A parallel and scalable algorithm for ADI method with pre-propagation and message vectorization

It is hard to implement the ADI method in an efficient way on distributed-memory parallel computers. We propose “P-scheme” which parallelizes a tridiagonal linear system of equations for the ADI method, but its effectiveness is limited to the cases where the problem size is large enough mainly because of the communication cost of the propagation phase of the scheme.

In order to overcome this difficulty, we propose an improved version of the P-scheme with “message vectorization” which aggregates several communication messages into one and alleviates the communication cost. Also we evaluate the effectiveness of message vectorization for the ADI method and show that the improved version of the P-scheme works well even for smaller problems and linear and super-linear speedups can be achieved for 8194 × 8194 and 16,386 × 16,386 problems, respectively.     

An implicit enthalpy scheme for one-phase Stefan problems

A compact finite-difference scheme to solve one-phase Stefan problems in one dimension is described. Numerical experiments indicate that the moving interface is obtained withO(t) accuracy when 3–4 iterations per time step are used to solve the nonlinear implicit scheme. The scheme can be adapted to ADI methods in higher dimensions.     

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet’s boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.     

Effect of austenitization on austempering of copper alloyed ductile iron

A ductile iron containing 0.6% copper as the main alloying element was austempered at a fixed austempering temperature of 330 °C for a fixed austempering time of 60 min after austenitization at 850 °C for different austenitization periods of 60, 90, and 120 min. The austempering process was repeated after changing austenitization temperature to 900 °C. The effect of austenitization temperature and time was studied on the carbon content and its distribution in the austenite after austenitization. The effect of austenitization parameters was also studied on austempered microstructure, structural parameters like volume fraction of austenite, X _γ , carbon content C _γ , and X _γ C _γ , and bainitic ferrite needle size, d _α after austempering. The average carbon content of austenite increases linearly with austenitization time and reaches a saturation level. Higher austenitization temperature results in higher carbon content of austenite. As regards the austempered structure, the lowering austenitization temperature causes significant refinement and more uniform distribution of austempered structure, and a decrease in the volume fraction of retained austenite.     

锰对奥贝球铁组织和性能的影响

奥贝球铁在实现高硬度的同时具有较高的韧性，适合制造在一定冲击条件下的耐磨零件。通过对高硅条件下锰对奥贝球铁组织和性能的影响的研究，为该材料的应用提供了基础。     

等温淬火奥—贝球铁抗磨性能的研究

对用３００℃和３６０℃等温淬火的奥－贝球铁的机械性能和抗磨性能进行了测试，结果表明：等温淬火奥－贝球铁是一种具有良好综合力学性能和抗磨性能的抗磨材料。     

等温淬火球铁(ADI)引锭杆的研制

介绍ADI引锭杆铸造生产工艺特点及其铸态组织要求,分析主要合金元素的作用,运用正交试验法对等温淬火球铁（ADI）引锭杆的热处理工艺进行了优化试验,并对该引锭杆的淬透性进行了检测。试验结果表明,最大壁厚为140mm的ADI引锭杆需要进行必要的合金化,合金元素的加入量为：0.2%～0.3%Mo、0.4%～0.5%Ni、0.5%～0.8%Cu;ADI引锭杆的优化热处理工艺为：在900℃奥氏体化保温90min,再进行360℃等温淬火,等温“时间窗口”为90～120min;在该成分与热处理工艺条件下,引锭杆可以淬透,能够获得以针状铁素体＋残余奥氏体为基体的组织,其力学性能达到QT900-8。     

含硅量及等温时间对奥贝球墨铸铁机械性能的影响

探讨了含硅量及等温时间对奥贝球铁冰冷处理前后机械性能及低温冲击韧性的影响。试验表明,随着含硅量的增加,不但冷处理前常温机械性能提高,而且冰冷处理后的机械性能及低温冲击韧性也提高。而含硅3.39％和3.68％的机械性能已趋一致,等温时间为120分钟的试样,冰冷处理前后的机械性能和低温冲击韧性均最高。     

预条件的平方Smith法求解大型Sylvester矩阵方程

提出了一种预条件的平方Smith算法求解大型连续Sylvester矩阵方程,该算法利用交替方向隐式迭代(ADI)来构造预条件算子,将原方程转换为非对称Stein方程,并在Krylov子空间中应用平方Smith法迭代产生低秩逼近解。数值实验表明,与已知的Jacobi迭代法等算法相比,该算法有更好的迭代效率和收敛精度。     

Reflections on the evolution of implicit Navier–Stokes algorithms

This article gives a historical perspective on the evolution of implicit algorithms for the Navier–Stokes equations that utilize time or Newton linearizations and various forms of approximate factorization including alternating-direction, lower/upper, and symmetric relaxation schemes. A theme of the paper is how progress in implicit Navier–Stokes algorithms has been influenced and enabled by the introduction of characteristic-based upwind approximations, unstructured-grid discretizations, parallelization, and by advances in computer performance and architecture. Historical examples of runtime, problem size, and estimated cost are given for actual and hypothetical Navier–Stokes flow cases from the past 40 years.