Mesh Parameters Research Articles

Extraction of English Keyword Information Based on CAD Mesh Model

Traditional methods only consider topic information in English vocabulary information extraction, lose the statistical feature information of the keywords themselves, and easily ignore the semantic information of the words. In order to improve the extraction efficiency of English keyword information, based on the CAD mesh model, this paper adds constraint factors such as vertex neighborhood flatness, vertex degree, side length, and flatness on both sides of the side on the basis of the original QEM quadratic error simplification algorithm, and it incorporates a smoothing effect into the edge folding cost function. Moreover, based on the proposed normal vector-based QEM mesh simplification algorithm, the point selection after the edge folding operation is fixed as the vertices of the original edge, and it is applied to the mesh parameterization. In addition, the algorithm solves the local parameterization problem of partially deleted vertices after the simplification operation of each layer is completed. After the model is constructed, the performance of the model is verified through experiments. The research shows that the English keyword information extraction model constructed in this paper is effective.

Linear regularized finite difference scheme for the quasilinear subdiffusion equation

Abstract A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded. For this problem, a linear regularized mesh scheme is constructed and investigated. A sufficient condition is derived for the regularization parameter that ensures the so-called local correctness of the mesh scheme. On the basis of correctness and approximation estimates for model problems with time-fractional Caputo or Caputo–Fabrizio derivatives, accuracy estimates are given in terms of mesh and regularization parameters under the assumption of the existence of a smooth solution to the differential problem. The presented results of the numerical experiments confirm the obtained asymptotic accuracy estimates.

Finite difference scheme on graded meshes to the time-fractional neutron diffusion equation with non-smooth solutions

In this paper, we construct and analyze an efficient numerical scheme based on graded meshes in time for solving the fractional neutron diffusion equation with delayed neutrons and non-smooth solutions, which can be found everywhere in nuclear reactors. Using the L1 discretization of each time fractional derivatives on graded meshes and the classical finite difference for the spatial derivatives on uniform meshes, we prove the order of convergence in time is at best (2−2α) instead of 2α under non-smooth solutions, where 0<α<1/2 is the anomalous diffusion order. Numerical experiments are designed to verify our theoretical analysis. Although we can pick any mesh parameter r provided r≥(2−2α)/2α to get the optimal order, we choose the minimum in consideration of both accuracy and convergence.

Adsorption of ammonia ([formula omitted]) on palladium oxide (PdO) surface (001): Ab initio study

Dacapo code with the GGA-PW91 approximation has been used to study the adsorption of ammonia molecular (NH3) on PdO(001) termination surfaces, via N atom. We have determined the geometrical parameters of NH3 in the free phase, the PdO mesh parameters, at different sites of PdO(001) surface, the adsorption energies, the geometrical parameters of NH3 in adsorbed phase, the PDOS of the system, as well as the decomposition. The hollow (H) site of the PdO-O(001) termination is found to be most energetically stable with an adsorption energy of −0.445 eV, while the bridge-oy (B2) site of the PdO-Pd(001) termination is the most energetically stable with an adsorption energy of −1.105 eV. The isosurface calculations of NH3/PdO(001) show an accumulation of charges around the nitrogen, oxygen and palladium atoms, and charge depletion for hydrogen atoms. The thermochemistry of NH3 is very favourable on the PdO-O(001) surface, however for the PdO-Pd(001) surface the last two reaction paths are unfavourable. Finally, all the obtained results are in agreement with those found in the literature.

Pre-split blasting design to reduce costs and improve safety in underground mining

To control the overbreaking of an underground mining development gallery, the controlled blasting technique was proposed and as a result it was possible to reduce costs and improve the physical stability of the periphery of the opening, achieving greater safety for personnel and equipment. With the support of the geomechanical studies, the rock quality of the advancing front was determined, serving for the design of the drilling mesh and the choice and distribution of the explosives in the respective drills. This study demonstrates that it is possible to make progress in efficient mining preparation and development work, achieving minimal damage to the roof and walls of the mining work. Performing the simulation with the software determines a difference between conventional blasting with the design of the pre-cut technique, optimizing the parameters of the perforation mesh, selection of the explosive charge, the order of detonation. As a result, the study found a 60%–70% reduction in excess excavation, showing a better finish of the tunnel contour, yielding a 16% reduction in support costs.

Parallel-in-time preconditioner for the Sinc-Nyström systems

The sinc-Nyström method is a high-order numerical method based on sinc basis functions for discretizing evolutionary differential equations in time. But in this method we have to solve all the time steps in one shot (i.e., all-at-once), which results in a large-scale nonsymmetric dense system that is expensive to handle. In this paper, we propose and analyze a parallel-in-time preconditioner for such a dense system arising from both the parabolic and hyperbolic PDEs. The proposed preconditioner is a low-rank perturbation of the original matrix and it has two advantages. First, we show that the eigenvalues of the preconditioned system are highly clustered with some uniform bounds which are independent of the mesh parameters. Second, the preconditioner can be computed in parallel for all the sinc time points via a block diagonalization procedure. Such a parallel potentials owing to the fact that the eigenvector matrix of the diagonalization is well conditioned. In particular, we show that the condition number of the eigenvector matrix only mildly grows as the number of sinc time points increases, and thus the roundoff error arising from the diagonalization procedure is controllable. The effectiveness of our proposed parallel-in-time preconditioners is verified by the observed mesh-independent convergence rates of the preconditioned GMRES in several numerical examples.

Neural jacobian fields

This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a triangulation, as well as producing highly detail-preserving maps whose accuracy exceeds current state of the art. The framework is based on reducing the neural aspect to a prediction of a matrix for a single given point, conditioned on a global shape descriptor. The field of matrices is then projected onto the tangent bundle of the given mesh, and used as candidate jacobians for the predicted map. The map is computed by a standard Poisson solve, implemented as a differentiable layer with cached pre-factorization for efficient training. This construction is agnostic to the triangulation of the input, thereby enabling applications on datasets with varying triangulations. At the same time, by operating in the intrinsic gradient domain of each individual mesh, it allows the framework to predict highly-accurate mappings. We validate these properties by conducting experiments over a broad range of scenarios, from semantic ones such as morphing, registration, and deformation transfer, to optimization-based ones, such as emulating elastic deformations and contact correction, as well as being the first work, to our knowledge, to tackle the task of learning to compute UV parameterizations of arbitrary meshes. The results exhibit the high accuracy of the method as well as its versatility, as it is readily applied to the above scenarios without any changes to the framework.

Differentiable signed distance function rendering

Physically-based differentiable rendering has recently emerged as an attractive new technique for solving inverse problems that recover complete 3D scene representations from images. The inversion of shape parameters is of particular interest but also poses severe challenges: shapes are intertwined with visibility, whose discontinuous nature introduces severe bias in computed derivatives unless costly precautions are taken. Shape representations like triangle meshes suffer from additional difficulties, since the continuous optimization of mesh parameters cannot introduce topological changes. One common solution to these difficulties entails representing shapes using signed distance functions (SDFs) and gradually adapting their zero level set during optimization. Previous differentiable rendering of SDFs did not fully account for visibility gradients and required the use of mask or silhouette supervision, or discretization into a triangle mesh. In this article, we show how to extend the commonly used sphere tracing algorithm so that it additionally outputs a reparameterization that provides the means to compute accurate shape parameter derivatives. At a high level, this resembles techniques for differentiable mesh rendering, though we show that the SDF representation admits a particularly efficient reparameterization that outperforms prior work. Our experiments demonstrate the reconstruction of (synthetic) objects without complex regularization or priors, using only a per-pixel RGB loss.

Application of magnesium alloy sacrificial anode for restraining chloride ingress into mortar

This study aims to restrain the chloride ingress into mortar by magnesium alloy sacrificial anode system. Cube reinforced mortar specimens with embedded magnesium alloy anode meshes were prepared. The output electrochemical parameters of magnesium alloy mesh, the chloride profiles and corrosion electrochemical performance of steel in mortars immersed in chloride-contaminated solutions were detected. Besides, the visual inspection of steel surface after immersion was performed. The results indicate that the magnesium alloy mesh can restrain effectively chloride ingress into mortar. With increasing water-cement ratio and chloride content, the galvanic potential and current density between the steel and magnesium alloy mesh increase. The chloride diffusion coefficient of mortar decreases after the application of magnesium alloy sacrificial anode and the decreased magnitude rises with increasing water-cement ratio, chloride concentration and decreasing steel cover thickness. The mitigation of steel corrosion and morphology of the steel surface after immersion further demonstrate the good effect of magnesium alloy sacrificial anode on reducing chloride ingress into mortar.

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

Behavior of ions from medium-density plasma in electric field created by plate–grid–plate geometry

The behavior of the ions from a medium-density plasma in an electric field created by the plate–grid–plate geometry was simulated with a two-dimensional one-fluid model in which electrons are assumed to be in thermal equilibrium, and the accuracy of the model was verified by comparing with other research results. The results show that the wire mesh parameters of the grid, including the wire mesh diameter and the spacing between the two wires of the grid, have an important influence on the ion extraction time and the ion collection ratio of the cathode plate. The blocking rate of the grid obtained by the theoretical simulation is almost equal to the geometrical blocking rate, and it is minimally affected by the initial ion density. These results can provide guidance for the optimization of wire mesh parameters of the grid, especially for the ion extraction and collection from a pulsed plasma.

A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a boundary layer

We construct a finite difference scheme for a first-order linear singularly perturbed Volterra integro-differential equation(SPVIDE) on Bakhvalov-Shishkin mesh. For the discretization of the problem, we use the integral identities and deal with the emerging integrals terms with interpolating quadrature rules which also yields remaining terms. The stability bound and the error estimates of the approximate solution are established. Further, we demonstrate that the scheme on Bakhvalov-Shishkin mesh is N ( O − 1 ) N(O−1) u n iformly convergent, where N is the mesh parameter. The numerical results are also provided for a couple of examples.

Modeling of the local anisotropic mechanical foam properties in polyisocyanurate metal panels using mesoscale FEM simulations

The local anisotropic mechanical foam properties of continuously produced polyisocyanurate metal panels were investigated. The main focus was the analysis of the anisotropic cell structure. Based on these investigations, a mesoscale FE-model of a representative volume element (RVE) was validated, which can provide a prediction of the mechanical properties of anisotropic foam structures with varying aspect ratios and orientations of the cells based on defined ellipsoid packings and an anisotropic tessellation model. During the validation of the model, the parameters mesh size, RVE size and strut partitioning were investigated. Due to the anisotropic cell structures, a method was developed to determine a directional RVE size, which has distinct advantages over cube-shaped RVEs. Finally, a comparison of experimental to numerical results was performed. Both in the experiment and the simulation, the structures show a strongly anisotropic behavior, whereby the degree of anisotropy tends to be slightly underestimated in the simulation. Despite small deviations, the simulation results are in good agreement with the experimental data. Accordingly, this simulation model is suitable for an estimation of the anisotropic mechanical foam properties.

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity

In this article, we consider a multi‐term fractional initial value problem which has a weak singularity at the initial time . The fractional derivatives are defined in Caputo sense. Due to such singular behavior, an initial layer occurs near which is sharper for small values of γ1 where γ1 is the highest order among all fractional differential operators. In addition, the analytical properties of the solution are provided. The classical L1 scheme is introduced on a uniform mesh to approximate the fractional derivatives. The error analysis is carried out, and it is shown that the numerical solution converges to the exact solution. Further analysis proves that the scheme is of order over the entire region, but it is of order O(τ) on any subdomain away from the origin. τ denotes the mesh parameter. To show the efficiency of the proposed scheme, this method is tested on several model problems, and the results are in agreement with the theoretical findings.

Two-level Overlapping Schwarz Methods Based on Local Generalized Eigenproblems for Hermitian Variational Problems

The research of the two-level overlapping Schwarz (TL-OS) methods based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g., mainly for a second order elliptic problem and too heavy computational cost of coarse space construction. In this paper, by introducing appropriate assumptions, we propose more concise coarse basis functions for general Hermitian positive and definite discrete systems, and establish the algorithmic and theoretical frameworks of the corresponding TL-OS methods. Furthermore, to enhance the practicability of the algorithm, we design two economical TL-OS preconditioners and prove the condition number estimate. As the first application of the frameworks, we prove that the assumptions hold for the linear finite element discretization of a second order elliptic problem with high contrast and oscillatory coefficient and the condition number of the TL-OS preconditioned system is robust with respect to the model and mesh parameters. In particular, we also prove that the condition number of the economically preconditioned system is independent of the jump range under a certain jump distribution. Experimental results show that the first kind of economical preconditioner is more efficient and stable than the existing one. Second, we construct TL-OS and the economical TL-OS preconditioners for the plane wave least squares discrete system of the Helmholtz equation by using the frameworks. The numerical results for homogeneous and nonhomogeneous cases illustrate that the preconditioned conjugate gradient method based on the proposed preconditioners has good stability in terms of the angular frequency, mesh parameters, and the number of degrees of freedom in each element.

TextureMe: High-Quality Textured Scene Reconstruction in Real Time

Three-dimensional (3D) reconstruction using an RGB-D camera has been widely adopted for realistic content creation. However, high-quality texture mapping onto the reconstructed geometry is often treated as an offline step that should run after geometric reconstruction. In this article, we propose TextureMe , a novel approach that jointly recovers 3D surface geometry and high-quality texture in real time. The key idea is to create triangular texture patches that correspond to zero-crossing triangles of truncated signed distance function (TSDF) progressively in a global texture atlas. Our approach integrates color details into the texture patches in parallel with the depth map integration to a TSDF. It also actively updates a pool of texture patches to adapt TSDF changes and minimizes misalignment artifacts that occur due to camera drift and image distortion. Our global texture atlas representation is fully compatible with conventional texture mapping. As a result, our approach produces high-quality textures without utilizing additional texture map optimization, mesh parameterization, or heavy post-processing. High-quality scenes produced by our real-time approach are even comparable to the results from state-of-the-art methods that run offline.

Combined parameterization of material distribution and surface mesh for stiffener layout optimization of complex surfaces

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener layout by means of B-spline. The other is to build the mapping relationship from the known 3D surface mesh of the thin-walled structure to its parametric domain by means of mesh parameterization. The influence of mesh parameterization upon the stiffener layout is discussed to reveal the matching issue of the combined parameterization. 3D complex surfaces represented by the triangular mesh can be dealt with even though analytical parametric equations are not available. Some numerical examples are solved to demonstrate the direct advantage and effectiveness of the proposed method.

Dynamic characteristics of a straight bevel gear drive system considering multi-state meshing and time-varying parameters

In order to investigate the dynamic characteristics of the straight bevel gear drive system, its torsional-bending-axial dynamics model considered the multi-state meshing characteristics is established. The time-varying load distribution ratio and meshing stiffness of the system are calculated by micro element method according to the performance of the straight bevel gear. Three different Poincaré sections are defined to study the dynamic characteristics of the system. The mechanism of tooth disengagement and back-side contacting is studied according to the time history diagram of the total normal force. The nonlinear dynamics equation of the system is solved by the variable step fourth-order Runge-Kutta method when the bevel gear drive system in automobile reducer is taken as the research object. The transition process of system dynamic characteristics and the influences of the meshing frequency, load coefficient and the comprehensive transmission error are studied by using the time history diagram of the total normal force, phase portraits, Poincaré maps, bifurcation diagrams and the corresponded top Lyapunov exponent (TLE). The chaotic motion found in the research is unfavorable from a practical point of view which can be avoided by adjusting the value of parameters or the initial value of state variables in engineering. The research can provide a theoretical basis for the parameter design and dynamic characteristic control of straight bevel gear drive system.

Degradation of sulfadiazine in a cyclic V-SDBD plasma system: Parameters analysis and degradation pathway

A cyclic volume and surface dielectric barrier discharge (V-SDBD) plasma wastewater treatment system with stainless steel net as discharge electrode was established and applied to the sulfadiazine (SDZ) degradation. The discharge characteristics, active substance yield and relative emission spectra in different net electrode systems were compared. The SDZ degradation as well as the UV–vis spectra and COD removal of the SDZ solutions under different treatment conditions were investigated to achieve the appropriate mesh parameter of the net electrode and circulating velocity of the solution. The obtained results show that the SDZ had a better degradation in the cyclic V-SDBD system than that in the intermittent DBD system. 10-mesh stainless steel net and 333 mL min−1 circulating flow rate were the optimal reaction conditions for the SDZ degradation. Compared with the other three net electrodes (14, 20 and 40-mesh), the 10-mesh electrode system could produce more H2O2 and O3, and the relative emission spectrum had stronger intensity. The results of voltage and current waveform and Lissajous figures show that the air ionization in the V-SDBD system with 10-mesh electrode was higher, and more micro-discharge channels could be generated in the discharge space. UV–vis spectra and COD removal analysis of SDZ solutions also stated the SDZ degradation in the V-SDBD plasma system. According to the byproducts’ identification, SDZ degradation pathway was speculated and the change of solution toxicity was analyzed. The results verified that the total toxicity of the initial SDZ solution could be reduced after treating in the V-SDBD plasma system.