We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

We investigate the construction, training and application of a neural net for assessing element shape quality of practical unstructured grids arising in mesh generation, adaptive refinement and moving grid applications. Results of numerical experiments are included to validate the process and demonstrate performance of the neural net for both triangulations in 2D and tetrahedral tessellation in...

Motivated by both theoretical and practical interests, we will consider n-rectangle (n ≥ 2) nonconforming finite elements for n-dimensional fourth order partial equations in this paper. In the two dimensional case, there are well-known nonconforming elements, such as the Morley element, the Zienkiewicz element and the Adini element, etc (see [1-4]). In a recent paper [10], we have discussed the...

Making an initial tetrahedral grid for complex geometry can be a tedious and time consuming task. This paper describes a novel procedure for generation of starting tetrahedral cells using hexahedral block topology. Hexahedral blocks are arranged around an aerodynamic body to form a flow domain. Each of the hexahedral blocks is then decomposed into six tetrahedral elements to obtain an initial t...

The solution chemistry of nine-atomic group 14 Zintl clusters [E9] (E = Si–Pb) shows a fascinating diversity. Mild oxidation or oxidative coupling of these clusters lead to free radicals or dimeric, oligomeric and polymeric structures of the elements [1 – 5]. Further oxidation even results in new element allotropes with tetrahedrally connected tetrel atoms [6], and structures that are exclusive...

Interpolation operators map a function u to an element Iu of a finite element space. Unlike more general approximation operators, interpolants are defined locally. Estimates of the interpolation error, i.e., the difference u− Iu, are of utmost importance in numerical analysis. These estimates depend on the size of the finite elements, the polynomial degree employed, and the regularity of u. In ...

Numerical homogenization is an efficient way to determine effective material properties of composite materials. Conventionally, the finite element technique has been widely used in implementing the homogenization. However, the standard finite element method (FEM) leads to an overly-stiff model which gives poor accuracy especially using triangular elements in 2D or tetrahedral elements in 3D wit...

A uni ed multigrid solution technique is presented for solving the Euler and Reynoldsaveraged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the...

low stacking fault energy face centered cubic (fcc) materials contain characteristic defect structures. stackingfault tetrahedral are one of those rare structures that occur under special experimental conditions. for the first time,stacking fault tetrahedral were observed in fe-30mn-3al-3si twinning induced plasticity (twip) steel. theirpresence resulted from a quenching heat treatment.

Advances in automotive lamp designs have resulted in a more compact, aerodynamic packaging and the use of less expensive plastic materials for the lens and housing. The smaller packaging and lower melting point of plastics have increased the need for a predictive tool for simulating the lamp temperature rise under operating conditions. The modeling of lamps requires sophisticated analysis tools...