangle re‐indexation. Previously proposed algorithms for encoding the connectivity for a known geometry were based on a canonical mesh traversal and predicting which vertex is to be connected to the part of the mesh that is already processed. In this paper, we take this scheme a step further by replacing the fixed traversal with a priority queue of open expansion gates, out of which in each step a gate is selected that has the most certain prediction, that is one in which there is a candidate vertex that exhibits the largest advantage in comparison with other possible candidates, according to a carefully designed quality metric. Numerical experiments demonstrate that this improvement leads to a substantial reduction in the required data rate in comparison with the state of the art.

Coverage Extension for the UK Smart Meter Implementation Programme Using Mesh Connectivity

Smart meters (SM) with wireless capabilities are one of the most meaningful applications of the Internet of Things. Standards like Zigbee have found a niche in transmitting data on energy usage to the user and the supplier wirelessly via these meters and communication hubs. There are still certain difficulties, notably in delivering wireless connectivity to meters situated in difficult-to-reach locations such as basements or deep indoors. To solve this issue, this paper investigates the usage of mesh networks at 868 MHz, particularly to increase coverage, and proposes an additional mounted antenna to significantly increase outside coverage while providing the necessary coverage extension for hard-to-reach indoor locations. Extensive measurements were made in Newbury in both suburban and open environments for validation and delivery of a simple statistical model for the 868 MHz band in United Kingdom conurbations. Results presented in this paper estimate that mesh networks at 868 MHz can accommodate large areas constituting several SMs with the proposed coverage extension method. With our findings and proposed methods on mesh connectivity, only 1% of UK premises will require mesh radios to achieve the desired coverage.

TCPMFNet: An infrared and visible image fusion network with composite auto encoder and transformer–convolutional parallel mixed fusion strategy

Infrared and visible image fusion could obtain the fused image with infrared radiation information and visible texture information. Various fusion methods for infrared and visible image fusion have been developed in recent years. However, the fused images generated by most existing fusion methods suffer losing of detailed information, fusion noise, low contrast effect and blurred edge of fused objects. To obtain the fused image with excellent detailed source image information preservation capacity, low fusion noise level, high contrast effect and sharp edge of fused objects, this study proposed an infrared and visible image fusion network with composite auto encoder and transformer–convolutional parallel mixed fusion strategy (TCPMFNet). The proposed fusion network is based on auto-encoder (AE) structure, a composite auto encoder is adopted to encode abundant features form source image pairs, the transformer–convolutional parallel mixed fusion strategy is designed to achieve outstanding feature fusion performance, and developed a mesh connection decoder to exploit the potential of reconstructing fused image in a fully utilizing of multi-level features manner. Ablation studies and comparison experiments have been conducted on the TNO test set, and the experimental results demonstrated the effectiveness of the proposed network structure and the superiority of the proposed network over other state of the arts fusion methods. Furthermore, comparison experiments dedicated to infrared and RGB image fusion are conducted on Road scenes test set, and the infrared and RGB image fusion results of the proposed network outperformed other state of the arts fusion methods.