Triangular and quadrilateral surface mesh quality optimization using local parametrization

Garimella, Rao V.; Shashkov, Mikhail; Knupp, Patrick

doi:10.1016/j.cma.2003.08.004

Cited by 87 publications

(45 citation statements)

References 16 publications

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“…Note that the special case with μ A = 0 would reduce to the most isometric parameterization (MIPS) of Hormann and Griener [18] and is closely related to the condition-number-based optimization in [7]. The direct minimization of E I may seem difficult because of the presence of κ 2 (A).…”

Section: Mesh Optimization and Isometric Mappingsmentioning

confidence: 99%

“…An example is the angle-based method of Zhou and Shimada [11]. Another notable example is the method of Garimella et al [7], which minimizes the condition numbers of the Jacobian of the triangles against some reference Jacobian matrices (RJM). More recently, the finite-element-based method is used in [8], but their method is relatively difficult to implement.…”

Section: Introductionmentioning

confidence: 99%

“…Mesh smoothing has a vast amount of literature (for example, see [7,8,9,10,11]). Laplacian smoothing is often used in practice for its simplicity, although it is not very effective for irregular meshes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimizing Surface Triangulation Via Near Isometry with Reference Meshes

Jiao

Bayyana

Zha

2007

Computational Science – ICCS 2007

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Abstract. Optimization of the mesh quality of surface triangulation is critical for advanced numerical simulations and is challenging under the constraints of error minimization and density control. We derive a new method for optimizing surface triangulation by minimizing its discrepancy from a virtual reference mesh. Our method is as easy to implement as Laplacian smoothing, and owing to its variational formulation it delivers results as competitive as the optimization-based methods. In addition, our method minimizes geometric errors when redistributing the vertices using a principle component analysis without requiring a CAD model or an explicit high-order reconstruction of the surface. Experimental results demonstrate the effectiveness of our method.

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Section: Mesh Optimization and Isometric Mappingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimizing Surface Triangulation Via Near Isometry with Reference Meshes

Jiao

Bayyana

Zha

2007

Computational Science – ICCS 2007

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“…However, local formulations tend to be easier to implement and require less computer memory. For linear elements, several local [46,47,48] and global [49,50,51,52,53,54,55] approaches have been proposed to improve the mesh quality. For high-order meshes, similar local [32] and global relocation methods [31,33,34,35] have also been developed.…”

Section: Related Workmentioning

confidence: 99%

Optimization of a regularized distortion measure to generate curved high‐order unstructured tetrahedral meshes

Gargallo-Peiró

Roca

Peraire

et al. 2015

Numerical Meth Engineering

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SUMMARYWe present a robust method for generating high-order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second, displacing the boundary nodes to ensure that they are on the CAD surface, and third, smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high-order mesh. The smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh. This means that whenever possible, the resulting mesh preserves the geometrical features of the initial linear mesh such as shape, stretching and size. We present several examples to illustrate the performance of the proposed algorithm. Furthermore, the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements. The meshes obtained are suitable for high-order finite element analyses.

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“…One approach commonly used to constrain nodes to the underlying smooth surface is to reposition each vertex in a locally derived tangent plane and then to pull the vertex back to the smooth surface [1,5]. Another one is to reposition them in a 2D parameterization of the surface and then to map them back to the physical space [6,7].…”

Section: Introductionmentioning

confidence: 99%

An Improved Laplacian Smoothing Approach for Surface Meshes

Chen

Zheng

Chen

et al. 2007

Computational Science – ICCS 2007

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Abstract. This paper presents an improved Laplacian smoothing approach (ILSA) to optimize surface meshes while maintaining the essential characteristics of the discrete surfaces. The approach first detects feature nodes of a mesh using a simple method, and then moves its adjustable or free node to a new position, which is found by first computing an optimal displacement of the node and then projecting it back to the original discrete surface. The optimal displacement is initially computed by the ILSA, and then adjusted iteratively by solving a constrained optimization problem with a quadratic penalty approach in order to avoid inverted elements. Several examples are presented to illustrate its capability of improving the quality of triangular surface meshes.

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Triangular and quadrilateral surface mesh quality optimization using local parametrization

Cited by 87 publications

References 16 publications

Optimizing Surface Triangulation Via Near Isometry with Reference Meshes

Optimizing Surface Triangulation Via Near Isometry with Reference Meshes

Optimization of a regularized distortion measure to generate curved high‐order unstructured tetrahedral meshes

An Improved Laplacian Smoothing Approach for Surface Meshes

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