Mesh Points Research Articles

On the applications of collocation method for numerically analyzing the nonlinear Degasperis–Procesi and Benjamin–Bona–Mahony equations

This research uses the Sinc Collocation method to numerically examine the Degasperis–Procesi and Benjamin–Bona–Mahony equations, achieving a high level of precision and accuracy on computational grounds with a variety of mesh points. The proposed technique involves global collocation using Sinc bases function (SBF) as an activation function. Initially, the time derivative discretization has been performed through finite difference scheme and the remaining spatial derivatives are approximated by [Formula: see text]-weighted scheme to minimize the complexity in numerical computations. The main contribution of research is in modifying the proposed scheme to overcome the complexity involved in the whole process of finding solutions with a cardinal expansion of Sinc functions in nonlinear and singular systems. The solutions of Degasperis–Procesi and Benjamin–Bona–Mahony stiff nonlinear systems are illustrated numerically and graphically and the validation and verification of the obtained results are examined through stability analysis by calculating the spectral radius by bounding the value of [Formula: see text]. A comparative study is presented with some of the well-known numerical techniques, which assured the accuracy and reliability of our technique.

A Three-Year Prospective Study Comparing Stereolithography Printed Models to Classical Impression and Plaster Cast Models in Orthodontic Therapy: A 3D Objectification Approach

The integration of computational intelligence and augmented reality has become increasingly prevalent in dental practices. Three-dimensional (3D) printing techniques have now become routine in orthodontics, prosthetics, and maxillofacial surgery. The objective of this study is to assess the effectiveness of stereolithography (SLA) printed models compared to traditional plaster casts over a three-year period. The experimental dataset consisted of 36 orthodontic patients, each with SLA printed models and plaster casts for both the upper and lower jaws, resulting in a total of 72 scans in the form of Standard Template Library (STL) files and 72 traditional impressions. The upper dental arch models were constructed using an SLA 3D printer, employing a blue 405 nm laser beam to solidify a liquid polymer. The classical plaster casts were prepared in a dental laboratory. The models were retained for long-term orthodontic therapy control. To evaluate the differences between the dental models, a laboratory scanner was used to generate virtual casts. The meshes obtained were adjusted and pre-aligned using the best-fit algorithm. Subsequently, registration of the models was performed using the iterative closest point (ICP) algorithm. Distances between the point clouds and meshes for each point of the printed model were calculated by determining the nearest triangle on the reference mesh (cast). Additionally, the model surfaces were assessed using a scanning electron microscope and a stereomicroscope. The results from 22 experimental datasets indicated a high level of agreement between the plaster casts and virtual surfaces, with a mean absolute difference of 0.018 mm and a standard deviation of 0.17 mm. These values were obtained by averaging 231,178 data points for each comparison. Overall, this study demonstrates the comparability and accuracy of SLA printed models in relation to traditional plaster casts, supporting their potential as reliable alternatives in dental practice.

NEURAL RADIANCE FIELDS (NERF): REVIEW AND POTENTIAL APPLICATIONS TO DIGITAL CULTURAL HERITAGE

Abstract. Neural Radiance Fields (NeRF or NeRFs) are to date emerging as a novel method for synthesizing novel views of complex 3D scenes, leveraging an artificial neural network to optimize a volumetric scene function using a set of input views. We conduct a preliminary critical review of the scientific and technical literature on NeRFs, and we highlight possible applications of the latter in the Cultural Heritage domain, for the image-based reconstruction of 3D models of real, multi-scale objects, even in combination with the more well-established photogrammetric techniques. A comparison is made between NeRFs and photogrammetry in terms of operating procedures and outputs (volumetric renderings vs. point clouds or meshes). It is demonstrated that NeRFs could be conveniently used for rendering objects (sculptures, archaeological remains, sites, paintings etc.) that are challenging for photogrammetry, typically: i) metallic, translucent, and/or transparent surfaces; ii) objects that present homogeneous textures; iii) occlusions, vegetation, and elements of very fine detail.

Analysis on mathematical model of convection system of micropolar fluid as darcy forchheimer flow undergoes heterogeneous and homogeneous chemical reaction

In this article, to study the fluid behavior on various specific conditions to improve the heat transfer system and here, analysis on mathematical model of dynamic fluid consist of micropolar fluid has allowed micro rotational effect with laminar flow of Darcy forchheimer model which allow inertia effect has incorporated with heterogeneous and homogenous chemical reaction undergoes heat exchanger system with boundary layer problem has modeled. The mathematical model of fluid mechanic governing equations are in the form of partial differential equation (PDE) and similarity transformation into numerical methods (PC4-FDM) of predictor and corrector technique undergoes discretized mesh point and convergence with fourth order finite difference method and shooting method is also equipped to get better solution. The additions of significant heterogeneous parameter depicts that increasing behavior in fluid concentration and homogeneous parameter depicts that decreasing in fluid concentration by allowed micro rotations leads to collision and on increasing the Eckert number related to viscous dissipation has exhibited that increased fluid velocity and decreased fluid temperature. Micro rotation parameter exhibits that similar increased fluid velocity and slight decreased in temperature of the fluid. Darcy forchheimer parameter which related to inertial effect has depicts that decreased in velocity with increased temperature of the fluid in convection system. Due to Industrialization, the study of convection heat transfer system has enormous scope which has necessity to improving the heating and cooling system of industrial mass machineries like powerplant, waste heat recovery unit, pharmaceutical industries etc.

Novel Baseline Facial Muscle Database Using Statistical Shape Modeling and In Silico Trials toward Decision Support for Facial Rehabilitation.

Backgrounds and Objective: Facial palsy is a complex pathophysiological condition affecting the personal and professional lives of the involved patients. Sudden muscle weakness or paralysis needs to be rehabilitated to recover a symmetric and expressive face. Computer-aided decision support systems for facial rehabilitation have been developed. However, there is a lack of facial muscle baseline data to evaluate the patient states and guide as well as optimize the rehabilitation strategy. In this present study, we aimed to develop a novel baseline facial muscle database (static and dynamic behaviors) using the coupling between statistical shape modeling and in-silico trial approaches. Methods: 10,000 virtual subjects (5000 males and 5000 females) were generated from a statistical shape modeling (SSM) head model. Skull and muscle networks were defined so that they statistically fit with the head shapes. Two standard mimics: smiling and kissing were generated. The muscle strains of the lengths in neutral and mimic positions were computed and recorded thanks to the muscle insertion and attachment points on the animated head and skull meshes. For validation, five head and skull meshes were reconstructed from the five computed tomography (CT) image sets. Skull and muscle networks were then predicted from the reconstructed head meshes. The predicted skull meshes were compared with the reconstructed skull meshes based on the mesh-to-mesh distance metrics. The predicted muscle lengths were also compared with those manually defined on the reconstructed head and skull meshes. Moreover, the computed muscle lengths and strains were compared with those in our previous studies and the literature. Results: The skull prediction's median deviations from the CT-based models were 2.2236 mm, 2.1371 mm, and 2.1277 mm for the skull shape, skull mesh, and muscle attachment point regions, respectively. The median deviation of the muscle lengths was 4.8940 mm. The computed muscle strains were compatible with the reported values in our previous Kinect-based method and the literature. Conclusions: The development of our novel facial muscle database opens new avenues to accurately evaluate the facial muscle states of facial palsy patients. Based on the evaluated results, specific types of facial mimic rehabilitation exercises can also be selected optimally to train the target muscles. In perspective, the database of the computed muscle lengths and strains will be integrated into our available clinical decision support system for automatically detecting malfunctioning muscles and proposing patient-specific rehabilitation serious games.

An efficient model for predicting complex delamination front of elastic coupling laminates

This work proposes a simple and efficient model to predict the variable crack front with any shape. The model contains a propagation criterion which defines the local growth direction of the delamination crack front by the vector perpendicular to the connection line of two adjacent mesh points. The angle between this vector and the pre-crack direction is calculated by the coordinates of two delamination front points. Crack front can be obtained by the local direction changes of the historical crack front. This model avoids the computing time caused by a high-fidelity finite element model. Its applicability is verified for composite laminates without coupling and with different couplings. The predicted crack front shows good agreements with the numerical results obtained by a high-fidelity FE model with refined mesh. Factors controlling the crack front shape are further discussed by analyzing strain energy release rate and mode mixture distribution at the crack front.

A Higher-Order Defect Correction Method Over an Adaptive Bakhvalov–Shishkin Mesh for Advection–Diffusion Equations

The paper presents a defect correction method based on finite difference discretizations over a Bakhvalov–Shishkin mesh for a class of convection-diffusion equations. The technique combines a stable, low-order accurate, computationally inexpensive upwind difference scheme with a higher-order less stable modified central difference operator at several grid points. We prove that the method is second-order uniformly convergent at all mesh points. We do not use asymptotic expansions of discretization errors in our analysis. The method has no directional bias, and it can be used in an adaptive procedure to refine the mesh in the non-smooth parts. Numerical results are presented, which indicate that defect correction on layer-adapted meshes is an excellent method to achieve higher-order accuracy for singular perturbation problems.

Applications of finite difference‐based physics‐informed neural networks to steady incompressible isothermal and thermal flows

AbstractPhysics‐informed neural networks (PINNs) have aroused an upsurge in scientific machine/deep learning community, especially in research areas involving solving partial differential equations. In this work, based on the multilayer perceptron neural network and finite difference (FD) method, we apply the finite difference‐based PINNs (FD‐PINNs) to simulate the steady incompressible flows. The spatial derivatives in nonlinear governing equations are discretized by the central FD scheme, and the physical boundary conditions can be exactly satisfied in a similar way to conventional fluid flow solvers. Compared to original PINNs using automatic differentiation (AD) to discretize the governing equations, FD‐PINNs hold three‐fold potential advantages in decoupling the predictive accuracy of derivatives from the network's approximating accuracy, fulfilling the physical boundary conditions, and saving computational costs when large‐size networks or meshes are used. We first attempt to make relatively fair comparisons between AD‐PINNs, FD‐PINNs and conventional flow solvers using a benchmark flow problem—steady incompressible laminar isothermal lid‐driven cavity flow across a wide range of Reynolds numbers (Re). Our results indicate that FD‐PINNs are superior to AD‐PINNs in both predictive precision, computational efficiency and training convergence. Moreover, FD‐PINNs exhibit higher accuracy than flow solvers when insufficient mesh points are used to solve high‐Re cavity flow. Even at Re = 10,000, with only 10 internal samples, FD‐PINNs can still precisely recover the flow details on a uniform mesh of size 51 × 51. Besides, the time consumption of FD‐PINNs grows much slower than that of conventional flow solvers. We also investigate the robustness of FD‐PINNs w.r.t. the noise level of samples and the effects of pressure boundary condition imposed on solid cavity walls. Furthermore, FD‐PINNs are extensively applied to predict the incompressible thermal flows: natural convective flows in a square cavity and in a concentric annulus, where the effects of governing equations on the predictive accuracy are discovered and discussed for the first time.

An efficient radial basis function generated finite difference meshfree scheme to price multi-dimensional PDEs in financial options

In this paper, the purpose is to focus on proposing a new solver for pricing financial option at the presence of several assets. Toward this goal, first we introduce the weighting coefficients of the radial basis function-finite difference (RBF-FD) procedure for approximating the derivatives of the functions under the inverse multi-quadric function (IMQ). The weights are employed on a nonuniform mesh of points when tackling multi-dimensional partial differential equations (PDEs). A new solver based on RBF-FD methodology is then constructed employing matrix notations for solving option pricing problems. The theoretical discussions will be confirmed via numerical experiments on several test problems consisting of four to five underlying assets.

Accuracy evaluation of UAS photogrammetry and structure from motion in 3D modeling and volumetric calculations

Photogrammetric surveying using unmanned aerial systems (UAS) and structure from motion (SfM) is a rapidly emerging technique that has been widely used as a valuable research tool in geodesy and related disciplines. We studied surveying and three-dimensional (3D) modeling based on UAS and SfM. In particular, we focus on the accuracy and quality of UAS-SfM in 3D modeling and volumetric calculation of a building with an overhanging feature. For this purpose, two aerial surveys were performed using a fixed-wing and a multirotor aircraft with nadir and oblique camera axes. For validating the results, field surveys were carried out using terrestrial laser scanner (TLS), differential global navigation satellite system, and total station. To study the performance of SfM software on the accuracy and quality of point clouds, UAS images were processed using three software packages: Agisoft PhotoScan, Pix4Dmapper, and 3Dsurvey. As a result of photogrammetric image processing, 3D dense point clouds, mesh models, and digital surface models were generated. For validating the UAS-SfM results, the models were compared with the TLS model and field measurements; absolute accuracy assessments and model versus model comparisons were performed. The most accurate and high-quality 3D models comparable to TLS models were obtained from oblique images. PhotoScan generated relatively more accurate 3D models with the horizontal and vertical accuracy of root mean square error 0.025 and 0.02 m, respectively. The maximum discrepancies in dimensions and volume measurements from the UAS-SfM-derived point cloud were at the level of 0.01 m and 0.66 m3 (0.03%). The results highlighted that using a low-cost UAS and SfM photogrammetry, high-accuracy and high-quality 3D models can be generated. The results confirm that with respect to its rapid data acquisition and centimeter-level accuracy, UAS-SfM can be considered as a suitable alternative approach to conventional measurement techniques, especially in engineering and emergency response.

A preconditioning method with auxiliary crack tip subproblems for dynamic crack propagation based on XFEM

In this paper, a domain decomposition based preconditioning method is developed to accelerate the Krylov subspace method for solving the linear system arising from the extended finite element discretization of the dynamic crack problem. Based on the observation that the crack tip area has a significant impact on the convergence of the iterative method while the other mesh points do not, the finite element mesh is partitioned into two types: the regular subdomains and the crack tip subdomains. To construct the additive Schwarz preconditioner, the global matrix is partitioned into submatrices which are solved exactly in the crack tip subdomains by the LU factorization and inexactly in the regular subdomains by an incomplete LU factorization. As the crack propagates, we develop a scheme to update the subdomain problems without resolving of them, in which, in order to save the computational cost, only the subdomains around the crack are updated, and all the other regular subdomains remain unchanged. To further speed up the Krylov subspace method, an auxiliary subproblem including crack tips of the previous and current time steps is constructed and solved to provide a better initial guess. We carefully studied the properties of the linear system and the performance of the proposed algorithm. The numerical experiments indicate that the proposed method works well for the simulation of dynamic crack propagation with multiple crack tips.

Interaction Between Gear Surface Wear and Contact Fatigue

Abstract A methodology is proposed to study the interplay between tooth wear and contact fatigue under elastohydrodynamic lubrication condition. The modeling methodology includes the influence of contact fatigue on wear and the influence of wear on contact fatigue. First, the changes in film pressure and film thickness of oil at each meshing point caused by contact fatigue are introduced according to the surface wear model, and the change of wear model is analyzed to study the effect of contact fatigue on wear. Then, according to the elastohydrodynamic lubrication theory, the change in film pressure affected by tooth surface wear is analyzed to study the effect of wear on contact fatigue. Finally, the influence of lubrication conditions on the interplay between tooth surface wear and contact fatigue is analyzed. In addition, an experimental fatigue study is performed and introduced into the model predictions to improve the accuracy of the proposed methodology.

Comparative anatomy of the ovine and human pelvis for laparoscopic sacrocolpopexy: evaluating the effectiveness of the ovine model.

Laparoscopic sacrocolpopexy (LSC) is a functional reconstructive surgery used to treat pelvic organ prolapse (POP) in middle-aged women. Although LSC is widely used, its implementation is hindered by perceived technical difficulties and surgical learning curves. Surgeons require adequate experience with LSC prior to performing the procedure on patients to improve their quality of life. This study is aimed at demonstrating the effectiveness of the ovine model (OM) for training and research in LSC, while also comparing anatomical differences between ovine and human models during the procedure. The animal model and training were provided by the Jesús Usón Minimally Invasive Surgery Centre. Urologists and gynecologists with experience in LSC participated in a course and their findings were recorded and documented. Differences in patient positioning, trocar placement, and reperitonealization were identified between the ovine and human models. Hysterectomy is always performed in the ovine model, whereas it is not mandatory in humans. There are also differences in the dissection of the levator ani muscle and attachment point of the posterior mesh to the uterus between the two models. Despite differences in some areas, the ovine pelvic structure and vagina are similar in size to those of humans. The ovine model is a valuable tool for surgeons in their learning curve for LSC, allowing for safe and effective practice prior to performing the procedure on patients. The use of the OM can help to improve the quality of life for women affected by pelvic organ prolapse.

An Efficient and Robust Numerical Solver for Impulsive Control of Fractional Chaotic Systems

This paper derives a computationally efficient and fast-running solver for the approximate solution of fractional differential equations with impulsive effects. In this connection, for approximating the fractional-order integral operator, a B-spline version of interpolation by corresponding equal mesh points is adopted. An illustrative example illustrates the accuracy of the new solver results as compared with those of the previous study. The proposed solver’s performance is evaluated by the fractional Rössler and susceptible-exposed-infectious impulsive systems. Moreover, the effect of impulsive behaviors is shown for various values of impulsive.

3D 치아 스캔 데이터를 위한 포인트 클라우드와 메쉬 기반의 분할 모델 성능 비교

최근 3D 구강 스캔 데이터를 이용하여 치아를 자동으로 분할 및 분류하거나 치아 형상을 예측하는 등의 시도가 활발히 진행되고 있다. 본 연구에서는 치아 표면 데이터에서 각 치아를 분할하는 데에 최근에 제안된 딥러닝 기반의 3D 분할 모델들을 적용하고 그 성능을 비교 평가하였다. 비교에 사용한 모델들은 데이터 형식에 따라 point cloud 기반의 모델과 mesh 기반의 모델로 구분된다. 또한, 예측된 결과물에 후처리 작업으로 graph cut 기법을 적용하여 각 모델의 분할 성능 향상을 비교 평가하였다. 실험 결과, point cloud 기반의 PointTransformer와 mesh 기반의 MeshSNet이 가장 우수한 분할 성능을 보였고, 특히 PointTransformer는 최적의 분할로 가장 빨리 수렴하였다. 결론적으로 치아 외관을 구성하는 포인트 또는 메쉬의 인접성 정보와 Transformer의 활용이 치아 분할 성능 향상에 중요한 영향을 주는 것으로 분석된다.

Topology optimization for isotropic elastic materials using honeycomb tessell

Topology optimization is gaining popularity as a primary tool for engineers in the initial stages of design. Essentially, the design domain is broken down into individual pixels, with the material density of each element or mesh point serving as a design variable. The optimization problem is then tackled through mathematical programming and optimization methods that rely on analytical gradient calculation. In this study, topology optimization using honeycomb tessellation elements is explored. Hexagonal elements have the ability to flexibly connect two adjacent elements. The use of the hexagonal element limits the occurrence of the checkerboard pattern to the finite elements of the quadrilateral standard Lagrangian type. A mathematical model is developed with the objective function being the minimum compliance value of the design domain. The element stiffness matrix is constructed using the strain-displacement matrix and the constitutive matrix, assuming a unit Young's modulus. Additionally, optimal conditions are established using Lagrangian multipliers. Two sensitivity and density filtering filters are employed to increase optimization efficiency, prevent the algorithm from reaching a local optimal state, and speed up convergence. If the suggested filter is employed, the objective function achieves a value of c=173,0293 and convergence is attained after 200 iterations. In contrast, without using the filter, the objective function has a larger value (c=186,7922) and convergence occurs at the 27th iteration. The results are significant for optimizing topology to meet specific boundary condition requirements. This paper proposes a novel approach using a combination of filters to advance topology optimization using hexagonal elements in future applications.

Supercloseness analysis of the nonsymmetric interior penalty Galerkin method for a singularly perturbed problem on Bakhvalov-type mesh

For a singularly perturbed convection diffusion problem, we study the supercloseness of the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh. In this process, a new composite interpolation is designed, which consists of Gauß Radau projection outside the layer and Gauß Lobatto projection inside the layer. Then by choosing the penalty parameters at different mesh points, we derive the supercloseness of k+12th order (k≥1) in an energy norm.

A Front Advancing Adaptive Triangular Mesh Dynamic Generation Algorithm and Its Application in 3D Geological Modeling

The traditional advancing front technique algorithm encounters many problems due to the complex geometric characteristics of the front edge shape. These problems include poor quality, a slow algorithm, low robustness, and the inability of the mesh unit to converge. To address these problems, an optimized adaptive triangular mesh dynamic generation algorithm called R-TIN is proposed and applied to 3D engineering geological modeling in this study. Firstly, all the shapes involved in advancing the front edge inward were classified into four types, and then the optimal triangular unit was constructed by using the candidate mesh point heuristic algorithm. Then, the robustness of this algorithm could be maintained by the graded concession of the included angle threshold in the adjacent front-line segments. Finally, based on 160 engineering geological boreholes in the study area, the 3D engineering geological model was constructed and the accuracy and visualization effect of the overall geological model have been greatly improved, which can better present the spatial distribution of strata and lithological characteristics. At the same time, this algorithm can be used in geoscience information services to support the regional or national exploration of resources and energy, sustainable development and utilization, environmental protection and the prevention of geological disasters.

Privacy preserving for AI-based 3D human pose recovery and retargeting

As an essential research task in artificial intelligence (AI), the estimation of 3D human poses has important application value in virtual reality, medical diagnosis, athlete training and other fields. However, human pose recovery and retargeting require the acquisition of detailed visual data containing private information, which has led to increasing concerns about user privacy and security. Therefore, we build a lightweight framework, called Human Motion Parameters Prediction (HMPP), which can infer the 3D mesh and 3D skeletal joint points of the human body while protecting the privacy of the user. The proposed method successfully reduces or suppresses privacy attributes while ensuring important features to perform human pose estimation. The 2D and 3D joints are used for supervision to improve the interpretability of the model at each stage. In addition, the prediction of the camera’s internal parameters is added so that the model can be augmented with projection supervision, thereby using more 2D datasets for training and improving the generalization ability of the model. Finally, the predicted motion parameters are used for 3D reconstruction and motion retargeting. Experiments show that our approach can achieve excellent evaluation results on multiple datasets and avoid inadvertently compromising private and sensitive data.

The Formability of Perforated TA1 Sheet in Single Point Incremental Forming.

In light of the analysis on the single point incremental forming (SPIF) principle of perforated titanium sheet and the corresponding peculiarities during the forming process, it is found that the wall angle constitutes the pivotal parameter influencing the SPIF quality of the perforated titanium sheet, and this is also the key evaluation index to test the application of SPIF technology on a complex surface. This method for integrating the experiment and the finite element modelling was utilized in this paper to study the wall angle range and fracture mechanism of Grade 1 commercially-pure α titanium (TA1) perforated plate, plus the effect of different wall angles on the quality of perforated titanium sheet components. The forming limiting angle, fracture, and deformation mechanism of the perforated TA1 sheet in the incremental forming were obtained. In accordance with the results, the forming limit is related to the forming wall angle. When the limiting angle of the perforated TA1 sheet in the incremental forming is around 60 degrees, the fracture mode is the ductile fracture. Parts with a changing wall angle have a larger wall angle than parts with a constant angle. The thickness of the perforated plate formed part does not fully satisfy the sine law, and the thickness of the thinnest point of the perforated titanium mesh with different wall angles is lower than that predicted by the sine law; therefore, the actual forming limit angle of the perforated titanium sheet should be less than that predicted by a theoretical calculation. With the increase in the forming wall angle, the effective strain, the thinning rate, and the forming force of the perforated TA1 titanium sheet all increase, while the geometric error decreases. When the wall angle of the perforated TA1 titanium sheet is 45 degrees, the parts with a uniform thickness distribution and good geometric accuracy can be obtained.