Quading triangular meshes with certain topological constraints

In computer graphics and geometric modeling, shapes are often represented by triangular meshes (also called 3D meshes or manifold triangulations). The quadrangulation of a triangular mesh has wide applications. In this paper, we present a novel method of quading a closed orientable triangular mesh into a quasi-regular quadrangulation, i.e., a quadrangulation that only contains vertices of degree four or five. The quasi-regular quadrangulation produced by our method also has the property that the number of quads of the quadrangulation is the smallest among all the quasi-regular quadrangulations. In addition, by constructing the so-called orthogonal system of cycles our method is more effective to control the quality of the quadrangulation.     

Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations

We present a new algorithm for generating layer-adapted meshes for the finite element solution of singularly perturbed problems based on mesh partial differential equations (MPDEs). The ultimate goal is to design meshes that are similar to the well-known Bakhvalov meshes, but can be used in more general settings: specifically two-dimensional problems for which the optimal mesh is not tensor-product in nature. Our focus is on the efficient implementation of these algorithms, and numerical verification of their properties in a variety of settings. The MPDE is a nonlinear problem, and the efficiency with which it can be solved depends adversely on the magnitude of the perturbation parameter and the number of mesh intervals. We resolve this by proposing a scheme based on $h$-refinement. We present fully working FEniCS codes [Alnaes et al., Arch. Numer. Softw., 3 (100) (2015)] that implement these methods, facilitating their extension to other problems and settings.     

Accuracy and convergence of element-by-element iterative solvers for incompressible fluid flows using penalty finite element model

The ability of two types of Conjugate Gradient like iterative solvers (GMRES and ORTHOMIN) to resolve large-scale phenomena as a function of mesh density and convergence tolerance limit is investigated. The flow of an incompressible fluid inside a sudden expansion channel is analysed using three meshes of 400, 1600 and 6400 bilinear elements. The iterative solvers utilize the element-by-element data structure of the finite element technique to store and maintain the data at the element level. Both the mesh density and the penalty parameter are found to influence the choice of the convergence tolerance limit needed to obtain accurate results. An empirical relationship between the element size, the penalty parameter, and the convergence tolerance is presented. This relationship can be used to predict the proper choice of the convergence tolerance for a given penalty parameter and element size.     

Adaptive mesh refinement for the control of cost and quality in finite element analysis

Adaptive strategies are a necessary tool to make finite element analysis applicable to engineering practice. In this paper, attention is restricted to mesh adaptivity. Traditionally, the most common mesh adaptive strategies for linear problems are used to reach a prescribed accuracy. This goal is best met with an h-adaptive scheme in combination with an error estimator. In an industrial context, the aim of the mechanical simulations in engineering design is not only to obtain greatest quality but more often a compromise between the desired quality and the computation cost (CPU time, storage, software, competence, human cost, computer used). In this paper, we propose the use of alternative mesh refinement criteria with an h-adaptive procedure for 3D elastic problems. The alternative mesh refinement criteria (MR) are based on: prescribed number of elements with maximum accuracy, prescribed CPU time with maximum accuracy and prescribed memory size with maximum accuracy. These adaptive strategies are based on a technique of error in constitutive relation (the process could be used with other error estimators) and an efficient adaptive technique which automatically takes into account the steep gradient areas. This work proposes a 3D method of adaptivity with the latest version of the INRIA automatic mesh generator GAMHIC3D.     

Identification and composition of cuticular hydrocarbons of the major Afrotropical malaria vector Anopheles gambiae s.s. (Diptera: Culicidae): analysis of sexual dimorphism and age-related changes

Forty-eight cuticular hydrocarbons (CHCs) were characterized by gas chromatography-mass spectrometry from the epicuticular surface of the major Afrotropical malaria vector Anopheles gambiae. The hydrocarbons identified were 14 n-alkanes, 16 monomethyl alkanes, 13 dimethyl alkanes, 5 alkenes, with main-chain lengths ranging from C(17) to C(47), and the results are consistent with those from other Culicidae species. Qualitative differences were not observed between laboratory pools of three females and males, between different age-groups (0-16 days) and between single field specimens, whereas quantitative differences in CHC profiles were observed. Differences between sexes were more marked in individuals aged 0-2 days than in older ones. Both sexes undergo strong CHC profile changes with age, and individuals aged 0-2 days differ remarkably from the older ones. The possibility of exploiting these changes for estimating the age of mosquito was explored through multivariate analyses of the relative abundance of the compounds, using either the whole CHC profile or a subset of CHCs. Such a method allows us to assign more than 85% of females and 75% of males to the correct age-group. Although preliminary, these results show that the method is promising, as it has already been shown in Aedes aegypti and An. stephensi. The correct determination of the vector age (particularly in the case of the An. gambiae complex of sibling species) provides valuable information in malaria epidemiology and in evaluation of the effectiveness of vector control strategies. Further efforts will be made to validate this method on single specimens reared in seminatural conditions before being proposed to medical entomologists working in the Afrotropical region.     

Associativity of crossed products by partial actions, enveloping actions and partial representations

Given a partial action of a group on an associative algebra , we consider the crossed product . Using the algebras of multipliers, we generalize a result of Exel (1997) on the associativity of obtained in the context of -algebras. In particular, we prove that is associative, provided that is semiprime. We also give a criterion for the existence of a global extension of a given partial action on an algebra, and use crossed products to study relations between partial actions of groups on algebras and partial representations. As an application we endow partial group algebras with a crossed product structure.

     

Three-dimensional susceptibility-weighted imaging at 3 T using various image analysis methods in the estimation of grading intracranial gliomas

Object

Although three-dimensional (3D), high-spatial resolution susceptibility-weighted imaging (SWI) appears to be valuable in the evaluation of central nervous system gliomas, several evaluation methods are proposed in the literature. The purpose of this study was to evaluate the use of 3D SWI for grading intracranial gliomas with various analysis methods.

Materials and Methods

Twenty-three patients suspected of having gliomas participated in this study. SWI was performed in addition to conventional MR sequences. In 15 cases, post-gadolinium enhanced SWI was also obtained. Imaging evaluation criteria were conventional grade, hypointensity ratio in the tumor-dominant structure of hypointensity on SWI (hemorrhage or vascular structure) and presence of abnormal enhancement surrounding the tumor.

Results

Mean grading scores of conventional grade showed no statistically significant difference among WHO grades. Mean grading scores of hypointensity ratios in the tumor were higher for WHO Grades 3 and 4 than for lower grade tumors (P=.05, Mann–Whitney U test). Hemorrhagic foci were more frequently seen in the higher grade tumor. Post-contrast susceptibility-weighted images of five of 11 WHO Grade 3 and 4 cases showed bright enhancement surrounding the tumor, suggesting a breakdown of the blood–brain barrier.

Conclusions

SWI at 3 T may be a useful method to analyze the structural characteristics of gliomas and to evaluate pathology in vivo. Assessment of hypointensity ratios in the glioma was the most preferable method in grading glioma. However, more studies, specifically concerning a suitable method for image analysis, are needed to establish SWI at 3 T as a useful tool in clinical routine.     

基于Markov过程的大学生就业移动预测模型

针对高职毕业生就业实际,分析了就业状态及其转移过程的马尔科夫性,依据转移矩阵建立了就业跟踪模型和时间效益模型,结合历年的就业实际对模型效果进行分析,给出加快就业转移速度的动态策略.     

Error Analysis of Adaptive Finite Difference Methods Using Stretching Functions for Polar Coordinate Form of Poisson-Type Equation

Abstract

This article treats of adaptive finite difference methods for the Dirichlet boundary value problems of Poisson-type equations on a sector or a disk. It is assumed that the exact solutions have singular derivatives on a part or the whole of the boundary. Some stretching functions are used to generate nonuniform grid points. It is then shown that, under some assumptions, the adaptive finite difference solutions are convergent and the convergence can be accelerated by varying parameters in the stretching functions. Numerical examples are given to illustrate how the accuracy of numerical solutions depends on the parameters.     

Superlinear PCG Algorithms: Symmetric Part Preconditioning and Boundary Conditions

The superlinear convergence of the preconditioned CGM is studied for nonsymmetric elliptic problems (convection-diffusion equations) with mixed boundary conditions. A mesh independent rate of superlinear convergence is given when symmetric part preconditioning is applied to the FEM discretizations of the BVP. This is the extension of a similar result of the author for Dirichlet problems. The discussion relies on suitably developed Hilbert space theory for linear operators.