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The human resources and work time required for mesh generation are relatively high in the overall numerical simulation cycle of a flow field and represent a bottleneck in computational fluid dynamics applications. A large body of literature provides examples of calculations in which structured mesh quality has an impact on the results of difference scheme calculations, but few analyses are given of the mechanisms by which orthogonality and smoothness affect the errors. In this paper, the geometrically induced errors generated by the MUSCL and WENO difference schemes on non-uniform meshes were analysed, and it was found that there was no direct correlation between orthogonality and errors, and that the geometrical parameter that affects the errors was the deflection angle of the neighbouring grid points. The theoretical derivation proves that the error mainly originates from the governing equations and the difference schemes, and the improvement of the mesh quality can significantly reduce the geometrically induced error, but not completely eliminate it. In recent years, the algorithms were improved, and the discrete equivalent equations and their equivalent discretisation rule(DEER) and the unstructured finite difference methods were successively proposed. Through the simulations of free-stream preservation and linear-stream preservation cases, these improved algorithms can be used to obtain better computational results on poor quality meshes.

Wind energy resources in complex terrain are abundant. However, the default mesh division of various terrains often needs more specificity, particularly in wind resource analysis. The mesh division method can diminish computational efficiency and quality in intricate topographical conditions. This article presents a combined algorithm for generating Delaunay triangular meshes in mountainous terrains with significant variations in terrain. The algorithm considers the uncertainty of inner nodes and mesh quality, addressing both the advantages and drawbacks of the Delaunay triangular mesh. The proposed method combines the triangular center of gravity insertion algorithm with an incremental inserting algorithm. Its main goal is to enhance the quality and efficiency of mesh generation, specifically tailored for this type of complex terrain. The process involves discretizing boundary edges and contour lines to obtain point sets, screening boundary triangles, and comparing the triangle area to the average boundary triangle area, combining with the incremental inserting algorithm to generate a triangular mesh of complex terrain. After an initial debugging of the mesh, it is determined whether increasing the internal nodes is necessary to insert the triangle centers of gravity. Upon implementing actual mountainous terrain in the simulation software, a comparison of the resulting meshing demonstrates that the proposed method is highly suitable for complex mountainous terrain with significant variations in elevation. Additionally, it effectively improves the quality of the Delaunay triangular mesh and reduces the occurrence of deformed cells during the meshing process. [ABSTRACT FROM AUTHOR]

With the rapid advancement of computer graphics and three-dimensional modeling technology, the processing and optimization of three-dimensional (3D) models have become contentious research topics. In the context of mobile devices or web applications, situations may arise where it becomes necessary to load a 3D model with a substantial memory footprint in real-time or dynamically adjust the level of detail of a model based on the scene's proximity. In such cases, it is imperative to optimize the original model to ensure smoothness and responsiveness. Due to the simplicity of their algorithm, quadric error metrics (QEMs) can deliver excellent results in simplifying 3D models while maintaining high efficiency. Therefore, QEM is widely employed in engineering applications within the realm of computer graphics development. Moreover, in the pursuit of enhanced quality and efficiency, numerous scholars have improved it based on QEM algorithms. This study aims to provide a systematic review and summary of the principles and applications of current research on QEM algorithms. First, we conducted a bibliometric analysis of 128 studies in related fields spanning from 1998 to 2022 using CiteSpace. This allowed us to sort QEM algorithms and gain insights into their development status and emerging trends. Second, we delve into the fundamental principles and optimizations of the QEM algorithms to provide a deeper understanding of their implementation process. Following that, we explore the advantages and limitations of the QEM algorithms in practical applications and analyze their potential in various domains, including virtual reality and game development. Finally, this study outlines future research directions, which encompass the development of more efficient error metric calculation methods, the exploration of adaptive simplification strategies, and the investigation of potential synergies with deep learning technologies. Current research primarily centers on enhancing QEM algorithms by incorporating additional geometric constraints to better differentiate between flat and irregular areas. This enables a more accurate determination of the areas that should be prioritized for folding. Nevertheless, it is important to note that these improvements may come at the cost of reduced computational efficiency. Therefore, future research directions could involve exploring parallel computing techniques and utilizing GPUs to enhance computational efficiency. [ABSTRACT FROM AUTHOR]

Biological structures are hierarchical and non-homogeneous objects. In particular, in each type of the biological cell various organelles exist. Also, in the cell many nonlinear processes, like the synaptic transmission, take place. The mesh, created for the purpose of numerical simulation, should reflect accurately their nature that is usually complicated. This, in connection with the fact that the mesh should fit precisely the aforementioned structures, create substantially new problems in comparison with well worked-out engineering applications. In this paper the problem of refining the mesh of a presynaptic bouton is considered. The refinement was tested by performing simulations of nonlinear diffusion-reaction type of propagation of neurotransmitters. The results for the original and for the refined mesh were compared. The latter reflected the nature of the biological object more precisely. The benefits and the disadvantages of the proposed refinement algorithm are discussed in detail. [ABSTRACT FROM AUTHOR]

Nowadays computational fluid dynamics now assists ventilation system designers and architects in understanding the induced flow behaviour in the indoor environment. The use of large-eddy simulation is a novel methodology for these types of assessments. The method requires that the computational domain be adequately discretized in order to resolve the majority of the flow. The last five years of publications of Elsevier, SAGE, and Multidisciplinary Digital Publishing Institute were screened. Indoor flow categories were utilized to assess the differences. Based on the papers reviewed, the cell size requirement was considered as a key factor of computational demand. Specifications were made for each type of indoor flow simulation. [ABSTRACT FROM AUTHOR]

Finite element mesh quality, which affects analysis accuracy and computational cost, is usually determined based on the designer's experience. In this study, we propose a GCN (Graph Convolutional network)-based method for evaluating the quality of 3D meshes composed of shell elements. In the proposed method, a three-layer network is constructed using GENConv with graph adjacency matrix and feature matrix as input. The feature matrix is created based on geometric shapes such as coordinates and the mesh qualities such as aspect ratio. A dual graph is constructed by converting finite elements into graph nodes and their adjacent parts into graph edges, and the created features are given to the graph nodes for learning. The proposed method is applied to a dataset of automotive side-member FE models and the effectiveness of the constructed network and the introduced mesh features is confirmed. We also visualize the attribution of mesh features and important factors in the obtained results by calculating the integrated gradients of the network. This allows us to select the important mesh features both positively and negatively and explains the basis for our predictions.

Wind energy resources in complex terrain are abundant. However, the default mesh division of various terrains often needs more specificity, particularly in wind resource analysis. The mesh division method can diminish computational efficiency and quality in intricate topographical conditions. This article presents a combined algorithm for generating Delaunay triangular meshes in mountainous terrains with significant variations in terrain. The algorithm considers the uncertainty of inner nodes and mesh quality, addressing both the advantages and drawbacks of the Delaunay triangular mesh. The proposed method combines the triangular center of gravity insertion algorithm with an incremental inserting algorithm. Its main goal is to enhance the quality and efficiency of mesh generation, specifically tailored for this type of complex terrain. The process involves discretizing boundary edges and contour lines to obtain point sets, screening boundary triangles, and comparing the triangle area to the average boundary triangle area, combining with the incremental inserting algorithm to generate a triangular mesh of complex terrain. After an initial debugging of the mesh, it is determined whether increasing the internal nodes is necessary to insert the triangle centers of gravity. Upon implementing actual mountainous terrain in the simulation software, a comparison of the resulting meshing demonstrates that the proposed method is highly suitable for complex mountainous terrain with significant variations in elevation. Additionally, it effectively improves the quality of the Delaunay triangular mesh and reduces the occurrence of deformed cells during the meshing process.

Evaluating mesh quality prior to performing the computational fluid dynamics (CFD) simulation is an essential step to ensure the acceptable accuracy of cylinder modelling. However, traditional mesh quality indicators are often insufficient since they only check geometric information on individual distorted elements. To yield more accurate results, the current evaluation process usually requires careful manual re-evaluation for quality properties such as mesh distribution and local refinement, which heavily increase the meshing overhead. In this paper, we introduce an efficient quality indicator for varisized cylinder meshes, consisting of a mesh pre-processing method and a neural network-based indicator, Mesh-Net. We also publish a cylinder mesh benchmark dataset. The proposed indicator is trained to study the role of CFD meshes on the accuracy of numerical simulations. It considers both the effect of element geometry (e.g., orthogonality) and quality properties (e.g., smoothness and distribution). Thereafter, the well-trained indicator is used as a black-box to predict the overall quality of the input mesh automatically. Experimental results demonstrate that the proposed indicator is accurate and can be applied in the mesh quality evaluation process without manual interactions. [ABSTRACT FROM AUTHOR]

• A large-scale benchmark dataset with airfoil mesh samples. • A lightweight deep neural network MQNet for mesh quality evaluation. • A MQNet-based meshing workflow for high-quality airfoil mesh generation. Evaluating mesh quality before solving is crucially important for error control in the numerical simulation of airfoils. Traditional mesh quality metrics are used to identify distorted mesh elements by analyzing their geometric shape information like angles and edges. However, these metrics fail to recognize numerical errors stemming from quality attributes such as improper mesh density or distribution. This deficiency has imposed a burden on intensive manual re-evaluation, which heavily increases the meshing cost. In this paper, we introduce deep neural networks to airfoil mesh quality evaluation to improve its automation and efficiency. Specifically, we propose a neural network-based evaluation model, MQNet, accompanied by the first large-scale mesh benchmark dataset, AirfoilSet. MQNet is trained on the dataset to learn the quality-related attributes including mesh orthogonality, smoothness, and density. Thereafter, the trained network can be used as a black box to automatically evaluate and output the overall quality of the airfoil mesh. To demonstrate the effectiveness and generalization behaviors of the proposed network, we establish an MQNet-based mesh generation workflow. Experimental results show that MQNet is small and accurate. It outperforms widely-used neural networks and can be a useful tool to guide the high-quality mesh generation process with minimal user intervention. [ABSTRACT FROM AUTHOR]

The Target Matrix Optimization Paradigm for improving mesh quality has always had, as its agenda, to create a direct path between application mesh quality requirements and a set of target matrices that can result in an optimal mesh that meets the requirements. A major step forward in this agenda is made through the introduction of a standard set of geometric parameters which can be used to analyze Jacobian-based quality metrics and to establish a fully geometric method of mesh optimization. While Jacobian-based metrics have been widely used in the past, it has not been explicitly recognized that these kinds of metrics are expressible in terms of geometric parameters related to the local volume, orientation, skew, and aspect ratio of the Jacobian and the target matrices. When this is done, one can express the global minimum of a metric in terms of relationships between the geometric parameters. This provides a better understanding of Jacobian-based metrics that have been used in the past, as well as the opportunity to devise more effective metrics. Ideally, optimization metrics should have global minimizers at which the geometric parameters of the Jacobian matrix are equal to the geometric parameters of the target. This observation allows a classification of metrics into those having a metric type and those which do not. It is shown that there are eight theoretical metric types, including the shape and shape+size types used informally in the past. Concrete metrics exist for each of the eight theoretical types. However, not all concrete typed metrics are equally well-posed. In particular, it is important that there exist concrete metrics of each metric type that are convex (or polyconvex, or invex). A well-posed typed metric should also simplify target construction. These additional requirements mean that only six of the eight theoretical metric types can be populated with well-posed, typed metrics. Nevertheless, the most important metric types are covered with well-posed metrics. With this framework, the burden of defining mesh quality is properly placed on the application because it is their requirements that determine which of the eight metric types should be used in the optimization. When this has been determined, the path toward appropriate target construction is clear.

Abstract In this paper, we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions. Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. With respect to marching directions, three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness. A novel weighted strategy is used in the normal smoothing scheme, which evidently reduces the possibility of early stop of front generation at complex corners. With respect to marching distances, the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first; a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries. These efforts, plus other special treatments such as multi-normal generation and fast detection of local/global intersection, as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities.

Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase both shape and volume mesh quality. For this, we employ pre-shape calculus as established in Luft and Schulz (2021). Existence of regularized solutions is guaranteed. Further, consistency of modified pre-shape gradient systems is established. We present pre-shape gradient system modifications, which permit simultaneous shape optimization with mesh quality improvement. Optimal shapes to the original problem are left invariant under regularization. The computational burden of our approach is limited, since additional solution of possibly larger (non-)linear systems for regularized shape gradients is not necessary. We implement and compare pre-shape gradient regularization approaches for a 2D problem, which is prone to mesh degeneration. As our approach does not depend on the choice of metrics representing shape gradients, we employ and compare several different metrics. [ABSTRACT FROM AUTHOR]

Abstract The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

Deformations of the computational mesh, arising from optimization routines, usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize the classical shape optimization and calculus. We define pre-shape derivatives and derive corresponding structure and calculus theorems. In particular, tangential directions are featured in pre-shape derivatives, in contrast to classical shape derivatives, featuring only normal directions. Techniques from classical shape optimization and calculus are shown to carry over to this framework. An optimization problem class for mesh quality is introduced, which is solvable with the use of pre-shape derivatives. This class allows for simultaneous optimization of the classical shape objectives and mesh quality without deteriorating the classical shape optimization solution. The new techniques are implemented and numerically tested for 2D and 3D. [ABSTRACT FROM AUTHOR]

Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios. [ABSTRACT FROM AUTHOR]

Mesh smoothing is an essential technique for the improvement of mesh quality in finite element analysis, due to the fact that mesh quality has a large impact on the convergence of the computational scheme and the accuracy of the numerical results. A novel mesh smoothing method based on regular-position-guided operations is presented in this paper. The method introduced here contains two main stages: The first stage computes the regular position of each vertex based on the shape of the element and conducts regular-position-oriented-based element transformations independently; the second stage determines the finial position of each vertex according to its surrounding elements with an assembly strategy. This method is not limited to planar triangular mesh, but applicable to surface polygonal mesh. Numerical experiments on various mesh models demonstrate the effectiveness and potential of this method. [ABSTRACT FROM AUTHOR]

In the field of physically based simulation, high quality of the simulation model is crucial for the correctness of the simulation results and the performance of the simulation algorithm. When working with spline or subdivision models in the context of isogeometric analysis, the quality of the parameterization has to be considered in addition to the geometric quality of the control mesh. Following Cohen et al.'s concept of model quality in addition to mesh quality, we present a parameterization quality metric tailored for Catmull–Clark (CC) solids. It measures the quality of the limit volume based on a quality measure for conformal mappings, revealing local distortions and singularities. We present topological operations that resolve these singularities by splitting certain types of boundary cells that typically occur in interactively designed CC-solid models. The improved models provide higher parameterization quality that positively affects the simulation results without additional computational costs for the solver. [ABSTRACT FROM AUTHOR]

Abstract Climate model components utilizing unstructured meshes enable variable resolution, regionally enhanced simulations within global domains. Here we investigate the relationship between mesh quality and simulation statistics using the JIGSAW unstructured meshing library and the Model for Prediction Across Scales‐Ocean (MPAS‐Ocean) with a focus on Gulf Stream dynamics. In the base configuration, the refined region employs 8 km cells that extend 400 km from the coast of North America. This coastal‐refined region is embedded within a low‐resolution global domain, with cell size varying latitudinally between 30 and 60 km. The resolution transition region between the refined region and background mesh is 600 km wide. Three sensitivity tests are conducted: (a) The quality of meshes is intentionally degraded so that horizontal cells are progressively more distorted; (b) the transition region from high to low resolution is steepened; and (c) resolution of the coastal refinement region is varied from 30 to 8 km. Overall, the ocean simulations are shown to be robust to mesh resolution and quality alterations. Meshes that are substantially degraded still produce realistic currents, with Southern Ocean transports within 0.4% and Gulf Stream transports within 12% of high‐quality mesh results. The narrowest transition case of 100 km did not produce any spurious effects. Refined regions with high‐resolution produce eddy kinetic energy and sea surface height variability that are similar to the high‐resolution reference simulation. These results provide heuristics for the design criteria of variable‐resolution climate model domains.

When mesh boundaries move in a simulation because of the motion of a target object such as translation, rotation, and oscillation, the mesh should be regenerated to the points it will obey the locations of its new boundaries. Because recreating new mesh from the beginning is a time-consuming task, new mesh is usually created by deforming an initial mesh, which is called the mesh moving method (or mesh deformation method). In this paper, we present a new mesh moving method that produces a higher quality deformed mesh than the current mesh moving methods. In the proposed method, the deformation of mesh is evaluated by two energy quantities that are related to (i) the distortion of mesh that is invariant to translation, rotation, and size changes of the elements of the mesh and (ii) the deformation of mesh calculated using elements' size based on stiffened-linear elasticity equations. The total deformation energy of mesh is defined as a weighted sum of these two quantities. Because there is no need to pre-fix the locations of the outer boundary points for most mesh moving problems, we use new constraints, allowing the outer boundary points to move along tangential directions in the proposed method. The deformed mesh is computed by calculating the positions of the mesh points where the total deformation energy of the mesh is minimized. For test purposes, the proposed method is applied to 2D triangular meshes and a 3D tetrahedral mesh, where the meshes are deformed by the motions of the target objects such as translation, rotation, and deformation. When the quality of the deformed meshes computed with the proposed method are compared with the ones computed with current mesh moving methods, the meshes from the proposed method are shown to be better than the other meshes. [ABSTRACT FROM AUTHOR]

Molecular surface mesh generation plays a vital role in molecular modeling and visualization. However, meshes extracted directly from Protein Data Bank files have several issues such as small and large triangles, redundant elements, self-intersections, and irregular vertices. The state-of-the-art mesh improvement methods often fail to deal with these issues. In this paper, we present a novel method for valence optimization and angle improvement. For valence optimization, we remove the bad valence vertices with its neighbor triangle making regular holes in the mesh. The holes are filled in a careful manner to improve their valences as well as angle quality. We also use a segmentation-based surface remeshing which segments the mesh into random segments and then each segment is independently remeshed. In addition, a point insertion scheme is applied to minimize the ratio of obtuse triangles. Experimental results show that our method not only improves the maximal and minimal angles to an angle bound of [ 30 ∘ 120 ∘ ] but also improves the vertices' regularity, reduces the ratio of obtuse triangles, preserves the area and volume, and always succeeds with downstream applications. [ABSTRACT FROM AUTHOR]

Tapered steel beams and columns have been increasingly used as primary load carrying members. The determination of their accurate ultimate capacity can only be achieved employing advanced numerical methods such as the finite element method (FEM). This paper presents a systematic study on the influence of FE model parameters on the ultimate load of I-section tapered beam-columns typically used in mediumspan steel frames. It aims the determination of optimal FE mesh size and sub-step number to be used during the arc-length scheme for the performance of an accurate, robust and efficient inelastic post-buckling parametric analysis (PA) as well as the evaluation of the parameters influence. Once validated the FE model, using hexahedral 8-node finite elements, FE edge sizes of 20, 25 and 30 mm and 10 sub-steps have been selected for use in the future PA. Several FE analyses were also carried out to evaluate how it is and quantify the influence of each of the parameters, leading to empirical equations with errors in the range of -35% to 35% for equations without crossed terms and -23% to 23% with first-order crossed terms. [ABSTRACT FROM AUTHOR]

The mesh quality is of vital importance to obtain the numerical results precisely. Poorly shaped or distorted elements can be produced by automatic mesh generation tools. In this article, the mesh smoothing algorithm based on the Markov chain Monte Carlo method is proposed to improve the quality of the mesh. The movement of nodes position is converted to a stochastic process to seek the best position for the element quality. Compared with the widely known Laplacian smoothing and optimization-based smoothing techniques, the mesh quality by the proposed method is found better than these methods. Examples are performed to illustrate the applicability of the approach. The numerical results show that the proposed algorithm is effective and valuable. [ABSTRACT FROM AUTHOR]

Purpose: To compute the effect of ambient light illuminance settings on the mesh quality of the digital scans accomplished in a subject. Material and methods: A subject was recruited. The maxillary dentition did not present any dental restoration. A prosthodontist recorded different complete‐arch maxillary digital scans by using an IOS (TRIOS 3; 3Shape) under 4 different illuminance light conditions namely chair light at 10,000‐lux illuminance (CL group), room light at 1000‐lux illuminance (RL group), natural light at 500‐lux illuminance (NL group), and no light at 0‐lux luminosity (ZL group). Ten digital scans for each group were consecutively obtained. Mesh quality was examined using the iso2mesh MATLAB package. Shapiro‐Wilk test revealed a nonnormally distributed data. Kruskal‐Wallis one‐way ANOVA, and pair‐wise comparison were selected to evaluate the data (α = 0.05). Results: Significant differences in mesh quality values were measured among the groups (p < 0.001). Pair‐wise comparisons revealed that significant difference was found across all pairs of lighting groups, except for the RL‐NL comparison (p = 0.279). However, the CL condition obtained the highest mean values, followed by RL and NL groups, and the lowest mean values were obtained on the ZL lighting condition. Conclusions: Chair light at 10,000‐lux illuminance condition is recommended to maximize the quality mesh values of the IOS system tested (TRIOS 3; 3Shape). [ABSTRACT FROM AUTHOR]

Numerical analysis, especially the finite volume method (FVM), is one of the primary approaches employed when evaluating a building environment. A complicated geometry can degrade the mesh quality, leading to numerical diffusions and errors. Thus, this study develops and evaluates an automatic building geometry simplification method based on integrating similar surfaces for the geometry of an indoor space. A regression model showed that the complexity of the simplified geometry and its similarity to the original geometry decreased linearly with the threshold of the method. The mesh quality was significantly improved by the simplification. In particular, the maximum skewness decreased exponentially with the threshold of the method. It is expected that the simplification method and regression model presented in this study can be used to quantitatively control the mesh quality. [ABSTRACT FROM AUTHOR]

In this paper, we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions. Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. With respect to marching directions, three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness. A novel weighted strategy is used in the normal smoothing scheme, which evidently reduces the possibility of early stop of front generation at complex corners. With respect to marching distances, the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first; a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries. These efforts, plus other special treatments such as multi-normal generation and fast detection of local/global intersection, as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities. [ABSTRACT FROM AUTHOR]

Theoretical methods are developed to understand the effect of non-uniform grids on Flux Reconstruction (FR) in multi-dimensions. A better theoretical understanding of the effect of wave angle and grid deformation is established. FR is shown to have a smaller variation in properties than some finite difference counterparts. Subsequent numerical experiments on the Taylor–Green Vortex with jittered elements show the effect of localised regions of expansion and contraction. The effect this had on Nodal DG-like schemes was to increase the dissipation, whereas for more typical FR schemes the effect was to increase the dispersion. Some comparison is made between second-order FR and a second-order finite volume (FV) scheme. FR is found to be more resilient to mesh deformation, however, FV is found to be more resolved when operated at second order on the same mesh. [ABSTRACT FROM AUTHOR]

Climate model components utilizing unstructured meshes enable variable resolution, regionally enhanced simulations within global domains. Here we investigate the relationship between mesh quality and simulation statistics using the JIGSAW unstructured meshing library and the Model for Prediction Across Scales‐Ocean (MPAS‐Ocean) with a focus on Gulf Stream dynamics. In the base configuration, the refined region employs 8 km cells that extend 400 km from the coast of North America. This coastal‐refined region is embedded within a low‐resolution global domain, with cell size varying latitudinally between 30 and 60 km. The resolution transition region between the refined region and background mesh is 600 km wide. Three sensitivity tests are conducted: (a) The quality of meshes is intentionally degraded so that horizontal cells are progressively more distorted; (b) the transition region from high to low resolution is steepened; and (c) resolution of the coastal refinement region is varied from 30 to 8 km. Overall, the ocean simulations are shown to be robust to mesh resolution and quality alterations. Meshes that are substantially degraded still produce realistic currents, with Southern Ocean transports within 0.4% and Gulf Stream transports within 12% of high‐quality mesh results. The narrowest transition case of 100 km did not produce any spurious effects. Refined regions with high‐resolution produce eddy kinetic energy and sea surface height variability that are similar to the high‐resolution reference simulation. These results provide heuristics for the design criteria of variable‐resolution climate model domains. Plain Language Summary: Computer simulations used to study the ocean use grids that cover the ocean's surface, and computations are conducted in each grid cell. The smaller these cells are, the more detailed the simulation is, but simulations with more cells are more expensive to run. We experiment with adding small cells in the region of interest, in this case the North American coast, and larger cells in the rest of the ocean. We conducted three series of tests and looked at the effects on the Gulf Stream, an ocean current off the East Coast of North America. (a) We wanted to know how much adding these small cells improved the simulation. We changed the size of the coastal cells from 30 km wide (less detailed) to 8 km wide (more detailed). Smaller cells improved the results along the North American coast. (b) We cannot go straight from the small to large cells and must have intermediate‐sized cells in between. We experiment with different numbers of these intermediate transition cells. The more intermediate cells we added, the better the results were. (c) We wanted to know whether the cells have to be a regular shape in order to get good results. We experimented with irregular cell shapes. The irregular cells produced results that were very similar to the regular cells. Key Points: Regionally refined MPAS‐Ocean simulations are comparable to global high‐resolution simulations for numerous metricsVariable‐resolution unstructured Voronoi meshes created using JIGSAW are evaluated for qualitySimulation quality remains high for steep resolution transitions and intentionally degraded meshes [ABSTRACT FROM AUTHOR]

Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios.

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification, an improved half-edge collapse mesh simplification algorithm is proposed. The concept of approximate measurement of edge curvature is introduced, and the edge curvature is added to the error measure, so that the order of half-edge collapse of the mesh is changed, and the simplified details of the mesh model can be preserved accurately. At the same time, by analyzing the quality of simplified triangular mesh, optimizing triangular mesh locally, reducing the amount of narrow triangles, the quality of the simplified model is improved. The proposed algorithm was tested on Cow model, Car model and Bunny model, and compared with another three algorithms, one of them is a classical mesh simplification algorithm based on edge collapse, the other is an improved algorithm of the classical one. The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio, and has reasonable mesh allocation, fast execution speed and small error. [ABSTRACT FROM AUTHOR]

To decide whether the perceived quality of a mesh is influenced by a certain modification such as compression or simplification, a metric for estimating the visual quality of 3D meshes is required. Today, machine learning and deep learning techniques are getting increasingly popular since they present efficient solutions to many complex problems. However, these techniques are not much utilized in the field of 3D shape perception. We propose a novel machine learning-based approach for evaluating the visual quality of 3D static meshes. The novelty of our study lies in incorporating crowdsourcing in a machine learning framework for visual quality evaluation. We deliberate that this is an elegant way since modeling human visual system processes is a tedious task and requires tuning many parameters. We employ crowdsourcing methodology for collecting data of quality evaluations and metric learning for drawing the best parameters that well correlate with the human perception. Experimental validation of the proposed metric reveals a promising correlation between the metric output and human perception. Results of our crowdsourcing experiments are publicly available for the community. [ABSTRACT FROM AUTHOR]

We consider the finite element method on locally damaged meshes allowing for some distorted cells which are isolated from one another. In the case of the Poisson equation and piecewise linear Lagrange finite elements, we show that the usual a priori error estimates remain valid on such meshes. We also propose an alternative finite element scheme which is optimally convergent and, moreover, well conditioned, i.e. the conditioning number of the associated finite element matrix is of the same order as that of a standard finite element method on a regular mesh of comparable size. [ABSTRACT FROM AUTHOR]