A Smooth Discretization Bridging Finite Element and Mesh-free Methods Using Polynomial Reproducing Simplex Splines

This work sets forth a `hybrid' discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing scheme constructed over a conventional Finite Element Method (FEM)-like domain discretization based on Delaunay triangulation. Careful construction of the simplex spline knotset ensures the success of the polynomial reproduction procedure at all points in the domain of interest, a significant advancement over its precursor, the DMS-FEM. The shape functions in the proposed method inherit the global continuity (Cp-1) and local supports of the simplex splines of degree p. In the proposed scheme, the triangles comprising the domain discretization also serve as background cells for numerical integration which here are near-aligned to the supports of the shape functions (and their intersections), thus considerably ameliorating an oft-cited source of inaccuracy in the numerical integration of mesh-free (MF) schemes. Numerical experiments show the proposed method requires lower order quadrature rules for accurate evaluation of integrals in the Galerkin weak form. Numerical demonstrations of optimal convergence rates for a few test cases are given and the method is also implemented to compute crack-tip fields in a gradient-enhanced elasticity model.

快速Delaunay逐点插入网格生成算法

对插入形心的Delaunay逐点插入算法,提出按单元可插度分组的双向链表组数据结构,避免了对最大可插度单元的搜索。采用了邻接单元搜索、双向链表存储、随机方向搜索、邻接旋转、几何量继承等技术,使算法的计算时间与生成单元数近似呈线性关系,时间复杂度达到O(N1.05),N为生成单元数。算例表明,在一台AMD Athlon3200+(主频2.0 GHz)PC上,该算法的四面体单元生成速度达50 000个/s以上。

快速Delaunay逐点插入网格生成算法

对插入形心的Delaunay逐点插入算法,提出按单元可插度分组的双向链表组数据结构,避免了对最大可插度单元的搜索。采用了邻接单元搜索、双向链表存储、随机方向搜索、邻接旋转、几何量继承等技术,使算法的计算时间与生成单元数近似呈线性关系,时间复杂度达到O(N1.05),N为生成单元数。算例表明,在一台AMD Athlon3200+(主频2.0GHz)PC上,该算法的四面体单元生成速度达每秒50000个以上。

Análise dos erros na estimação de gradientes em malhas de Voronoi

Este trabalho apresenta um estudo teórico e numérico sobre os erros que ocorrem nos cálculos de gradientes em malhas não estruturadas constituídas pelo diagrama de Voronoi, malhas estas, formadas também pela triangulação de Delaunay. As malhas adotadas, no trabalho, foram as malhas cartesianas e as malhas triangulares, esta última é gerada pela divisão de um quadrado em dois ou quatro triângulos iguais. Para tal análise, adotamos a escolha de três metodologias distintas para o cálculo dos gradientes: método de Green Gauss, método do Mínimo Resíduo Quadrático e método da Média do Gradiente Projetado Corrigido. O texto se baseia em dois enfoques principais: mostrar que as equações de erros dadas pelos gradientes podem ser semelhantes, porém com sinais opostos, para pontos de cálculos em volumes vizinhos e que a ordem do erro das equações analíticas pode ser melhorada em malhas uniformes quando comparada as não uniformes, nos casos unidimensionais, e quando analisada na face de tais volumes vizinhos nos casos bidimensionais.

Uma Metodologia de Estudo de Simulação Tridimensional de Escoamento Turbulento Estratificado no Reservatório de Plantas Hidrelétricas.

Uma simulação numérica que leva em conta os efeitos de estratificação e mistura escalar (como a temperatura, salinidade ou substância solúvel em água) é necessária para estudar e prever os impactos ambientais que um reservatório de usina hidrelétrica pode produzir. Este trabalho sugere uma metodologia para o estudo de escoamentos ambientais, principalmente aqueles em que o conhecimento da interação entre a estratificação e mistura pode dar noções importantes dos fenômenos que ocorrem. Por esta razão, ferramentas de simulação numérica 3D de escoamento ambiental são desenvolvidas. Um gerador de malha de tetraedros do reservatório e o modelo de turbulência algébrico baseado no número de Richardson são as principais ferramentas desenvolvidas. A principal dificuldade na geração de uma malha de tetraedros de um reservatório é a distribuição não uniforme dos pontos relacionada com a relação desproporcional entre as escalas horizontais e verticais do reservatório. Neste tipo de distribuição de pontos, o algoritmo convencional de geração de malha de tetraedros pode tornar-se instável. Por esta razão, um gerador de malha não estruturada de tetraedros é desenvolvido e a metodologia utilizada para obter elementos conformes é descrita. A geração de malha superficial de triângulos utilizando a triangulação Delaunay e a construção do tetraedros a partir da malha triangular são os principais passos para o gerador de malha. A simulação hidrodinâmica com o modelo de turbulência fornece uma ferramenta útil e computacionalmente viável para fins de engenharia. Além disso, o modelo de turbulência baseado no número de Richardson leva em conta os efeitos da interação entre turbulência e estratificação. O modelo algébrico é o mais simples entre os diversos modelos de turbulência. Mas, fornece resultados realistas com o ajuste de uma pequena quantidade de parâmetros. São incorporados os modelos de viscosidade/difusividade turbulenta para escoamento estratificado. Na aproximação das equações médias de Reynolds e transporte de escalar é utilizando o Método dos Elementos Finitos. Os termos convectivos são aproximados utilizando o método semi-Lagrangeano, e a aproximação espacial é baseada no método de Galerkin. Os resultados computacionais são comparados com os resultados disponíveis na literatura. E, finalmente, a simulação de escoamento em um braço de reservatório é apresentada.

叠前地震数据规则化、重建及噪音压制

I address of reconstruction of spatial irregular sampling seismic data to regular grids. Spatial irregular sampling data impairs results of prestack migration, multiple attenuations, spectra estimation. Prestack 5-D volumes are often divided into sub-sections for further processing. Shot gathers are easy to obtain from irregular sampling volumes. My strategy for reconstruction is as follows: I resort irregular sampling gathers into a form of easy to bin and perform bin regularization, then utilize F-K inversion to reconstruct seismic data. In consideration of poor ability of F-K regularization to fill in large gaps, I sort regular sampling gathers to CMP and proposed high-resolution parabolic Radon transform to interpolate data and extrapolate offsets. To strong interfering noise--multiples, I use hybrid-domain high-resolution parabolic Radon transform to attenuate it. F-K regularization demand ultimately for lower computing costs. I proposed several methods to further improve efficiency of F-K inversion: first I introduce 1D and 2D NFFT algorithm for a rapid calculation of DFT operators; then develop fast 1D and 2D CG method to solve least-square equations, and utilize preconditioner to accelerate convergence of CG iterations; what’s more, I use Delaunay triangulation for weight calculation and use bandlimit frequency and varying bandwidth technique for competitive computation. Numerical 2D and 3D examples are offered to verify reasonable results and more efficiency. F-K regularization has poor ability to fill in large gaps, so I rearrange data as CMP gathers and develop hybrid-domain high-resolution parabolic Radon transforms which be used ether to interpolate null traces and extrapolate near and far offsets or suppress a strong interfere noise: multiples. I use it to attenuate multiples to verify performances of our algorithm and proposed routines for industrial application. Numerical examples and field data examples show a nice performance of our method.

地震勘探三维可视化方法研究与实现

This thesis mainly studies the technologies of 3-D seismic visualization and Graphic User Interface of seismic processing software. By studying Computer Graphics and 3-D geological modeling, the author designs and implements the visualization module of seismic data processing software using OpenGL and Motif. Setting seismic visualization flow as the subject, NURBS surface approximation and Delaunay Triangulation as the two different methods, the thesis discusses the key algorithms and technologies of seismic visualization and attempts to apply Octree Space Partitioning and Mip Mapping to enhance system performance. According to the research mentioned above, in view of portability and scalability, the author adopts Object-oriented Analysis and Object-oriented Design, uses standard C++ as programming language, OpenGL as 3-D graphics library and Motif as GUI developing tool to implement the seismic visualization framework on SGI Irix platform. This thesis also studies the solution of fluid equations in porous media. 2-D alternating direction implicit procedure has been turned into 3-D successive over relaxation iteration, which possesses such virtues as faster computing speed, faster convergence rate, better adaptability to heterogeneous media and less memory demanding.

An automated machine vision system for the histological grading of cervical intraepithelial neoplasia (CIN)

The histological grading of cervical intraepithelial neoplasia (CIN) remains subjective, resulting in inter- and intra-observer variation and poor reproducibility in the grading of cervical lesions. This study has attempted to develop an objective grading system using automated machine vision. The architectural features of cervical squamous epithelium are quantitatively analysed using a combination of computerized digital image processing and Delaunay triangulation analysis; 230 images digitally captured from cases previously classified by a gynaecological pathologist included normal cervical squamous epithelium (n = 30), koilocytosis (n = 46), CIN 1 (n = 52), CIN 2 (n = 56), and CIN 3 (n=46). Intra- and inter-observer variation had kappa values of 0.502 and 0.415, respectively. A machine vision system was developed in KS400 macro programming language to segment and mark the centres of all nuclei within the epithelium. By object-oriented analysis of image components, the positional information of nuclei was used to construct a Delaunay triangulation mesh. Each mesh was analysed to compute triangle dimensions including the mean triangle area, the mean triangle edge length, and the number of triangles per unit area, giving an individual quantitative profile of measurements for each case. Discriminant analysis of the geometric data revealed the significant discriminatory variables from which a classification score was derived. The scoring system distinguished between normal and CIN 3 in 98.7% of cases and between koilocytosis and CIN 1 in 76.5% of cases, but only 62.3% of the CIN cases were classified into the correct group, with the CIN 2 group showing the highest rate of misclassification. Graphical plots of triangulation data demonstrated the continuum of morphological change from normal squamous epithelium to the highest grade of CIN, with overlapping of the groups originally defined by the pathologists. This study shows that automated location of nuclei in cervical biopsies using computerized image analysis is possible. Analysis of positional information enables quantitative evaluation of architectural features in CIN using Delaunay triangulation meshes, which is effective in the objective classification of CIN. This demonstrates the future potential of automated machine vision systems in diagnostic histopathology. Copyright (C) 2000 John Wiley and Sons, Ltd.

The Housing Triangulation: A discourse on Quality, Affordability and Lifestyles in India

Since 1991 with the advent of globalization and economic liberalisation, basic conceptual and discursive changes are taking place in housing sector in India. The new changes suggest how housing affordability, quality and lifestyles reality is shifting for various segments of the population. Such shift not only reflects structural patterns but also stimulates an ongoing transition process. The paper highlights a twin impetus that continue to shape the ongoing transition: expanding middle class and their wealth - a category with distinctive lifestyles, desires and habits and corresponding ‘market defining’ of affordable housing standards - to articulate function of housing as a conceptualization of social reality in modern India. The paper highlights the contradictions and paradoxes, and the manner in which the concept of affordability, quality and lifestyles are embedded in both discourse and practice in India. The housing ‘dream’ currently being packaged and fed through to the middle class population has an upper middle class bias and is set to alienate those at the lower end of the middle-and low-income population. In the context of growing agreement and inevitability of market provision of ‘affordable housing’, the unbridled ‘market-defining’ of housing quality and lifestyles must be checked.

A TMA De-Arraying Method for High Throughput Biomarker Discovery in Tissue Research

Background: Tissue MicroArrays (TMAs) represent a potential high-throughput platform for the analysis and discovery of tissue biomarkers. As TMA slides are produced manually and subject to processing and sectioning artefacts, the layout of TMA cores on the final slide and subsequent digital scan (TMA digital slide) is often disturbed making it difficult to associate cores with their original position in the planned TMA map. Additionally, the individual cores can be greatly altered and contain numerous irregularities such as missing cores, grid rotation and stretching. These factors demand the development of a robust method for de-arraying TMAs which identifies each TMA core, and assigns them to their appropriate coordinates on the constructed TMA slide.

Methodology: This study presents a robust TMA de-arraying method consisting of three functional phases: TMA core segmentation, gridding and mapping. The segmentation of TMA cores uses a set of morphological operations to identify each TMA core. Gridding then utilises a Delaunay Triangulation based method to find the row and column indices of each TMA core. Finally, mapping correlates each TMA core from a high resolution TMA whole slide image with its name within a TMAMap.

Conclusion: This study describes a genuine robust TMA de-arraying algorithm for the rapid identification of TMA cores from digital slides. The result of this de-arraying algorithm allows the easy partition of each TMA core for further processing. Based on a test group of 19 TMA slides (3129 cores), 99.84% of cores were segmented successfully, 99.81% of cores were gridded correctly and 99.96% of cores were mapped with their correct names via TMAMaps. The gridding of TMA cores were also extensively tested using a set of 113 pseudo slide (13,536 cores) with a variety of irregular grid layouts including missing cores, rotation and stretching. 100% of the cores were gridded correctly.