Rectangular Mesh Research Articles

CNN-based weight estimation from point clouds obtained from walking breed sows

In the livestock industry, reducing the cost of raising animals while maintaining quality is of utmost importance. Growth management is crucial for livestock quality control, with weight being a primary focus. This study proposes a method for estimating the weight of a breed sow from point clouds using a convolutional neural network (CNN). The proposed method consists of two stages: first, 2D images are generated from point clouds of a walking breed sow; next, these images are used as input in a CNN model to estimate the weight. The point clouds are divided into two halves along a longitudinal plane. Then, distances are calculated between each element of the 128 × 64 rectangular mesh created on the aforementioned plane and the corresponding points in the divided point cloud. A 2D image is generated by varying the grayscale intensity according to the calculated distances. Three types of CNNs, namely, VGG16, DenseNet121, and EfficientNet B0, were employed to estimate the weight using the generated 2D images as input. The CNNs were trained using approximately 150,000 images of 71 pigs. To verify the effectiveness of the method, the trained networks were used to conduct weight estimation experiments on test cases. The results of the experiments demonstrate a high weight estimation accuracy, with an error rate as low as 1.35%.

Numerical modeling of infrasounds radiation and propagation in hurricanes

Infrasound can be useful for monitoring natural or human-induced energetic events in the atmosphere. For high-energy sources, the infrasonic signals can propagate over large distances around the globe, given the low rate of atmospheric absorption. This study focuses on the numerical simulation of infrasound propagation in realistic large-scale three-dimensional (3D) environments. More precisely, we are interested in the simulation of infrasound, called microbaroms, which are radiated from extreme weather conditions such as hurricanes. The simulation of hurricane-induced microbaroms relies on three main components: i) a hurricane model describing the atmospheric wind and pressure fields, ii) a microbarom source model, and iii) an infrasound propagation model. 3D simulations have been performed on a rectangular mesh. Azimuthal deviation caused by the hurricane and the stratified atmosphere can be seen in 3D. Further studies are needed to improve each model, and the correlation between them. The ultimate goal is to be able to simulate radiated infrasound propagation for any meteorological conditions.

An improved affine mixed‐grid method for frequency‐domain finite‐difference elastic modelling

AbstractIn seismic frequency‐domain finite‐difference modelling, the affine mixed‐grid method effectively eliminates the spatial sampling restriction associated with square meshes of the rotated mixed‐grid method. Nevertheless, the affine mixed‐grid method makes a weighted average of the entire elastic wave equations, resulting in reduced accuracy compared to the average‐derivative method in the case of rectangular meshes. It is worth noting, however, that the average‐derivative method is presently inapplicable to free‐surface scenarios, whereas the affine mixed‐grid method is applicable. By performing weighted averages of the derivative terms instead of the entire elastic wave equations in Cartesian and affine rotated coordinate systems, we have developed an improved affine mixed‐grid method for elastic‐wave frequency‐domain finite‐difference modelling. The proposed improved affine mixed‐grid method 9‐point scheme overcomes the drawback that the accuracy of affine mixed‐grid method is lower than that of average‐derivative method for unequal directional grid intervals. Moreover, the improved affine mixed‐grid method 6‐point scheme provides much higher numerical accuracy than the affine mixed‐grid method 6‐point scheme at either equal or unequal directional grid intervals. On the other hand, the proposed improved affine mixed‐grid method simplifies the coding complexity for implementing free‐surface condition in elastic‐wave frequency‐domain finite‐difference modelling by modifying the elastic parameters of the free‐surface layer and thus constructing the impedance matrix containing the free‐surface condition directly.

Superconvergence analysis of an energy-conserving Galerkin FEM for the two-dimensional sine-Gordon equation

In this paper, the superconvergence error analysis of an energy-conserving Galerkin fully discrete scheme is proposed and investigated for the two-dimensional sine-Gordon equation. The unique solvability of the numerical scheme as well as the energy conservation are studied firstly. Then, based on the special property of the bilinear element on the rectangular mesh and the superclose estimate between interpolation and Ritz projection of the exact solution in H 1 -norm, the global superconvergence result in H 1 -norm is obtained in terms of a post-processing technique. Finally, numerical results are provided to confirm the energy conservation and superconvergence properties.

An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws

High order accuracy fast sweeping methods have been developed in the literature to efficiently solve steady state solutions of hyperbolic partial differential equations (PDEs) on rectangular meshes, while they were not available yet on unstructured meshes. In this paper, we extend high order accuracy fast sweeping methods to unstructured triangular meshes by applying fixed-point iterative sweeping techniques to a fifth-order finite volume unstructured WENO scheme, for solving steady state solutions of hyperbolic conservation laws. Similar as other fast sweeping methods, fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady state solutions. An advantage of fixed-point fast sweeping methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems. This also provides certain convenience in designing high order fast sweeping methods on unstructured meshes. As in the first order fast sweeping methods on triangular meshes, we introduce multiple reference points to determine alternating sweeping directions on unstructured meshes. All the cells on the mesh are ordered according to their centroids' distances to those reference points, and the resulted orderings provide sweeping directions for iterations. To make the residue of the fast sweeping iterations converge to machine zero / round off errors, we follow the approach in our early work of developing the absolutely convergent fixed-point fast sweeping WENO methods on rectangular meshes, and adopt high order WENO scheme with unequal-sized sub-stencils, specifically here a fifth-order finite volume unstructured WENO scheme for spatial discretization. Extensive numerical experiments, including problems with complex domain geometries, are performed to show the accuracy, computational efficiency, and absolute convergence of the presented fifth-order fast sweeping scheme on triangular meshes. Furthermore, the proposed method is compared with the forward Euler time marching method and the popular third order total variation diminishing Rung-Kutta (TVD-RK3) time-marching method for steady state computations. Numerical examples show that the developed fixed-point fast sweeping WENO method is the most efficient scheme among them, and especially it can save up to 70% CPU time costs than TVD-RK3 in order to converge to steady state solutions.

A modified lattice Boltzmann approach based on radial basis function approximation for the non‐uniform rectangular mesh

AbstractWe have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non‐uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision‐streaming evolution. This is why the present study is inspired by the idea of the interpolation‐supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non‐uniform rectangular mesh allows grid refinement while obtaining precise flow predictions.

Fast Implementation of FEM for Integral Fractional Laplacian on Rectangular Meshes

Fast Implementation of FEM for Integral Fractional Laplacian on Rectangular Meshes

Anatomy-guided multi-resolution image reconstruction in PET

Objective. In this paper, we propose positron emission tomography image reconstruction using a multi-resolution triangular mesh. The mesh can be adapted based on patient specific anatomical information that can be in the form of a computed tomography or magnetic resonance imaging image in the hybrid imaging systems. The triangular mesh can be adapted to high resolution in localized anatomical regions of interest (ROI) and made coarser in other regions, leading to an imaging model with high resolution in the ROI with clearly reduced number of degrees of freedom compared to a conventional uniformly dense imaging model. Approach. We compare maximum likelihood expectation maximization reconstructions with the multi-resolution model to reconstructions using a uniformly dense mesh, a sparse mesh and regular rectangular pixel mesh. Two simulated cases are used in the comparison, with the first one using the NEMA image quality phantom and the second the XCAT human phantom. Main results. When compared to the results with the uniform imaging models, the locally refined multi-resolution mesh retains the accuracy of the dense mesh reconstruction in the ROI while being faster to compute than the reconstructions with the uniformly dense mesh. The locally dense multi-resolution model leads also to more accurate reconstruction than the pixel-based mesh or the sparse triangular mesh. Significance. The findings suggest that triangular multi-resolution mesh, which can be made patient and application specific, is a potential alternative for pixel-based reconstruction.

Fog collection rate investigation for a hydrophobic surface and different inclinations of rectangular meshes

Fog collection rate investigation for a hydrophobic surface and different inclinations of rectangular meshes

Research on pin-by-pin calculation method of rectangular mesh based on quasi-diffusion theory

With the development of nuclear energy techniques, pin-by-pin calculation using the SP3 method based on pin cell homogenization attracts researchers. This study proposed a pin-by-pin calculation method of rectangular mesh based on quasi-diffusion (QD) theory. The QD equation and boundary condition were derived from a transport equation similar to the P1 equation derivation. The Eddington factor was treated as a few-group homogenized parameter and calculated based on a deterministic code ALPHA. The numerical method of QD equation was developed based on nodal expansion method of nonlinear iteration. Some benchmarks were used to verify the Eddington factor and the numerical method of QD. 4 colorset models with different neutron anisotropy levels were analyzed by pin-by-pin-QD method. Pin-by-pin-QD can reduce keff error by about 600 pcm and agree better with reference results. Additionally, it has better accuracy and similar efficiency as diffusion calculation and is suitable for problems with strong anisotropy.

Superconvergence error analysis of linearized semi-implicit bilinear-constant SAV finite element method for the time-dependent Navier–Stokes equations

In this paper, based on the scalar auxiliary variable (SAV) approach, the superconvergence error analysis is investigated for the time-dependent Navier–Stokes equations. In which, an equivalent system of the Navier–Stokes equations with three variables and a fully-discrete scheme is developed with semi-implicit Euler discretization for the temporal direction and low-order bilinear-constant finite element discretization for the spatial direction, respectively. With the help of the high-precision estimations of the bilinear-constant finite element pair on the rectangular meshes, the superclose error estimates for velocity in H1-norm and pressure in L2-norm are obtained by treating the trilinear term carefully and skillfully. The global superconvergence results are also derived in terms of a simple and efficient interpolation post-processing technique. Finally, some numerical results are provided to demonstrate the correctness of the theoretical analysis.

A compact circularly polarized dual port MIMO antenna with DGS and parasitic patch for modern wireless communication and IOT applications

Abstract The article proposes a broadband dual-port planar multiple-input-multiple-output (MIMO) antenna for the lower sub-6 GHz band (1.67 GHz to 3.15 GHz) applications. The simple structure of the MIMO antenna system consists of a semi-annular ring-shaped patch with a covering cap-like structure connected with two symmetrical L-shaped structures. A partial ground with a rectangular mesh-like structure at the center is designed and the same rectangular mesh has been added as the parasitic element with the driven patch to attain circular polarization and enhanced isolation. The miniaturized dimensions of the two-port MIMO antenna system are 0.28 λ 0 × 0.54 λ 0. The suggested two-port MIMO antenna offers a wider impedance bandwidth (IBW) of 61.41% around the versatile resonant frequency of 2.4 GHz. The proposed MIMO also depicts a minimum isolation of 26 dB with an edge-to-edge spacing of 0.19 λ 0. An axial ratio bandwidth of 280 MHz is attained between 2.36 GHz and 2.64 GHz. The proposed antenna shows good IBW with excellent isolation, along with good radiation and MIMO diversity characteristics to operate at 2.4 GHz with circular polarization. The designed MIMO antenna can be utilized for IoT and modern mobile wireless applications as the broad bandwidth covers various IoT communication protocol frequencies such as 1.8 GHz (NB-IoT) and 2.4 GHz (Wireless LAN).

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

Melting and Heat Transfer Characteristics of Phase Change Material: A Comparative Study on Wire Mesh Finned Structure and Other Fin Configurations

Abstract In the present paper, a two-dimensional transient numerical study has been performed to investigate the influence of different fin designs on the melting and heat transfer characteristics of a phase change material (PCM), i.e., Paraffin wax, filled in square enclosures equipped with fin structures. Five distinct fin designs were examined: single rectangular, double rectangular, double triangular, double angled, and wire mesh. It is worth noting that all these fin designs have the equal heat transfer area. An isothermal heat source of temperature 350 K is provided at the left wall of the square enclosure and the remaining walls are assumed to be adiabatic. Six parameters were evaluated to determine the best fin configurations: melting time, enhancement ratio (ER), time savings, energy stored, mean power, and Nusselt number. The results show that all the fin designs outperformed as compared to model 1 (no fin configuration). Among the finned configurations, model 2 had the poorest performance, taking 1314 s to complete the melting, while model 6 had the most efficient fin design, with a melting time reduced by 67.53% compared to model 1. Model 6 also had the highest ER and mean power, i.e., 70.43% and 199.51%, respectively and as the melting process continued, the Nusselt number decreased. In addition to the above, we optimized the element size of the wire-mesh fin design using RSM methodology. This optimized design decreases the melting period by 70.04%. Overall, present study provides a comprehensive analysis of different finned configurations for improving the melting performance of the PCM in square enclosures and found wire-mesh fin design most appropriate and promising.

Semigroup theory and finite element method applied to a non-linear dissipative wave equation

We study the wave equation with a non-linear dissipative term associated to a bidimensional membrane with fixed boundary. We use the semigroup theory to consider the existence and uniqueness of solutions to the problem and we implement the finite element method to analyse the vibrating evolutionary equation. In particular we use Comsol Multiphysics software with a rectangular mesh to analyze the corresponding evolutionary system. We mention that this system can appear, for example, in the diaphragm of a centrifugal pump in mining processes.

A discrete fracture-matrix approach based on Petrov-Galerkin immersed finite element for fractured porous media flow on nonconforming mesh

In this paper, the Petrov-Galerkin immersed finite element method is developed for simulating flow in fractured porous media. We consider the hybrid-dimensional fracture model as an elliptic interface problem with multiple physical coupling interface conditions, and embed the information of low-dimensional fractures into the local functions of interface elements. The immersed finite element space is constructed by explicitly representing the local solution functions in the interface element. This approach addresses the limitation of conforming meshes. More importantly, it can capture both the continuity and discontinuity of pressure, making it effective for both conductive and blocking fractures. We provide a detailed illustration of how to construct local functions on triangular and rectangular meshes. Finally, numerical examples and benchmarks are presented to validate the effectiveness of our proposed method.

Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes

Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes

Study on Resistivity Imaging of Urban Landfill Leachate Channel Using 3D Electrical Resistivity Tomography with Annular Electrode Configuration

Urban garbage landfills are distributed mostly in a nearly circular shape with complex internal and external environments. The conditions on the top of the landfills are not conducive to the layout of electrical measuring lines and electrodes, resulting in difficulties in using the conventional linear or rectangular mesh high density electrical surveying system to achieve good results for the detection of leachate channel under the garbage body. This paper proposed 3D electrical resistivity tomography (ERT) method by annular electrode configuration with electrodes placed around the landfill. Through numerical simulation and indoor physical simulation experiments, we have discussed the feasibility and effectiveness of this method for circling the pollution range and channel location of landfill leachate. The study shows that the 3D ERT method with annular electrode configuration can effectively detect the spatial location and extension of garbage leachate channel, reflect the leakage of garbage leachate in landfills, and thus provide technical support for the fine detection of garbage leachate channel.

Evaluating Mesh Geometry and Shade Coefficient for Fog Harvesting Collectors

The most valuable resource for sustaining life on earth is water. In dry and semi-arid areas, the problem of water scarcity can be resolved with the aid of fog collection techniques employing fog collectors. Fog collection is greatly influenced by a variety of factors. Some are design parameters, while others depend on ambient circumstances. Geometry and the mesh’s shade coefficient are important design factors that can be modified and have an impact on the rate at which fog collects in fog collectors. The shape of the mesh holes and the process used to create the mesh serve to identify geometry and measure the shade coefficient. In this paper, a straightforward mathematical technique is proposed to make it easier to calculate the shade coefficient of various mesh shapes used in fog harvesting and to provide an approximation of the mesh volume and cost. Five alternative geometries were used: the rectangular mesh, square mesh, Raschel mesh, triangular mesh, and hexagonal mesh. The current simple method will facilitate the design of the fog mesh collector and can assist in achieving the ideal shade coefficient and most effective mesh geometry for fog harvesting. Rectangular meshes were solely used as an example to evaluate the results. Stainless steel rectangular meshes with various shade coefficients were tested for fog collection, and the amount of water collected by each mesh varied. It was concluded that the optimum shade coefficient ranged 50–60% for fog collection.

Finite element analysis of bird impact with windshield of a vehicle

The car's windscreen, which birds frequently come into contact when driving, determined to be one of the primary causes of severe bird as well as passengers, injuries. For the design and assessment of vehicle safety performance, finite element-based analysis of object strike to the windshield is commonly employed. The majority of the simpler windshield models utilized in simulations for various object strike research. However, for a reliable prediction of injuries during a car to bird accident, accurate modelling of the windshield and different glass materials considered as mechanical behaviour is required. The goal of this article is to look into potential windshield replacement options that simulate a collision between a bird and a car. Different materials' laminated glass windshields put to the test. The finite element simulation model's stress and crack patterns recorded, and they verified against actual work or common car windshield glass. The three-layer laminated glass finite element models created. For the crack propagation pattern, the element deletion method and share node techniques used. The assessment and simulation findings compared using fine mesh sizes based on the four different glass material qualities and a chosen alternative glass material, as well as existing research on ball drop testing for pedestrian head injuries. The simulated results of the laminated model of annealed glass of three layers and a 5 mm rectangular mesh demonstrate good agreement with the results of the experiments and previous simulations using finite elements. Next, the car's windshield was fitted with this model of annealed glass. In accordance with the EEVC protocol on pedestrian protection, impact testing simulating bird strikes conducted. When results for bird deceleration, fracture pattern, and windshield energy absorption compared to test results for pedestrian head injury, a good agreement shown.