非结构网格的并行多重网格解算器

多重网格方法作为非结构网格的高效解算器,其串行与并行实现在时空上都具有优良特性.以控制方程离散过程为切入点,说明非结构网格在并行数值模拟的流程,指出多重网格方法主要用于求解时间推进格式产生的大规模代数系统方程,简述了算法实现的基本结构,分析了其高效性原理;其次,综述性地概括了几何多重网格与代数多种网格研究动态,并对其并行化的热点问题进行重点论述.同时,针对非结构网格的实际应用,总结了多重网格解算器采用的光滑算子;随后列举了非结构网格应用的部分开源项目软件,并简要说明了其应用功能;最后,指出并行多重网格解算器在非结构网格应用中的若干关键问题和未来的研究方向.     

基于网格技术的并行搜索引擎

研究现有网格技术和搜索技术,分析并行搜索引擎的优点和不足,提出基于网格技术的并行搜索引擎解决方案,其中包含一个3层结构的应用框架和一个并行搜索引擎的应用方案。根据该方案实现并部署一个基于网格的并行搜索引擎——MSE1．0,获得了较好的检索结果。     

二维弹塑性流体力学LSPIC并行程序研究

针对二维弹塑性流体力学非结构网格拉氏应用程序(LSPIC),应用双线性插值、点排序和网格排序三种方法对计算区域进行分解。基于格式所需邻区网格的个数实现区与区之间的消息传递,建立一种非结构网格拉氏程序并行化方法,实现二维弹塑性流体力学拉氏应用程序(LSPIC)程序的并行化。同时进行程序测试和并行效率分析。     

并行自适应有限元计算中的负载平衡研究

偏微分方程的并行求解,关键问题之一是网格划分,它不仅要求每个进程拥有相等的计算负载,同时要求有良好的划分质量,以减少进程间通信.在自适应有限元计算过程中,网格/基函数不断调整,会导致负载不平衡,必须动态地调整网格分布,从而实现动态负载平衡.本文研究了不同的负载平衡方法,并在并行自适应有限元平台PHG中实现.数值实验表明我们的动态负载平衡算法具有很高的划分质量,运行速度快,可有效划分网格并减少运行时间.     

并行多块结构重叠网格装配算法及应用

针对多块结构重叠网格并行装配的问题,设计了支持初始网格系统细分的多块结构重叠网格框架,并在此框架基础上提出了基于局部洞映射的并行挖洞算法、格心网格下可跨块寻点的并行搜索算法,使之可适应大规模并行数值模拟时的分布式计算环境。此算法被模块化的集成到了自主研发的大规模多块结构网格数值求解器（CCFD-MGMB）中,可支持大规模并行非定常多体分离数值模拟。并行测试结果表明,本文发展的算法具有良好的局部数据结构组织,数据可扩展性强。数值应用模拟结果表明了该算法的有效性及正确性,千核并行非定常数值计算效率（相对于64核）可达58%。     

基于图模型的图像分割并行算法研究与实现

为了提高图模型方法的分割速度,本文提出该方法的一种并行实现方案.该方案通过网格划分来实现相似度矩阵的并行计算.同时考虑到相似度矩阵的稀疏性和矩阵向量乘运算的内在并行性,在该方案中本文设计并行Lanczos算法来求解特征值问题.在MPI环境下的实验结果表明,该并行方案是提高图模型分割方法实时性的有效途径.     

基于非结构网格隐式算法的GPU加速研究

针对非结构网格隐式算法在GPU上的加速效果不佳的问题,通过分析GPU的架构及并行模式,研究并实现了基于非结构网格格点格式的隐式LU-SGS算法的GPU并行加速.通过采用RCM和Metis网格重排序（重组）方法,优化非结构网格的数据局部性,改善非结构网格的隐式算法在GPU上的并行加速效果.通过三维机翼算例验证了本文实现的正确性及效率.结果表明两种网格重排序（重组）方法分别得到了63%和69%的加速效果提高.优化后的LU-SGS隐式GPU并行算法获得了相较于CPU串行算法27倍的加速比,充分说明了本文方法的高效性.     

面向服务的计算网格中间件的实现及性能测试

针对NetSolve系统与Web服务的结合技术,提出面向服务的计算网格中间件的系统结构,在该结构中对计算网格中间件系统的3层功能结构进行体现,采用Java技术实现基于Web服务与原NetSolve系统的数值计算网格中间件WebSolve。应用并行预条件共轭梯度算法在新系统上进行多次大规模方程组求解,测试结果证明该系统接口友好,对粗粒度并行的加速比可达O（n）。     

非结构网格上弹性力学数值模拟的并行实现

弹性力学数值模拟被广泛应用到建筑、机械、化工、材料、航天等工程领域.随着计算规模和精度的不断提高,普通串行程序已经不能满足应用的需求,需要研制并行应用程序.面向非结构网格,提出了一种基于层次化网格数据结构的并行有限元算法,并用来求解弹性力学方程组.最后,用数值结果验证了网格数据结构和并行算法的正确性和扩展性.数值结果显示弹性力学并行程序可成功扩展到4 080进程,网格规模达到15亿单元.     

采用PETSc的有限元并行计算实现与优化

可移植可扩展科学计算工具箱PETSc提供了高性能求解偏微分方程组的大量对象和解法库,基于此进行结构有限元并行计算,可降低难度和成本。给出了基于PETS的结构有限元并行计算实现方法,包括有限元方程组的并行形成和并行求解的实现。根据PETSc的特点,提出了提高计算性能的优化措施,即数据局部化和存储预分配。数值实验表明实现方法可行,优化措施效果明显。     

Parallel hexahedral meshing from volume fractions

In this work, we introduce a new method for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to Eulerian-based codes that generate volume fraction data on a Cartesian grid. A step-by-step procedure for generating an all-hexahedral mesh is presented. We focus specifically on the challenges of developing a parallel implementation using the message passing interface to ensure a continuous, conformal and good quality hex mesh.     

Interactive Mesh Smoothing for Medical Applications

Surface models derived from medical image data often exhibit artefacts, such as noise and staircases, which can be reduced by applying mesh smoothing filters. Usually, an iterative adaption of smoothing parameters to the specific data and continuous re‐evaluation of accuracy and curvature is required. Depending on the number of vertices and the filter algorithm, computation time may vary strongly and interfere with an interactive mesh generation procedure. In this paper, we present an approach to improve the handling of mesh smoothing filters. Based on a GPU mesh smoothing implementation of uniform and anisotropic filters, model quality is evaluated in real‐time and provided to the user to support the mental optimization of input parameters. This is achieved by means of quality graphs and quality bars. Moreover, this framework is used to find appropriate smoothing parameters automatically and to provide data‐specific parameter suggestions. These suggestions are employed to generate a preview gallery with different smoothing suggestions. The preview functionality is additionally used for the inspection of specific artefacts and their possible reduction with different parameter sets.     

Massively parallel adaptive mesh refinement and coarsening for dynamic fracture simulations

We use the graphical processing unit (GPU) to perform dynamic fracture simulation using adaptively refined and coarsened finite elements and the inter-element cohesive zone model. Due to the limited memory available on the GPU, we created a specialized data structure for efficient representation of the evolving mesh given. To achieve maximum efficiency, we perform finite element calculation on a nodal basis (i.e., by launching one thread per node and collecting contributions from neighboring elements) rather than by launching threads per element, which requires expensive graph coloring schemes to avoid concurrency issues. These developments made possible the parallel adaptive mesh refinement and coarsening schemes to systematically change the topology of the mesh. We investigate aspects of the parallel implementation through microbranching examples, which has been explored experimentally and numerically in the literature. First, we use a reduced-scale version of the experimental specimen to demonstrate the impact of variation in floating point operations on the final fracture pattern. Interestingly, the parallel approach adds some randomness into the finite element simulation on the structured mesh in a similar way as would be expected from a random mesh. Next, we take advantage of the speedup of the implementation over a similar serial implementation to simulate a specimen whose size matches that of the actual experiment. At this scale, we are able to make more direct comparisons to the original experiment and find excellent agreement with those results.     

数字流域复杂地形仿真中的网格技术

针对目前数字流域开发中的实际情况，该文介绍了一个依托通用GIS平台的复杂地形仿真系统的可视化核心问题——地形网格化。在研究非结构化网格生成体系的过程中，作者结合研究所正在进行的流域“洪水演进”仿真项目实施了该体系，并初步实现了全流域淹没以及区域洪水演进过程的动态模拟。最后，该文叙述了该技术的设计思想和实现，并给出了可视化结果。     

细分曲面的有序邻接顶点表数据结构*

细分曲面的实现过程中使用的网格数据结构都是基于边的结构,它们只是提供了一种通用的网格遍历方法;而对于细分曲面来说,基于顶点和多边形的网格表示却是更合理有效的选择。给出了一种适用于细分曲面的数据结构OAVL,它具有简便易于实现的特点,可以方便地获取网格中邻接顶点、边和面的信息,并且具有较高的空间效率,最后分析了基于OAVL的细分曲面的存储。     

基于CSR存储的三维网格最短路径算法

论文针对数据组织结构导致Dijkstra算法的存储空间、邻接关系检索效率等关键问题,介绍了相关研究工作。并针对三维网格模型的邻接关系为稀疏图这一要点,基于三维网格模型的CSR存储结构,给出了记录Dijkstra最短路径的算法。该文算法返回了最短路径长度,记录最短路径上点集,充分利用了中间计算结果。     

基于径向基函数与B样条的散乱数据拟合方法

针对散乱数据的曲面拟合问题,提出一种径向基函数与B样条插值结合使用的曲面拟合方法.通过分片径向基函数插值,三维散乱点,再从分片插值曲面上获取预先设定好的有序网格点的值,最后利用张量积B样条插值有序网格点,从而得到拟合曲面.该方法较好地解决散乱数据插值和拟合的计算不稳定性问题,最后给出算法实例.     

Parallel adaptive mesh generation and decomposition

An important class of methodologies for the parallel processing of computational models defined on some discrete geometric data structures (i.e. meshes, grids) is the so calledgeometry decomposition or splitting approach. Compared to the sequential processing of such models, the geometry splitting parallel methodology requires an additional computational phase. It consists of the decomposition of the associated geometric data structure into a number of balancedsubdomains that satisfy a number of conditions that ensure the load balancing and minimum communication requirement of the underlying computations on a parallel hardware platform. It is well known that the implementation of the mesh decomposition phase requires the solution of a computationally intensive problem. For this reason several fast heuristics have been proposed. In this paper we explore a decomposition approach which is part of a parallel adaptive finite element mesh procedure. The proposed integrated approach consists of five steps. It starts with a coarse background mesh that isoptimally decomposed by applying well known heuristics. Then, the initial mesh is refined in each subdomain after linking the new boundaries introduced by its decomposition. Finally, the decomposition of the new refined mesh is improved so that it satisfies the objectives and conditions of the mesh decomposition problem. Extensive experimentation indicates the effectiveness and efficiency of the proposed parallel mesh and decomposition approach.     

Cooperative Caching in Wireless P2P Networks: Design, Implementation, and Evaluation

Some recent studies have shown that cooperative cache can improve the system performance in wireless P2P networks such as ad hoc networks and mesh networks. However, all these studies are at a very high level, leaving many design and implementation issues unanswered. In this paper, we present our design and implementation of cooperative cache in wireless P2P networks, and propose solutions to find the best place to cache the data. We propose a novel asymmetric cooperative cache approach, where the data requests are transmitted to the cache layer on every node, but the data replies are only transmitted to the cache layer at the intermediate nodes that need to cache the data. This solution not only reduces the overhead of copying data between the user space and the kernel space, it also allows data pipelines to reduce the end-to-end delay. We also study the effects of different MAC layers, such as 802.11-based ad hoc networks and multi-interface-multichannel-based mesh networks, on the performance of cooperative cache. Our results show that the asymmetric approach outperforms the symmetric approach in traditional 802.11-based ad hoc networks by removing most of the processing overhead. In mesh networks, the asymmetric approach can significantly reduce the data access delay compared to the symmetric approach due to data pipelines.     

Estimating the Laplace-Beltrami Operator by Restricting 3D Functions

We present a novel approach for computing and solving the Poisson equation over the surface of a mesh. As in previous approaches, we define the Laplace-Beltrami operator by considering the derivatives of functions defined on the mesh. However, in this work, we explore a choice of functions that is decoupled from the tessellation. Specifically, we use basis functions (second-order tensor-product B-splines) defined over 3D space, and then restrict them to the surface. We show that in addition to being invariant to mesh topology, this definition of the Laplace-Beltrami operator allows a natural multiresolution structure on the function space that is independent of the mesh structure, enabling the use of a simple multigrid implementation for solving the Poisson equation.