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Journal articles on the topic 'Curved meshes'

Author: Grafiati

Published: 7 December 2024

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1

Rangarajan, Ramsharan, and Adrián J. Lew. "Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes." International Journal for Numerical Methods in Engineering 98, no. 4 (March 4, 2014): 236–64. http://dx.doi.org/10.1002/nme.4624.

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2

Kilian, Martin, Anthony S. Ramos Cisneros, Christian Müller, and Helmut Pottmann. "Meshes with Spherical Faces." ACM Transactions on Graphics 42, no. 6 (December 5, 2023): 1–19. http://dx.doi.org/10.1145/3618345.

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Discrete surfaces with spherical faces are interesting from a simplified manufacturing viewpoint when compared to other double curved face shapes. Furthermore, by the nature of their definition they are also appealing from the theoretical side leading to a Möbius invariant discrete surface theory. We therefore systematically describe so called sphere meshes with spherical faces and circular arcs as edges where the Möbius transformation group acts on all of its elements. Driven by aspects important for manufacturing, we provide the means to cluster spherical panels by their radii. We investigate the generation of sphere meshes which allow for a geometric support structure and characterize all such meshes with triangular combinatorics in terms of non-Euclidean geometries. We generate sphere meshes with hexagonal combinatorics by intersecting tangential spheres of a reference surface and let them evolve - guided by the surface curvature - to visually convex hexagons, even in negatively curved areas. Furthermore, we extend meshes with circular faces of all combinatorics to sphere meshes by filling its circles with suitable spherical caps and provide a remeshing scheme to obtain quadrilateral sphere meshes with support structure from given sphere congruences. By broadening polyhedral meshes to sphere meshes we exploit the additional degrees of freedom to minimize intersection angles of neighboring spheres enabling the use of spherical panels that provide a softer perception of the overall surface.

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3

Zhang, Jiayi Eris, Jérémie Dumas, Yun (Raymond) Fei, Alec Jacobson, Doug L. James, and Danny M. Kaufman. "Progressive Shell Qasistatics for Unstructured Meshes." ACM Transactions on Graphics 42, no. 6 (December 5, 2023): 1–17. http://dx.doi.org/10.1145/3618388.

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Thin shell structures exhibit complex behaviors critical for modeling and design across wide-ranging applications. Capturing their mechanical response requires finely detailed, high-resolution meshes. Corresponding simulations for predicting equilibria with these meshes are expensive, whereas coarse-mesh simulations can be fast but generate unacceptable artifacts and inaccuracies. The recently proposed progressive simulation framework [Zhang et al. 2022] offers a promising avenue to address these limitations with consistent and progressively improving simulation over a hierarchy of increasingly higher-resolution models. Unfortunately, it is currently severely limited in application to meshes and shapes generated via Loop subdivision. We propose Progressive Shells Quasistatics to extend progressive simulation to the high-fidelity modeling and design of all input shell (and plate) geometries with unstructured (as well as structured) triangle meshes. To do so, we construct a fine-to-coarse hierarchy with a novel nonlinear prolongation operator custom-suited for curved-surface simulation that is rest-shape preserving, supports complex curved boundaries, and enables the reconstruction of detailed geometries from coarse-level meshes. Then, to enable convergent, high-quality solutions with robust contact handling, we propose a new, safe, and efficient shape-preserving upsampling method that ensures non-intersection and strain limits during refinement. With these core contributions, Progressive Shell Quasistatics enables, for the first time, wide generality for progressive simulation, including support for arbitrary curved-shell geometries, progressive collision objects, curved boundaries, and unstructured triangle meshes - all while ensuring that preview and final solutions remain free of intersections. We demonstrate these features across a wide range of stress-tests where progressive simulation captures the wrinkling, folding, twisting, and buckling behaviors of frictionally contacting thin shells with orders-of-magnitude speed-up in examples over direct fine-resolution simulation.

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4

Khattri, Sanjay Kumar. "An Adaptive Quadrilateral Mesh in Curved Domains." Serdica Journal of Computing 3, no. 3 (November 3, 2009): 249–68. http://dx.doi.org/10.55630/sjc.2009.3.249-268.

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An nonlinear elliptic system for generating adaptive quadrilateral meshes in curved domains is presented. The presented technique has been implemented in the C++ language with the help of the standard template library. The software package writes the converged meshes in the GMV and the Matlab formats. Grid generation is the first very important step for numerically solving partial differential equations. Thus, the presented C++ grid generator is extremely important to the computational science community.

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5

Zhang, Juan, Lin Hua, and Fu Sheng Wang. "An Stress Correction Method Applied to Doubly Curved Composite Laminated Plate." Advanced Materials Research 148-149 (October 2010): 523–28. http://dx.doi.org/10.4028/www.scientific.net/amr.148-149.523.

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Aim: presents a stress correction method to improve calculation accuracy of doubly curved composite laminated plate with big meshing size to save computational effort. With the application of Marc’s secondary development function, a subroutine is embedded to simulate the mechanical properties of material, and the amendment factors are added so that the stress calculation results have the same computational accuracy when the model is compartmentalized to big meshes as the case under small meshes. We Compare the calculation results in big meshes and what in small meshes, which prove the error request can be satisfied.

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Kozhemyachenko, A. A., and A. V. Favorskaya. "Grid Convergence Analysis of Grid-Characteristic Method on Chimera Meshes in Ultrasonic Nondestructive Testing of Railroad Rail." Журнал вычислительной математики и математической физики 63, no. 10 (October 1, 2023): 1687–705. http://dx.doi.org/10.31857/s0044466923100071.

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A three-dimensional direct problem of ultrasonic nondestructive testing of a railroad rail treated as a linear elastic medium is solved by applying a grid-characteristic method on curved structured Chimera and Cartesian background meshes. The algorithm involves mutual interpolation between Chimera and Cartesian meshes that takes into account the features of the transition from curved to Cartesian meshes in three-dimensional space. An analytical algorithm for generating Chimera meshes is proposed. The convergence of the developed numerical algorithms under mesh refinement in space is analyzed. A comparative analysis of the full-wave fields of the velocity modulus representing the propagation of a perturbation from its source is presented.

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7

Ren, Yingying, Uday Kusupati, Julian Panetta, Florin Isvoranu, Davide Pellis, Tian Chen, and Mark Pauly. "Umbrella meshes." ACM Transactions on Graphics 41, no. 4 (July 2022): 1–15. http://dx.doi.org/10.1145/3528223.3530089.

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We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems. We build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques.

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8

Hewett, Dennis W. "The Embedded Curved Boundary Method for Orthogonal Simulation Meshes." Journal of Computational Physics 138, no. 2 (December 1997): 585–616. http://dx.doi.org/10.1006/jcph.1997.5835.

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9

Yang Hao and C. J. Railton. "Analyzing electromagnetic structures with curved boundaries on Cartesian FDTD meshes." IEEE Transactions on Microwave Theory and Techniques 46, no. 1 (1998): 82–88. http://dx.doi.org/10.1109/22.654926.

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10

Tellier, Xavier, Cyril Douthe, Laurent Hauswirth, and Olivier Baverel. "Caravel meshes: A new geometrical strategy to rationalize curved envelopes." Structures 28 (December 2020): 1210–28. http://dx.doi.org/10.1016/j.istruc.2020.09.033.

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11

Lee, Seung-Yong, Seong-Hyeon Kweon, and Seung-Hyun Yoon. "An Effective Method for Slicing Triangle Meshes Using a Freeform Curve." Mathematics 12, no. 10 (May 7, 2024): 1432. http://dx.doi.org/10.3390/math12101432.

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Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user’s viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing.

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12

Fortes, Lucas Lobo Latorre, and Sandro Trindade Mordente Gonçalves. "Wideband performance limitations of the C-FDTD in the discretization impoverishment of a curved surface." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 5 (June 30, 2020): 1005–15. http://dx.doi.org/10.1108/compel-01-2020-0048.

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Purpose This paper aims to explore the limitations of the conformal finite difference time-domain method (C-FDTD or Dey–Mittra) when modeling perfect electric conducting (PEC) and lossless dielectric curved surfaces in coarse meshes. The C-FDTD is a widely known approach to reduce error of curved surfaces in the FDTD method. However, its performance limitations are not broadly described in the literature, which are explored as a novelty in this paper. Design/methodology/approach This paper explores the C-FDTD method applied on field scattering simulations of two curved surfaces, a dielectric and a PEC sphere, through the frequency range from 0.8 to 10 GHz. For each sphere, the mesh was progressively impoverished to evaluate the accuracy drop and performance limitations of the C-FDTD with the mesh impoverishment, along with the wideband frequency range described. Findings This paper shows and quantifies the C-FDTD method’s accuracy drops as the mesh is impoverished, reducing C-FDTD’s performance. It is also shown how the performance drops differently according to the frequency of interest. Practical implications With this study, coarse meshes, with smaller execution time and reduced memory usage, can be further explored reliably accounting the desired accuracy, enabling a better trade-off between accuracy and computational effort. Originality/value This paper quantifies the limitations of the C-FDTD in coarse meshes in a wideband manner, which brings a broader and newer insight upon C-FDTD’s limitations in coarse meshes or relatively small objects in electromagnetic simulation.

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13

Архипов, Борис Витальевич, and Дмитрий Алексеевич Шапочкин. "Modelling of salinity penetration into the Ob bay using curved meshes." Вычислительные технологии, no. 4 (October 6, 2022): 4–14. http://dx.doi.org/10.25743/ict.2022.27.4.002.

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Рассмотрена задача проникновения солености в Обскую губу и влияния на него морского канала в Обском баре. Возможно, единственным методом решения такой задачи является математическое моделирование, которое осуществляется на основе трехмерной модели геофизической гидродинамики с учетом турбулентных механизмов вертикального перемешивания. При наличии “малого параметра” в виде канала решение выполнено на криволинейной ортогональной сетке, которая сгущается в области канала. Сравниваются результаты расчетов и наблюдений для экспедиции 1993 г. Дополнительно проведено сравнение результатов расчетов на декартовой сетке с постоянными шагами 3000 и 1500 м и криволинейной сетке с минимальными шагами 200 и 100 м. Показано, что результаты в разных вариантах расчетов близки. The paper considers the problem of salinity penetration into the Ob Bay and the influence of the sea channel in the Ob bar on it. The dimensions of the channel are about 50 km in length, 300-400 m in width and 4-5 m in depth, while the size of the Gulf of Ob is about 800 km in length, about 60 km wide and no more than 30 m deep in the northern part. It follows that the complexity of the problem under consideration lies, on the one hand, in the need to connect two spatial scales: a small one, associated with the size of the channel, and a large one, associated with the size of the estuary, and on the other hand, in the need to consider different time scales. Perhaps the only method of solving such a problem is the method of mathematical modelling, which is carried out on the basis of a three-dimensional model of geophysical hydrodynamics, taking into account the turbulent mechanisms of vertical mixing. To take into account the presence of a “small parameter” in the form of a channel, the solution is carried out on a curved orthogonal grid, which is condensed in the channel region. The degree of grid deformation can be estimated by comparing the minimum cell size in the channel area, which is about 200 m with the maximum cell size of 30 km or more. The paper compares calculations and observations for the 1993 expedition, additionally compares Cartesian grids with constant steps of 3000 m and 1500 m with calculations on a curved grid with a minimum step of 200 m and 100 m, it is shown that the results in different variants are close. Channel accounting is possible only when using a curved and/or nested grid. The comparison carried out on a curved grid with a channel and without a channel showed that the influence of the channel is not significant and cannot cause a significant restructuring of the salinity field.

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14

Gargallo-Peiró, A., G. Houzeaux, and X. Roca. "Subdividing triangular and quadrilateral meshes in parallel to approximate curved geometries." Procedia Engineering 203 (2017): 310–22. http://dx.doi.org/10.1016/j.proeng.2017.09.814.

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15

Flemisch, Bernd, and Barbara I. Wohlmuth. "Stable Lagrange multipliers for quadrilateral meshes of curved interfaces in 3D." Computer Methods in Applied Mechanics and Engineering 196, no. 8 (January 2007): 1589–602. http://dx.doi.org/10.1016/j.cma.2006.03.022.

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16

Okawa, Marina, Takafumi Taketomi, Goshiro Yamamoto, Makoto Fujisawa, Toshiyuki Amano, Jun Miyazaki, and Hirokazu Kato. "A model-based tracking framework for textureless 3D rigid curved objects." Journal on Interactive Systems 3, no. 2 (January 23, 2013): 1. http://dx.doi.org/10.5753/jis.2012.611.

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This paper addresses the problem of tracking texturelessrigid curved objects. A common approach uses polygonalmeshes to represent curved objects inside an edge-based trackingsystem. However, in order to accurately recover their shape,high quality meshes are required, creating a trade-off betweencomputational efficiency and tracking accuracy. To solve thisissue, we suggest the use of quadrics calculated for each patchin the mesh to give local approximations of the object contour.This representation reduces considerably the level of detail of thepolygonal mesh while maintaining tracking accuracy. The noveltyof our research lies in using curves to represent the quadrics’projection in the current viewpoint for distance evaluation insteadof comparing directly the edges from the mesh and detectededges in the video image. In our tracking framework, we alsoinclude a method to calculate the measurable Degrees of Freedom(DoF) of the target object. This is used to recover the poseparameters when the object has less than 6DoF. Experimentalresults compare our approach to the traditional method ofusing sparse and dense meshes. Finally, we present a potentialAugmented Reality application of the proposed method.

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Yue, Jun Hong, Guirong Liu, Ruiping Niu, and Ming Li. "A Four-Noded Triangular (Tr4) Element for Solid Mechanics Problems with Curved Boundaries." International Journal of Computational Methods 17, no. 01 (September 30, 2019): 1844003. http://dx.doi.org/10.1142/s0219876218440036.

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Linear triangular elements with three nodes (Tr3) were the earliest, simplest and most widely used in finite element (FE) developed for solving mechanics and other physics problems. The most important advantages of the Tr3 elements are the simplicity, ease in generation, and excellent adaptation to any complicated geometry with straight boundaries. However, it cannot model well the geometries with curved boundaries, which is known as one of the major drawbacks. In this paper, a four-noded triangular (Tr4) element with one curved edge is first used to model the curved boundaries. Two types of shape functions of Tr4 elements have been presented, which can be applied to finite element method (FEM) models based on the isoparametric formulation. FE meshes can be created with mixed linear Tr3 and the proposed Tr4 (Tr3-4) elements, with Tr3 elements for interior and Tr4 elements for the curved boundaries. Compared to the pure FEM-Tr3, the FEM-Tr3-4 can significantly improve the accuracy of the solutions on the curved boundaries because of accurate approximation of the curved boundaries. Several solid mechanics problems are conducted, which validate the effectiveness of FEM models using mixed Tr3-4 meshes.

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Ruiz-Gironés, Eloi, Josep Sarrate, and Xevi Roca. "Generation of Curved High-order Meshes with Optimal Quality and Geometric Accuracy." Procedia Engineering 163 (2016): 315–27. http://dx.doi.org/10.1016/j.proeng.2016.11.108.

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Xie, Zhong Q., Ruben Sevilla, Oubay Hassan, and Kenneth Morgan. "The generation of arbitrary order curved meshes for 3D finite element analysis." Computational Mechanics 51, no. 3 (June 8, 2012): 361–74. http://dx.doi.org/10.1007/s00466-012-0736-4.

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20

Jaiman, R. K., X. Jiao, P. H. Geubelle, and E. Loth. "Conservative load transfer along curved fluid–solid interface with non-matching meshes." Journal of Computational Physics 218, no. 1 (October 2006): 372–97. http://dx.doi.org/10.1016/j.jcp.2006.02.016.

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21

Galbraith, Marshall C., John A. Benek, Paul D. Orkwis, and Mark G. Turner. "A discontinuous Galerkin scheme for Chimera overset viscous meshes on curved geometries." Computers & Fluids 119 (September 2015): 176–96. http://dx.doi.org/10.1016/j.compfluid.2015.07.002.

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22

Dassi, F., and P. Di Barba. "Enriched Virtual Element space on curved meshes with an application in magnetics." Computers & Mathematics with Applications 161 (May 2024): 43–50. http://dx.doi.org/10.1016/j.camwa.2024.02.036.

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23

Verhoeven, Floor, Amir Vaxman, Tim Hoffmann, and Olga Sorkine-Hornung. "Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces." ACM Transactions on Graphics 41, no. 3 (June 30, 2022): 1–18. http://dx.doi.org/10.1145/3510002.

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We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input that connect the PQ strips. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling-based representations of developable surfaces while still obtaining developable, curvature-aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its isolines are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight isolines is non-linear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle-based interactive freeform modeling of developable shapes.

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Khanteimouri, Payam, and Marcel Campen. "3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing." ACM Transactions on Graphics 42, no. 6 (December 5, 2023): 1–19. http://dx.doi.org/10.1145/3618332.

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We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).

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BREZZI, FRANCO, KONSTANTIN LIPNIKOV, and MIKHAIL SHASHKOV. "CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES." Mathematical Models and Methods in Applied Sciences 16, no. 02 (February 2006): 275–97. http://dx.doi.org/10.1142/s0218202506001157.

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New mimetic finite difference discretizations of diffusion problems on unstructured polyhedral meshes with strongly curved (non-planar) faces are developed. The material properties are described by a full tensor. The optimal convergence estimates, the second order for a scalar variable (pressure) and the first order for a vector variable (velocity), are proved.

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Nahara, Syeda Sabikun, Md Sadekur Rahman, and Md Shajedul Karim. "Auto Mesh generation algorithm for the convex domain with the triangular elements." GANIT: Journal of Bangladesh Mathematical Society 43, no. 1 (August 2, 2023): 017–35. http://dx.doi.org/10.3329/ganit.v43i1.67856.

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Mesh creation is one of the primary tasks in implementing the Finite Element Method (FEM) to solve two- and three-dimensional boundary value problems. However, the whole procedure becomes tedious and problematic when higher-order finite elements are employed to construct mesh and prepare corresponding element data. In this study, we strive to develop a versatile algorithm for discretizing the two-dimensional domain using linear, quadratic, and cubic triangular finite elements. The algorithm is developed based on n vertices (actual or more in number) that constitute the boundary of the domain, along with a computed (n+1)-th point such as the centroid. The algorithm, using this input, generates an initial mesh consisting of n triangular elements. Then, in every subsequent step, the algorithm increases the number of triangles in the mesh fourfold compared to the previous step. The algorithm we present here can employ (a) straight-sided (linear, quadratic, and cubic) triangular elements to generate the mesh for domains with polygonal boundaries and (b) both straight-sided and curved (quadratic and cubic) triangular elements with two straight sides and one curved side to generate meshes for domains with curved boundaries. Thus, the algorithm generates the desired meshes if the vertices are specified once at the initial step. Additionally, the inclusion of the mathematical expression of the curved boundary enables the algorithm to generate the fine mesh for the curved domain utilizing higher-order curved and straight-sided triangular elements. We also present a computer code in MATLAB incorporating the algorithm to create the mesh, prepare the element's data, and determine the element's connectivity. GANIT J. Bangladesh Math. Soc. 43.1 (2023) 017- 035

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Calhoun, Donna A., and Christiane Helzel. "A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes." SIAM Journal on Scientific Computing 31, no. 6 (January 2010): 4066–99. http://dx.doi.org/10.1137/08073322x.

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28

Gargallo-Peiró, A., X. Roca, J. Peraire, and J. Sarrate. "Optimization of a regularized distortion measure to generate curved high-order unstructured tetrahedral meshes." International Journal for Numerical Methods in Engineering 103, no. 5 (February 24, 2015): 342–63. http://dx.doi.org/10.1002/nme.4888.

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29

Aparicio-Estrems, Guillermo, Abel Gargallo-Peiró, and Xevi Roca. "Defining metric-aware size-shape measures to validate and optimize curved high-order meshes." Computer-Aided Design 168 (March 2024): 103667. http://dx.doi.org/10.1016/j.cad.2023.103667.

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30

Conchin Gubernati, Alice Conchin, Fabio Freschi, Luca Giaccone, and Riccardo Scorretti. "Analysis of Numerical Artifacts Using Tetrahedral Meshes in Low Frequency Numerical Dosimetry." Applied Sciences 12, no. 13 (June 27, 2022): 6526. http://dx.doi.org/10.3390/app12136526.

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Anatomical realistic voxel models of human beings are commonly used in numerical dosimetry to evaluate the human exposure to low-frequency electromagnetic fields. The downside of these models is that they do not correctly reproduce the boundaries of curved surfaces. The stair-casing approximation errors introduce computational artifacts in the evaluation of the induced electric field and the use of post-processing filtering methods is essential to mitigate these errors. With a suitable exposure scenario, this paper shows that tetrahedral meshes make it possible to remove stair-casing errors. However, using tetrahedral meshes is not a sufficient condition to completely remove artifacts, because the quality of the tetrahedral mesh plays an important role. The analyses carried out show that in real exposure scenarios, other sources of artifacts cause peak values of the induced electric field even with regular meshes. In these cases, the adoption of filtering techniques cannot be avoided.

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Wang, C. Q., J. H. Yue, and Ming Li. "A Class of Novel Tetrahedron Elements with Curved Surfaces for Three-Dimensional Solid Mechanics Problems with Curved Boundaries." International Journal of Computational Methods 17, no. 04 (November 29, 2019): 1950006. http://dx.doi.org/10.1142/s0219876219500063.

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Linear tetrahedral elements with four nodes (Te4) are currently the simplest and most widely used ones in the finite element (FE) developed for solving three-dimensional (3D) mechanics problems. However, the standard Te4 element cannot be used to simulate accurately the 3D problems with curved boundaries because of the flat surfaces. In this paper, we develop a set of new elements having curved surfaces to properly simulate the curved boundaries. At the same time, additional nodes are put on the curved boundaries to improve the accuracy of the approximation. These novel elements are defined as five-noded, six-noded, and seven-noded tetrahedron elements (Te5, Te6, and Te7) according to the number of the nodes in one element. Based on the Te4 FE mesh, a hybrid mesh can be conveniently built for 3D problems with curved boundaries, in which the standard Te4 elements are used for the interior elements, and Te5, Te6, and Te7 elements are used for the curved boundary elements. Compared with the standard FEM using Te4 elements, our hybrid mesh can significantly improve the accuracy of the solutions at the curved boundaries. Several solid mechanics problems are studied using the hybrid meshes to validate the effectiveness of the present new elements.

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32

Gansen, A., M. El Hachemi, S. Belouettar, O. Hassan, and K. Morgan. "A 3D Unstructured Mesh FDTD Scheme for EM Modelling." Archives of Computational Methods in Engineering 28, no. 1 (January 17, 2020): 181–213. http://dx.doi.org/10.1007/s11831-019-09395-z.

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AbstractThe Yee finite difference time domain (FDTD) algorithm is widely used in computational electromagnetics because of its simplicity, low computational costs and divergence free nature. The standard method uses a pair of staggered orthogonal cartesian meshes. However, accuracy losses result when it is used for modelling electromagnetic interactions with objects of arbitrary shape, because of the staircased representation of curved interfaces. For the solution of such problems, we generalise the approach and adopt an unstructured mesh FDTD method. This co-volume method is based upon the use of a Delaunay primal mesh and its high quality Voronoi dual. Computational efficiency is improved by employing a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of curved interfaces and hexahedral elements elsewhere. Difficulties associated with ensuring the necessary quality of the generated meshes will be discussed. The power of the proposed solution approach is demonstrated by considering a range of scattering and/or transmission problems involving perfect electric conductors and isotropic lossy, anisotropic lossy and isotropic frequency dependent chiral materials.

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Hsu, L. C., J. Z. Ye, and C. H. Hsu. "Simulation of Flow Past a Cylinder With Adaptive Spectral Element Method." Journal of Mechanics 33, no. 2 (September 9, 2016): 235–47. http://dx.doi.org/10.1017/jmech.2016.77.

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AbstractThe simulations of flow past a two-dimensional circular cylinder are conducted to investigate the feasibility of adaptive mesh refinement applied on curved spectral elements. The nonconforming spectral element method and adaptive meshes technique are used to the curve surfaces and observe whether any discontinuity of the solutions. The adaptive nonconforming spectral element method is implemented to compare with those obtained by conforming mesh method with respect to several existing numerical and experimental studies. Meanwhile, three kinds of estimated error base mesh adaptation are conducted to compare their accuracy and efficiency with conforming mesh method. The results show adaptive nonconforming mesh method is more efficient than the conforming method. Especially, the vorticity error based method performs highest accuracy and fastest convergence. The results show this mesh refinement technique is applicable on the curved elements with satisfactory accuracy. It releases this technique may be applied on the simulations of flow past objects with more general geometries.

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Zhong, Saishang, Zhong Xie, Jinqin Liu, and Zheng Liu. "Robust Mesh Denoising via Triple Sparsity." Sensors 19, no. 5 (February 26, 2019): 1001. http://dx.doi.org/10.3390/s19051001.

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Mesh denoising is to recover high quality meshes from noisy inputs scanned from the real world. It is a crucial step in geometry processing, computer vision, computer-aided design, etc. Yet, state-of-the-art denoising methods still fall short of handling meshes containing both sharp features and fine details. Besides, some of the methods usually introduce undesired staircase effects in smoothly curved regions. These issues become more severe when a mesh is corrupted by various kinds of noise, including Gaussian, impulsive, and mixed Gaussian–impulsive noise. In this paper, we present a novel optimization method for robustly denoising the mesh. The proposed method is based on a triple sparsity prior: a double sparse prior on first order and second order variations of the face normal field and a sparse prior on the residual face normal field. Numerically, we develop an efficient algorithm based on variable-splitting and augmented Lagrange method to solve the problem. The proposed method can not only effectively recover various features (including sharp features, fine details, smoothly curved regions, etc), but also be robust against different kinds of noise. We testify effectiveness of the proposed method on synthetic meshes and a broad variety of scanned data produced by the laser scanner, Kinect v1, Kinect v2, and Kinect-fusion. Intensive numerical experiments show that our method outperforms all of the compared select-of-the-art methods qualitatively and quantitatively.

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Branets, Larisa, and Graham F. Carey. "Extension of a Mesh Quality Metric for Elements With a Curved Boundary Edge or Surface." Journal of Computing and Information Science in Engineering 5, no. 4 (June 15, 2004): 302–8. http://dx.doi.org/10.1115/1.2052827.

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The formulation of a local cell quality metric [Branets, L., and Carey, G. F., 2003, Proceedings of the 12th International Meshing Roundtable, Santa Fe, NM, pp. 371–378;Engineering with Computers (in press)] for standard elements defined by affine maps is extended here to the case of elements with quadratically curved boundaries. We show for two-dimensional and three-dimensional simplex elements with quadratically curved boundaries that all cases of map degeneracy can be identified by the metric. Moreover, we establish a “maximum principle” which allows estimating the bounds on the quality metric. The nondegeneracy conditions for biquadratic quadrilaterals with one curved edge are also determined. The metric is implemented in an untangling/smoothing algorithm for improving unstructured meshes including simplex elements that have curved boundary segments. The behavior and efficiency of this algorithm is illustrated for numerical test problems in two and three dimensions.

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Attene, M., B. Falcidieno, J. Rossignac, and M. Spagnuolo. "Sharpen&Bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling." IEEE Transactions on Visualization and Computer Graphics 11, no. 2 (March 2005): 181–92. http://dx.doi.org/10.1109/tvcg.2005.34.

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Leung, Yuen-Shan, Charlie C. L. Wang, and Yunbo Zhang. "Localized construction of curved surfaces from polygon meshes: A simple and practical approach on GPU." Computer-Aided Design 43, no. 6 (June 2011): 573–85. http://dx.doi.org/10.1016/j.cad.2011.01.010.

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Botti, Lorenzo, and Daniele A. Di Pietro. "Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods." Journal of Computational Physics 370 (October 2018): 58–84. http://dx.doi.org/10.1016/j.jcp.2018.05.017.

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Ciallella, Mirco, Elena Gaburro, Marco Lorini, and Mario Ricchiuto. "Shifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes." Applied Mathematics and Computation 441 (March 2023): 127698. http://dx.doi.org/10.1016/j.amc.2022.127698.

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Claisse, A., B. Després, E. Labourasse, and F. Ledoux. "A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes." Journal of Computational Physics 231, no. 11 (June 2012): 4324–54. http://dx.doi.org/10.1016/j.jcp.2012.02.017.

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Favorskaya, A. V., N. I. Khokhlov, V. I. Golubev, and A. V. Shevchenko. "Boundary Conforming Chimera Meshes to Account for Surface Topography and Curved Interfaces in Geological Media." Lobachevskii Journal of Mathematics 45, no. 1 (January 2024): 191–212. http://dx.doi.org/10.1134/s1995080224010141.

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Caubet, Fabien, Joyce Ghantous, and Charles Pierre. "A Priori Error Estimates of a Poisson Equation with Ventcel Boundary Conditions on Curved Meshes." SIAM Journal on Numerical Analysis 62, no. 4 (August 8, 2024): 1929–55. http://dx.doi.org/10.1137/23m1582497.

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You, Hojun, and Chongam Kim. "Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes I. Volume integration." Journal of Computational Physics 395 (October 2019): 223–46. http://dx.doi.org/10.1016/j.jcp.2019.06.015.

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You, Hojun, and Chongam Kim. "Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes II. Surface integration." Journal of Computational Physics 416 (September 2020): 109514. http://dx.doi.org/10.1016/j.jcp.2020.109514.

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Haut, Terry S., Ben S. Southworth, Peter G. Maginot, and Vladimir Z. Tomov. "Diffusion Synthetic Acceleration Preconditioning for Discontinuous Galerkin Discretizations of $S_N$ Transport on High-Order Curved Meshes." SIAM Journal on Scientific Computing 42, no. 5 (January 2020): B1271—B1301. http://dx.doi.org/10.1137/19m124993x.

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Abgrall, R., C. Dobrzynski, and A. Froehly. "A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems." International Journal for Numerical Methods in Fluids 76, no. 4 (July 12, 2014): 246–66. http://dx.doi.org/10.1002/fld.3932.

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Shetty, Ramya Deepak, Indira Narayana Swamy, and Govind R. Kadambi. "Riemann Surface Structure for a Curved Surface with Punctured Features." Nepal Journal of Mathematical Sciences 2, no. 1 (April 30, 2021): 7–16. http://dx.doi.org/10.3126/njmathsci.v2i1.36504.

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In this paper, a generic procedure for the development and subsequent validation of the Riemann surface structure (RSS) for a punctured curved surface lying on a Riemann surface is discussed. The proposed procedure differs from the existing methods involving triangular meshes and rectangular grids that rely on induced patches on surfaces. This procedure can be applied to non-punctured surfaces as well as to surfaces with irregularly located punctures. Further, by defining appropriate transition functions, the proposed procedure eliminates the requirement for smooth transitions across the boundaries of adjacent patches. The analytic formulations of the RSS for an ellipsoid and a sphere are elaborated using the proposed procedure. Moreover, the RSS of a sphere defined through a family of conformal unit discs is proven equivalent to that defined by an existing method based on stereographic projection. This study proves that a smooth projection between the surface and (a subset of) the complex plane , can be remapped to the original surface.

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Vadla, Sai Rajkumar, and Jeffrey Doom. "Analysis of Jet Characteristics Among Various Cold Spray Nozzles." Journal of Thermal Spray and Engineering 1, no. 1 (2018): 24–31. http://dx.doi.org/10.52687/2582-1474/115.

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This research is conducted mainly to analyze the jet characteristics of various cold spray nozzles. This study presents the theoretical and practical aspects of Cold Spray process modeling, discusses multiple numerical analysis research areas, and determines the significant parameters to be considered while developing a custom cold spray setup and exhibits analysis-based correlations. The simulations were performed on some meshes of different density using the SST turbulent model in Star CCM+ solver. For the first time, in this work, the jet characteristics inside a step drilled nozzle was presented; Furthermore, shock diamond formation was found inside the divergent section of step drilled nozzle which strongly influence the flow regime with sharp fluctuations. The comprehensive comparison between step drilled nozzle, conical nozzle and curved nozzle indicates that curved nozzle results in slightly higher nozzle exit velocity. However, results have suggested that the curved nozzle can achieve much higher velocities by optimizing the nozzle length.

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Anand, Nikhil, Neda Ebrahimi Pour, Harald Klimach, and Sabine Roller. "Utilization of the Brinkman Penalization to Represent Geometries in a High-Order Discontinuous Galerkin Scheme on Octree Meshes." Symmetry 11, no. 9 (September 5, 2019): 1126. http://dx.doi.org/10.3390/sym11091126.

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We investigate the suitability of the Brinkman penalization method in the context of a high-order discontinuous Galerkin scheme to represent wall boundaries in compressible flow simulations. To evaluate the accuracy of the wall model in the numerical scheme, we use setups with symmetric reflections at the wall. High-order approximations are attractive as they require few degrees of freedom to represent smooth solutions. Low memory requirements are an essential property on modern computing systems with limited memory bandwidth and capability. The high-order discretization is especially useful to represent long traveling waves, due to their small dissipation and dispersion errors. An application where this is important is the direct simulation of aeroacoustic phenomena arising from the fluid motion around obstacles. A significant problem for high-order methods is the proper definition of wall boundary conditions. The description of surfaces needs to match the discretization scheme. One option to achieve a high-order boundary description is to deform elements at the boundary into curved elements. However, creating such curved elements is delicate and prone to numerical instabilities. Immersed boundaries offer an alternative that does not require a modification of the mesh. The Brinkman penalization is such a scheme that allows us to maintain cubical elements and thereby the utilization of efficient numerical algorithms exploiting symmetry properties of the multi-dimensional basis functions. We explain the Brinkman penalization method and its application in our open-source implementation of the discontinuous Galerkin scheme, Ateles. The core of this presentation is the investigation of various penalization parameters. While we investigate the fundamental properties with one-dimensional setups, a two-dimensional reflection of an acoustic pulse at a cylinder shows how the presented method can accurately represent curved walls and maintains the symmetry of the resulting wave patterns.

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zhou, Longquan, Hongjuan Wang, Xinming Lu, Wei Zhang, and Xingli Zhang. "Algorithm for Curved Surface Mesh Generation Based on Delaunay Refinement." International Journal of Pattern Recognition and Artificial Intelligence 34, no. 04 (July 29, 2019): 2050007. http://dx.doi.org/10.1142/s021800142050007x.

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Curved surface mesh generation is a key step for many areas. Here, a mesh generation algorithm for closed curved surface based on Delaunay refinement is proposed. We focus on improving the shape quality of the meshes generated and making them conform to 2-manifold. The Delaunay tetrahedralization of initial sample is generated first, the initial surface mesh which is a subset of the Delaunay tetrahedralization can be achieved. A triangle is refined by inserting a new point if it is large or of bad quality. For each sample, we also check the triangles that adjoin it whether from a topological disk. If not, the largest triangle will be refined. Finally, the surface mesh is updated after a new point is inserted into the sample. The definition of mesh size function for surface mesh generation is also put in this paper. Meshing experiments of some models demonstrate that the new algorithm is advantageous in generating high quality surface mesh, the count of mesh is suitable and can well approximate the curved surface. The presented method can be used for a wide range of problems including computer graphics, computer vision and finite element method.

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