A Survey of Indicators for Mesh Quality Assessment

Abstract

We analyze the joint efforts made by the geometry processing and the numerical analysis communities in the last decades to define and measure the concept of “mesh quality”. Researchers have been striving to determine how, and how much, the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depends on the particular mesh adopted to model the problem, and which geometrical features of the mesh most influence the result. The goal was to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. We overview the most common quality indicators, measures, or metrics that are currently used to evaluate the goodness of a discretization and drive mesh generation or mesh coarsening/refinement processes. We analyze a number of local and global indicators, defined over two‐ and three‐dimensional meshes with any type of elements, distinguishing between simplicial, quadrangular/hexahedral, and generic polytopal elements. We also discuss mesh optimization algorithms based on the above indicators and report common libraries for mesh analysis and quality‐driven mesh optimization.

Finite Element modeling and convergence analysis of a new Biomimetic Branching Structure.

“…They focused on the importance of displacement convergence and utilized 6 beam elements in their analysis. Compared to the present results, it is noticeable that the optimal number of bars in this model is low compared to literature, since the convergence can be quickly reached when using stain energy as a convergence criterion [21,25,26]. Stiffness convergence 14 per strut Guo et al [23] BBC lattice (d = 0.5) Experimental testing 10 per strut Guo et al [23] BBC lattice (d = 0.75) Experimental testing 20 per strut Uddin et al [24] Two-layered composite beam Displacement conver-gence 6 beam elements This work MAD quarter Strain energy convergence 3 to 6 RSA frame per legs…”

“…In finite elements analysis (FEA), number of output values such as strain energy, reaction force, and stress, could be employed as a convergence criterion. However, previous research, especially in micro-architected structures field showed that obtaining a convergent result was simple when using the strain energy or the reaction force, but utilizing stress as the criterion made obtaining a convergent solution challenging [21,25,26]. As a result, anytime stress is utilized as a convergence condition, the findings of finite element analyses should be carefully examined.…”

“…For regular lattices, these strategies are effective. However, when dealing with a geometrically non-linear structure, it is more appropriate to utilize potential strain energy as a convergence criterion [21,25,26].…”

Fast and robust parallel simplification algorithm for triangular mesh

“…In this paper, we convert 32-bit floating-point numbers to 64-bit for calculating triangular normal vectors to avoid floating-point calculation errors as much as possible. For the detection of sharp triangles, we use its ratio [10] value to measure. When the ratio of a triangle is greater than 100, we consider it to be a sharp triangle that does not participate in the normal discrimination calculation.…”

Computational Modelling and Simulation of Scaffolds for Bone Tissue Engineering

“…In FEM, the scaffold geometry is partitioned into a finite number of elements using the process of meshing. Generally, increasing the number of finite elements improves the accuracy and fidelity of simulation results but also leads to an increase in computation time [79]. An FE model combines FE meshes and material properties such as Poisson's ratio and Young's modulus.…”