Distortion and quality measures for validating and generating high-order tetrahedral meshes

Gargallo-Peiró, Abel; Roca, Xevi; Peraire, J.; Sarrate, Josep

doi:10.1007/s00366-014-0370-1

Cited by 46 publications

(26 citation statements)

References 42 publications

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“…To overcome this issue, we propose an untangling and smoothing process based on minimizing a global objective function defined only in terms of the distortion of the volume mesh [23], that takes the coordinates of the high-order nodes as arguments [22,[24][25][26]. The novelty of the approach is that we consider a single target objective function (mesh distortion) where all the nodes, except the nodes located on the geometry vertices, are free to move on the corresponding container CAD entity.…”

Section: Introductionmentioning

confidence: 99%

High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation

Ruiz‐Gironés

Roca

Sarrate

2016

Computer-Aided Design

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We propose a 3D mesh curving method that converts a straight-sided mesh to an optimal-quality curved high-order mesh that interpolates a CAD boundary representation. The main application of this method is the generation of discrete approximations of curved domains that are valid for simulation analysis with unstructured high-order methods. We devise the method as follows. First, the boundary of a straight-sided high-order mesh is curved to match the curves and surfaces of a CAD model. Second, the method minimizes the volume mesh distortion with respect to the coordinates of the inner nodes and the parametric coordinates of the curve and surface nodes. The proposed minimization features untangling capabilities and therefore, it repairs the invalid elements that may arise from the initial curving step. Compared with other mesh curving methods, the only goal of the proposed residual system is to minimize the volume mesh distortion. Furthermore, it is less constrained since the boundary nodes are free to slide on the CAD curves and surfaces. Hence, the proposed method is well suited to generate curved high-order meshes of optimal quality from CAD models that contain thin parts or high-curvature entities. To illustrate these capabilities, we generate several curved high-order meshes from CAD models with the implementation detailed in this work. Specifically, we detail a node-by-node non-linear iterative solver that minimizes the proposed objective function in a block Gauss-Seidel manner.Peer ReviewedPostprint (author's final draft

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Section: Introductionmentioning

confidence: 99%

High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation

Ruiz‐Gironés

Roca

Sarrate

2016

Computer-Aided Design

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“…Recent works have focused on defining a quality measure for curved simplicial finite elements of any order [18,19]. The general approach is to consider the inverse of a Jacobian-based quality measure as proposed in [16], which constitutes a pointwise distortion measure.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of the minimum of shape quality measures on curvilinear finite elements

Johnen¹,

Geuzaine²,

Toulorge³

et al. 2018

Computer-Aided Design

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We present a method for computing robust shape quality measures defined for any order of finite elements. All type of elements are considered, including pyramids. The measures are defined as the minimum of the pointwise quality of curved elements. The computation of the minimum, based on previous work presented by Johnen et al. (2013) [1,2], is very efficient. The key feature is to expand polynomial quantities into Bézier bases which allows to compute sharp bounds on the minimum of the pointwise quality measures.

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“…To facilitate a comparison between material models for producing the higher-order curvilinear meshes, all isotropic materials described in Table 2 can be expressed in terms of the Poisson's ratio ν using (26). For transversely isotropic material, the relationship between material constants and ν is given in Table 2, cf.…”

Section: The Classical Linear Elastic Casementioning

confidence: 99%

“…Methods to produce high-order curvilinear meshes are traditionally classified into direct methods and a posteriori methods [20,21]. Direct methods build the curvilinear highorder mesh directly from the CAD boundary representation of the domain whereas a posteriori approaches rely on mature low-order mesh generation algorithms to produce an initial mesh that is subsequently curved using different techniques, such as local modification of geometric entities [20,21,50,65,66], solid mechanics analogies [58,77] or optimisation [26,71].…”

Section: Introductionmentioning

confidence: 99%

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

2016

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The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh

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Distortion and quality measures for validating and generating high-order tetrahedral meshes

Cited by 46 publications

References 42 publications

High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation

High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation

Efficient computation of the minimum of shape quality measures on curvilinear finite elements

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

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