ADAPTIVE SOLVER FOR THE p-VERSION OF FINITE ELEMENT METHOD

An adaptive solver for large-scale hierarchic finite element systems has been developed. A decision-making methodology aimed at selecting an optimal solution strategy on the basis of estimated conditioning, sparsity and memory requirements for a given problem has been devised. Numerical experiments have been conducted on selected shell and 3-D problems in the range of 1000–100 000 degrees of freedom. © 1997 by John Wiley & Sons, Ltd.     

A Generalised Conjugate Residual method for the solution of non‐symmetric systems of equations with multiple right‐hand sides

This paper presents an iterative algorithm for solving non‐symmetric systems of equations with multiple right‐hand sides. The algorithm is an extension of the Generalised Conjugate Residual method (GCR) and combines the advantages of a direct solver with those of an iterative solver: it does not have to restart from scratch for every right‐hand side, it tends to require less memory than a direct solver, and it can be implemented efficiently on a parallel computer. We will show that the extended GCR algorithm can be competitive with a direct solver when running on a single processor. We will also show that the algorithm performs well on a Cray T3E parallel computer. Copyright © 1999 John Wiley & Sons, Ltd.     

On the Transient Numerical Simulation of Solid Rocket Motor by Coupling Quasi One-Dimension Internal Flow with Three- Dimension Propellant Grain Burnback

固体火箭发动机内三维药柱燃烧的瞬态拟一维流场仿真

段娟^1,2,熊永亮^1,2,胡宁东^1,2

（1．华中科技大学 力学系,武汉 430074;

2．湖北省工程结构分析与安全评定重点实验室,武汉 430074）

创新点说明：

开发了固体火箭发动机内弹道混合维度求解器——耦合三维水平集法与一维TVD-MacCormack法降阶求解三维固体药柱燃烧退移时的瞬态流场及主要性能参数,该求解器可计算出较高精度的流场参数。

研究目的：

利用拟一维可压缩流场代替三维瞬态流场,并耦合三维水平集法从而降低固体发动机瞬态仿真的计算量,为进一步研究与指导设计提供可行性指导。

研究方法：

文中利用水平集法来捕捉三维药柱的实时界面并以此确定流场计算域,同时利用一维流场代替三维流场可大大节省计算成本,其原理是因为在药柱燃烧过程中径向和周向的流场参数变化对内部流场的影响相对较小。水平集法利用五阶WENO格式的有限差分进行离散,一维流场使用TVD-MacCormack法进行求解。耦合方法中考虑了药柱燃烧速率和喉部烧蚀对流场参数的影响。

结果与结论：

使用三维水平集耦合一维流场法可以准确高效地计算出药柱退移过程中的流场参数。为实际三维发动机整体工作过程仿真提供可行性实施方案。

关键词：瞬态可压缩流场求解器,固体火箭发动机内弹道仿真,水平集法,固体火箭发动机

     

基于可满足性模理论求解器的程序路径验证方法

针对程序中因存在路径条数过多或复杂循环路径而导致路径验证时的路径搜索空间过大,直接影响验证的效率和准确率的问题,提出一种基于可满足性模理论（SMT）求解器的程序路径验证方法。首先利用决策树的方法对复杂循环路径提取不变式,构造无循环控制流图（NLCFG）;然后通过基本路径法对控制流图（CFG）进行遍历,提取基本路径信息;最后利用SMT求解器作为约束求解器,将路径验证问题转化为约束求解问题来进行处理。与同样基于SMT求解器的路径验证工具CBMC和FSoft-SMT相比,该方法在对测试集程序的验证时间上比CBMC降低了25%以上,比FSoft-SMT降低了15%以上;在验证精度上,该方法有明显的提升。实验结果表明,方法可以有效解决路径搜索空间过大的问题,同时提高路径验证的效率和准确率。     

深水钻井隔水管静态有限元求解器设计

借助仿真分析来确定钻井作业的最佳参数,对于降低钻井过程中隔水管系统失效危险性意义重大。在对深水钻井隔水管系统静态有限元求解研究的基础上,采用Matlab程序设计深水钻井隔水管静态有限元分析求解器,以1 500 m水深某井为例进行实例分析,并对分析结果进行了验证。设计时隔水管单根采用二维梁单元进行模拟,所支持的单元类型包括所有关键的隔水管部件,隔水管张力以恒定载荷的形式施加在隔水管系统顶部。研究结果表明,软件的计算结果与ABAQUS的计算结果吻合,二者形状规律一致,在数值上也很接近。     

An overlapping Yee finite‐difference time‐domain method for material interfaces between anisotropic dielectrics and general dispersive or perfect electric conductor media

A novel stable anisotropic finite‐difference time‐domain (FDTD) algorithm based on the overlapping cells is developed for solving Maxwell's equations of electrodynamics in anisotropic media with interfaces between different types of materials, such as the interface between anisotropic dielectrics and dispersive medium or perfect electric conductor (PEC). The previous proposed conventional anisotropic FDTD methods suffer from the late‐time instability due to the extrapolation of the field components near the material interface. The proposed anisotropic overlapping Yee FDTD method is stable, as it relies on the overlapping cells to provide the collocated field values without any interpolation or extrapolation. Our method has been applied to simulate electromagnetic invisibility cloaking devices with both anisotropic dielectrics and PEC included in the computational domain. Numerical results and eigenvalue analysis confirm that the conventional anisotropic FDTD method is weakly unstable, whereas our method is stable. Copyright © 2013 John Wiley & Sons, Ltd.     

Full‐wave optoelectrical modeling of optimized flattened light‐scattering substrate for high efficiency thin‐film silicon solar cells

The flattened light‐scattering substrate (FLiSS) is formed by a combination of two materials with a high refractive index mismatch, and it has a flat surface. A specific realization of this concept is a flattened two‐dimensional grating. When applied as a substrate for thin‐film silicon solar cells in the nip configuration, it is capable to reflect light with a high fraction of diffused component. Furthermore, the FLiSS is an ideal substrate for growing high‐quality microcrystalline silicon (µc‐Si:H), used as bottom cell absorber layer in most of multijunction solar cell architectures. FLiSS is a three‐dimensional structure; therefore, a full‐wave analysis of the electromagnetic field is necessary for its optimal implementation. Using finite element method, different shapes, materials, and geometrical parameters were investigated to obtain an optimized FLiSS. The application of the optimized FLiSS in µc‐Si:H single junction nip cell (1‐µm‐thick i‐layer) resulted in a 27.4‐mA/cm² implied photocurrent density. The absorptance of µc‐Si:H absorber exceeded the theoretical Yablonovitch limit for wavelengths larger than 750 nm. Double and triple junction nip solar cells on optimal FLiSS and with thin absorber layers were simulated. Results were in line with state‐of‐the‐art optical performance typical of solar cells with rough interfaces. After the optical optimization, a study of electrical performance was carried out by simulating current–voltage characteristics of nip solar cells on optimized FLiSS. Potential conversion efficiencies of 11.6%, 14.2%, and 16.0% for single, double, and triple junction solar cells with flat interfaces, respectively, were achieved. Copyright © 2012 John Wiley & Sons, Ltd.     

Local discretization error bounds using interval boundary element method

In this paper, a method to account for the point‐wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd.     

基于振速测量单全息面直接声场分离方法

摘 要：为了更精确的分离质点振速,以波叠加法作为声场分离算法基础,提出单全息面测量振速直接声场分离方法。建立了单面振速测量声场分离模型,并推导了理论计算方法,通过数值仿真,分析算法的计算精度,验证了该方法可以有效分离声场。然后对比本文分离方法和单面声压测量声场分离方法分离简单源和脉动声源的误差,结果表明：单面振速测量的直接声场分离方法可以有效分离目标声源,而且可以获得更高的振速分离精度。     

格点QCD基础求解器及其异构计算实现的性能优化

格点量子色动力学(格点QCD)是研究夸克、胶子等微观粒子间相互作用的重要理论和方法.通过将时空离散化为四维结构网格,并将量子色动力学的基本场量定义在网格上,让研究人员可以使用数值模拟方法,从第一性原理出发研究强子间相互作用和性质,但这个过程中的计算量极大,需要进行大规模并行计算.格点QCD计算的核心基础为格点QCD求解器,是程序运行主要的计算热点模块.本文研究在国产异构计算平台下格点QCD求解器的实现与优化,提出一套格点QCD求解器的设计实现,实现了BiCGSTAB求解器,显著降低了迭代次数;通过对奇偶预处理技术,降低了所求问题的计算规模;针对国产异构加速卡的特点,优化了Dslash模块的访存操作.实验测试表明,相比优化前的求解器获得了约30倍的加速比,为国产异构超算下格点QCD软件性能优化提供了有益的参考价值.