Adaptive moving mesh upwind scheme for the two-species chemotaxis model

Chemotaxis systems are used to model the propagation, aggregation and pattern formation of bacteria/cells in response to an external stimulus, usually a chemical one. A common property of all chemotaxis systems is their ability to model a concentration phenomenon—rapid growth of the cell density in small neighborhoods of concentration points/curves. More precisely, the solution may develop singular, spiky structures, or even blow up in finite time. Therefore, the development of accurate and computationally efficient numerical methods for the chemotaxis models is a challenging task.We study the two-species Patlak–Keller–Segel type chemotaxis system, in which the two species do not compete, but have different chemotactic sensitivities, which may lead to a significantly difference in cell density growth rates. This phenomenon was numerically investigated in Kurganov and Luká?ová-Medvi?ová (2014) and Chertock et al. (2018), where second- and higher-order methods on uniform Cartesian grids were developed. However, in order to achieve high resolution of the density spikes developed by the species with a lower chemotactic sensitivity, a very fine mesh had to be utilized and thus the efficiency of the numerical method was affected.In this work, we consider an alternative approach relying on mesh adaptation, which helps to improve the approximation of the singular structures evolved by chemotaxis models. We develop, in particular, an adaptive moving mesh (AMM) finite-volume semi-discrete upwind method for the two-species chemotaxis system. The proposed AMM technique allows one to increase the density of mesh nodes at the blowup regions. This helps to substantially improve the resolution while using a relatively small number of finite-volume cells.     

Optimization models and methods for planning wireless mesh networks

In this paper novel optimization models are proposed for planning Wireless Mesh Networks (WMNs), where the objective is to minimize the network installation cost while providing full coverage to wireless mesh clients. Our mixed integer linear programming models allow to select the number and positions of mesh routers and access points, while accurately taking into account traffic routing, interference, rate adaptation, and channel assignment. We provide the optimal solutions of three problem formulations for a set of realistic-size instances (with up to 60 mesh devices) and discuss the effect of different parameters on the characteristics of the planned networks. Moreover, we propose and evaluate a relaxation-based heuristic for large-sized network instances which jointly solves the topology/coverage planning and channel assignment problems. Finally, the quality of the planned networks is evaluated under different traffic conditions through detailed system level simulations.     

Adaptive finite element methods for the analysis of inviscid compressible flow: Part I. Fast refinement/unrefinement and moving mesh methods for unstructured meshes

New adaptive finite element methods are presented for the analysis of unsteady inviscid compressible flow in arbitrary two-dimensional domains. The procedures described herein are used in conjunction with a semi-explicit two-step algorithm for solving the time-dependent Euler equations in two space dimensions. Two schemes are presented for monitoring the evolution of error, and error estimates are used as a basis for a mesh refinement strategy. The capability of unrefinement (adaptively coarsening the mesh) is also included. The methods do not require a structured mesh and are applicable to quite general geometries.     

Vector-potential finite-element formulations for two-dimensional resistive magnetohydrodynamics

Vector-potential formulations are attractive for electromagnetic problems in two dimensions, since they reduce both the number and complexity of equations, particularly in coupled systems, such as magnetohydrodynamics (MHD). In this paper, we consider the finite-element formulation of a vector-potential model of two-dimensional resistive MHD. Existence and uniqueness are considered separately for the continuum nonlinear equations and the discretized and linearized form that arises from Newton’s method applied to a modified system. Under some conditions, we prove that the solutions of the original and modified weak forms are the same, allowing us to prove convergence of the discretization and well-posedness of the nonlinear iteration near a solution.     

三角网格的自适应细分研究

提出面向三角网格全局细分和局部自适应的细分算法。在原三角网格模型上计算每个面片的中心坐标,据此生成的中心坐标点作为新的顶点坐标进行重新绘制得到三角基网格,然后进行多次迭代,达到基本的全局细分目标。在最后生成的基网格上,可以通过调节最大网格面积和平均网格面积之间的比例系数等,来得到更加均匀的三角网格。实验表明该方法能到得到质量较高的细分结果。     

针对层次式累进网格模型的动态评估与调整

针对层次式累进网格模型提出一种动态评估与动态调整的方法,为交互式变形构建最合理的数据信息。分别从细节层次和规范程度两个角度对网格模型进行评估,其中细节层次不仅包括由模型位置决定的全局细节层次,还包括由视锥原则、曲面法向量、屏幕空间几何误差和变形参与度确定的局部细节层次;规范程度衡量分为流形和定向性确定的拓扑结构规范,以及由几何元素确定的几何属性规范。依据评估结果,动态调整模块使用一系列调整操作,对模型的拓扑结构和几何属性进行修正。实验结果证明该方法能够保证良好的渲染效果,很好地保持合理的模型拓扑结构,而且在保证视觉效果和变形需求的情况下具有实时性与自适应性。     

Adaptive patch-based mesh fitting for reverse engineering

In this paper,  we propose a novel adaptive mesh fitting algorithm that fits a triangular model with G¹ smoothly stitching bi-quintic Bézier patches. Our algorithm first segments the input mesh into a set of quadrilateral patches, whose boundaries form a quadrangle mesh. For each boundary of each quadrilateral patch, we construct a normal curve and a boundary-fitting curve, which fit the normal and position of its boundary vertices respectively. By interpolating the normal and boundary-fitting curves of each quadrilateral patch with a Bézier patch, an initial G¹ smoothly stitching Bézier patches is generated. We perform this patch-based fitting scheme in an adaptive fashion by recursively subdividing the underlying quadrilateral into four sub-patches. The experimental results show that our algorithm achieves precision-ensured Bézier patches with G¹ continuity and meets the requirements of reverse engineering.     

Adaptive mesh subdivision for efficient light baking

Light baking has long been a popular technique for real-time rendering. It usually precomputes and bakes the global lighting effects as vertex attributes or textures. Vertex baking requires less memory but can cause artifacts for large triangles. Texture baking can avoid this and generate a high-quality visual effect in real-time rendering. However, it requires significant memory consumption, which may limit the real-time performance and usage. To address this problem, we propose an adaptive mesh subdivision algorithm for memory-efficient light baking, including a fast triangle subdivision level determination method and an optimized solution to calculate vertex colors. Only the subdivided mesh is required during the real-time rendering. Therefore, memory requirements can be significantly reduced while keeping the visual effect. Besides, the subdivision level is allowed to be intuitively controlled by users with a specified parameter. Our algorithm can be easily implemented on commodity graphics hardware and integrated in existing real-time applications such as online preview systems.     

一种自适应阈值的运动目标提取算法*

为了准确地划分运动目标和背景区域,提出一种自适应阈值的运动目标提取算法,对现有基于背景差的提取算法进行改进。本算法将运动目标和背景作为两个聚类,对图像中的点按像素灰度进行分类,以聚类间的方根—算术均值距离最大作为分割阈值选择的准则,使得运动目标提取算法中二值化阈值能够自动更新,从而实现对运动目标的准确完整提取。实验结果表明,该算法能够较准确快速地提取运动目标,并对环境亮度突变、背景存在微小运动等情况具有较好的鲁棒性。     

针对PRT的大规模场景的自适应网格细分

针对Pre-computed Radiance Transfer(PRT)全局光照算法的特点,提出了一种针对大规模场景的模型细分方法.基于PRT的全局光照算法的渲染结果和模型的精细程度密切相关,对于小规模的场景,可以使用比较精细的模型以得到很好的绘制结果,但对于大规模场景,对整个模型都使用精细的网格是十分浪费资源和不可接受的.通过加入PRT算法中计算的一些权重值,对模型中影响全局光照效果很大的地方进行精细的细分,对全局光照效果影响很小的地方进行较粗的细分或者不细分,从而实现既能提升全局光照效果,又不会过量增加模型规模的自适应网格细分.     

Adaptive mesh refinement for chevron nozzle jet flows

In this paper an adaptive mesh generation procedure is presented for improving the resolution of the numerical simulation of a turbulent jet exhausting from a chevron nozzle. This procedure is based on the minimization of a variational integral whose integrand depends on the metric (also called the monitor function) induced by a curvilinear grid generated in the physical domain. Specifically, it leads to solving parabolic equations involving the monitor function, which is carefully designed to resolve the flow gradients, and which, in the present instance, is determined by the time-averaged axial velocity profile within the jet. This mesh redistribution strategy is incorporated into a flow computation code (that solves the compressible three-dimensional Navier-Stokes equations using a prefactored optimized fourth-order compact difference scheme for spatial derivatives and the Beam-Warming method for the time derivative on a multi-block overset grid) and is demonstrated to be efficient and effective.     

Adaptive hexahedral mesh generation and quality optimization for solid models with thin features using a grid-based method

This paper presented an automatic inside-out grid-based hexahedral element mesh generation algorithm for various types of solid models. For the thin features with small thickness of the geometric model, corresponding treatment methods were given for successfully implementing each meshing step, containing the techniques for adaptive refinement, boundary match, topological optimization and local refinement. In order to realize the reasonable identification of refinement regions and resolve the expansion problem of refinement information fields, a thin-feature criterion and a supplementary criterion were proposed aiming at thin features of the geometry. To implement accurate boundary match for thin features, ten basic types and five complementary types of facet configurations were established, and a priority-node identification method was proposed additionally. Three topological optimization modes were newly proposed to improve the topological connections of the boundary mesh in thin features. Local refinement techniques were also built to refine the thin features of solid models. Finally, several examples were provided to demonstrate the effectiveness and reliability of the proposed algorithms.     

多信道无线网状网自适应路由算法

针对无线网状网的网络容量优化问题,通过建立无线网状网容量优化的数学模型,利用线性规划公式对无线网状网的路由问题进行描述,在此基础上提出了一个自适应路由算法。根据网络的拓扑结构和业务请求特点,自适应地改变路由扩张因子和负载均衡率进行优化路由,达到提高无线网状网的网络容量的目的。仿真结果表明,该算法能明显提高网络容量。     

Feature sensitive deformation for triangular mesh models

Shape deformation is a useful tool for shape modeling and animation in computer graphics. In this paper, we propose a novel surface deformation method based on a feature sensitive (FS) metric. Firstly, taking unit normal vectors into account, we derive a FS Laplacian operator, which is more sensitive to featured regions of mesh models than existing operators. Secondly, we use the 1‐ring tetrahedron in the dual mesh, a volumetric structure, to encode geometric details. To preserve the shape of the tetrahedron, we introduce linear tetrahedron constraints minimizing both the distortion of the base triangle and the change of the corresponding height. These ensure that geometric details are accurately preserved during deformation. The time complexity of our new method is similar to that of existing linear Laplacian methods. Examples are included to show that our FS deformation method better preserves mesh details, especially features, than existing Laplacian methods. Copyright © 2010 John Wiley & Sons, Ltd.     

A framework for unsupervised mesh based segmentation of moving objects

Multimedia analysis usually deals with a large amount of video data with a significant number of moving objects. Often it is necessary to reduce the amount of data and to represent the video in terms of moving objects and events. Event analysis can be built on the detection of moving objects. In order to automatically process a variety of video content in different domain, largely unsupervised moving object segmentation algorithms are needed. We propose a fully unsupervised system for moving object segmentation that does not require any restriction on the video content. Our approach to extract moving objects relies on a mesh-based combination of results from colour segmentation (Mean Shift) and motion segmentation by feature point tracking (KLT tracker). The proposed algorithm has been evaluated using precision and recall measures for comparing moving objects and their colour segmented regions with manually labelled ground truth data. Results show that the algorithm is comparable to other state-of-the-art algorithms. The extracted information is used in a search and retrieval tool. For that purpose a moving object representation in MPEG-7 is implemented. It facilitates high performance indexing and retrieval of moving objects and events in large video databases, such as the search for similar moving objects occurring in a certain period.     

网格分割的3维网格模型非盲水印算法

目的 信息技术的发展使得面向3维模型版权保护的问题越来越突出,提出一种新的基于网格分割的3维网格模型非盲水印算法。方法 首先使用基于形状直径函数的网格分割算法对3维网格模型进行有意义的网格分割,然后计算每个分块的鲁棒重心并以此为中心将模型由直角坐标系转换到球面坐标系,最后通过调制每个顶点范数的分布来嵌入水印,在水印检测阶段使用非盲检测的方法提取水印。结果 针对目前基于网格分块的水印算法的网格分割不一致以及对分割边界依赖性过强等问题,引入基于形状直径函数的网格分割算法并在重对齐、重采样过程中加入待检测模型与原始模型分块匹配过程以保证网格分割的一致性,并且选取分块的顶点范数的分布作为水印嵌入基元,使得算法能够有效地减弱对分割边界的依赖性。结论 实验结果表明,该算法可以有效抵抗平移、旋转、缩放、噪声、细分、简化、剪切等常见的攻击以及多种攻击的联合攻击。     

一种基于偏微分方程的车辆加速度信号自适应降噪方法

提出一种针对MEMS加速度计信号的基于偏微分方程的自适应降噪方法,该方法不仅能有效克服由于传感器本身原因及车载环境振动噪声带来的影响,获得准确的加速度信号,而且实现容易、实时性好.通过对车辆加速度信号进行建模并叠加真实加速度噪声作为仿真信号,将该方法与选用db6小波基、heursure自适应阈值、4层分解的最佳小波进行降噪性能对比,证明在车辆正常行驶的加速度幅值下,该方法不仅能够取得和小波近似的降噪性能,而且很大程度上减少了运算时间.最后通过对实际车载加速度信号的降噪处理和倾角测量中的应用,再次证明该方法在滤除噪声的同时能够较好体现细节信息,很适合应用在对实时性和准确性要求高的实际工程中.