A Fast Domain Decomposition High Order Poisson Solver

We present a fast high-order Poisson solver for implementation on parallel computers. The method uses deferred correction, such that high-order accuracy is obtained by solving a sequence of systems with a narrow stencil on the left-hand side. These systems are solved by a domain decomposition method. The method is direct in the sense that for any given order of accuracy, the number of arithmetic operations is fixed. Numerical experiments show that these high-order solvers easily outperform standard second-order ones. The very fast algorithm in combination with the coarser grid allowed for by the high-order method, also makes it quite possible to compete with adaptive methods and irregular grids for problems with solutions containing widely different scales.     

超声速和高超声速燃烧的数值研究

为了研究HLLC黎曼求解器在超声速和高超声速燃烧问题中的适用性,对4个典型算例进行了数值模拟。基于多组分方程的完全N-S方程,对时间项和空间项离散分别采用2阶Runge-kutta方法和HLLC格式,考虑了H_2/Air燃烧的详细化学反应机理,用有限速率化学反应模型模拟燃烧现象。对Sod激波管问题和高超声速钝体绕流进行数值模拟,分析了流场内密度、压力和激波位置;对超声速燃烧和高超声速钝体激波诱导燃烧进行数值模拟,分析了流场内组分特性。数值模拟结果与实验结果或相关文献的计算结果吻合良好,表明了HLLC黎曼求解器在模拟复杂化学非平衡流场中能够准确地分析复杂的物理现象且具有较广的应用范围。     

陶瓷坯釉料配方设计及其优化方法研究

针对陶瓷坯釉料配方设计问题,提出以每吨釉料成本最低作为目标函数并建立相应的数学模型,然后将Excel 2003的“规划求解”功能应用于陶瓷坯釉料配方优化设计中,实现了多种因素影响条件下成本最低的陶瓷坯釉料配方设计方案,得到了满意的优化结果。该设计方法使用方便,操作简单,大大提高了工作效率,具有一定的实用和推广价值。     

A Study of 3D Aerodynamic Design for a Transonic Compressor Blading Optimized by the Locations of Aerofoil Maximum Thickness and Maximum Camber

A design procedure for improving the efficiency of a transonic compressor blading was proposed based on a rapid generation method for three-dimensional blade configuration and computational meshes, a three-dimensional Navier-Stokes solver and an optimization approach. The objective of the present paper is to design a transonic compressor blading optimized only by selection of the locations of maximum camber and maximum thickness for the airfoils at different span heights and to study how do these two design parameters affect the blade performance. The blading configuration and the computational meshes can be obtained very rapidly for any given combination of maximum camber and maximum thickness. The computational grid system generated is used for the Navier-Stokes solution to predict adiabatic efficiency, total pressure ratio and flow rate. As a main result of the optimization, adiabatic efficiency was successfully improved.     

弹性损伤理论的几何-拓扑描述

材料内部微观几何缺陷通常是作为物理非线性问题在本构方程中考虑。针对连续介质弹性损伤理论作几何拓扑,采用非完整标架方法把材料内部微观几何缺陷转化为材料空间的弯曲,并体现在基本几何法则中。首先由连续损伤变量定义拟塑性张量,给出这些基本张量所满足的连续性方程和基本几何法则。由此建立了弹性损伤缺陷与Riemann流形的对应关系,将物理非线性问题转化为物理线性和材料所在空间的弯曲之和。最后讨论了二维情况下,各向同性晶格材料受各向异性损伤的算例。     

Graph grammar‐driven parallel partial differential equation solver

The paper presents an extension of the composite programmable graph grammar (CP‐graph grammar) suitable for modeling the parallel direct solver algorithm utilized by the hp finite element method (hp‐FEM). In the proposed graph grammar model, the computational mesh is represented by a CP‐graph. The presented graph grammar models the solver algorithm by a set of graph grammar productions. The graph grammar model makes it possible to examine the concurrency of the algorithm by analyzing the interdependence between the atomic tasks, tasks and super‐tasks. The atomic tasks correspond to the graph grammar productions, representing basic undividable parts of the algorithms. The level of atomic tasks models the concurrency for the shared memory architectures. On the other hand, the tasks correspond to the groups of atomic tasks with predefined inter‐task communication channels. They constitute the grain for the decomposition of the parallel algorithm for the distributed memory architecture. Finally, the super‐tasks correspond to a group of tasks resulting from the execution of load balancing algorithm. The solver algorithm is tested on distributed memory linux cluster for up to 192 processors. Copyright © 2009 John Wiley & Sons, Ltd.     

KLU稀疏直接求解器在状态估计中的应用

稀疏矩阵及稀疏线性方程组求解已成为大规模电网状态估计计算效率的瓶颈,阐释了基于BTF和Gilbert-Peierls算法的稀疏矩阵直接求解器KLU（Clark Kent LU）,并将其嵌入到智能调度技术支持系统中生产运行的状态估计程序功能。首先在计算得到雅可比矩阵的基础上基于OpenMP并行化技术快速求解信息矩阵;然后使用KLU求解器进行信息矩阵的因子表符号分析和数值分解;最后在状态估计计算过程中使用KLU求解器求解线性方程组,从而提高大规模电网状态估计的计算效率。通过省中心、分中心、模型数据中心D5000的状态估计实际应用,证明了该方法的有效性和实用性。     

基于黎曼积分的连续最优潮流模型

在实际电力系统中,负荷在多种因素的综合影响下时刻变化着,一般将其看成是一个连续变化的函数,且目前智能电网的发展使连续时间的数据获取和发电机控制成为可能,所以对连续时间的负荷调度迫在眉睫。但是原先的静态、动态最优潮流仅能考虑离散函数的优化,其经济性和安全性受到了一定的局限。文中应用黎曼积分的思想对最优潮流进行拓展,考虑变量在时间上的连续性,从而建立基于黎曼积分的连续最优潮流模型。基于此理论对IEEE 5节点系统进行仿真,验证了此模型的准确性和实用性。最终结果表明了该模型能够解得一段连续时间内满足所有约束的连续调度时间方案,且发电机出力能很好地跟随负荷波动。     

利用规划求解工具验证在线冶金数模系统

针对在线冶金数模系统结构的整体性和复杂性,利用规划求解设计一套简化的数学运算工具验证在线系统,经与原始模型反复测试,运算结果与在线系统严格吻合,具有结构灵活简单、易于调整,便于验证等特点,对于闪速炉冶金控制模型原理的深入研究有着深远的意义.     

A new hybrid solver with two‐level parallel computing for large‐scale structural analysis

With the advancement of new processor and memory architectures, supercomputers of multicore and multinode architectures have become general tools for large‐scale engineering and scientific simulations. However, the nonuniform latencies between intranode and internode communications on these machines introduce new challenges that need to be addressed in order to achieve optimal performance. In this paper, a novel hybrid solver that is especially designed for supercomputers of multicore and multinode architectures is proposed. The new hybrid solver is characterized by its two‐level parallel computing approach on the basis of the strategies of two‐level partitioning and two‐level condensation. It distinguishes intranode and internode communications to minimize the communication overheads. Moreover, it further reduces the size of interface equation system to improve its convergence rate. Three numerical experiments of structural linear static analysis were conducted on DAWNING‐5000A supercomputer to demonstrate the validity and efficiency of the proposed method. Test results show that the proposed approach was superior in performance compared with the conventional Schur complement method. Copyright © 2014 John Wiley & Sons, Ltd.