A multi-purpose Schrödinger-Poisson Solver for TCAD applications

We present the Vienna Schrödinger-Poisson Solver (VSP), a multi-purpose quantum mechanical solver for investigations on nano-scaled device structures. VSP includes a quantum mechanical solver for closed as well as open boundary problems on fairly arbitrary one-dimensional cross sections within the effective mass framework. For investigations on novel gate dielectrics VSP holds models for bulk and interface trap charges, and direct and trap assisted tunneling. Hetero-structured semiconductor devices, like resonant tunneling diodes (RTD), can be treated within the closed boundary model for quick estimation of resonant energy levels. The open boundary model allows evaluation of current voltage characteristics.     

k‐version of finite element method in gas dynamics: higher‐order global differentiability numerical solutions

In this paper, we consider and examine alternate finite element computational strategies for time‐dependent Navier–Stokes equations describing high‐speed compressible flows with shocks in a viscous and conducting medium, with the ultimate objective of establishing the desired features of a general mathematical and computational framework for such initial value problems (IVP) in which: (a) the numerically computed solutions are in agreement with the physics of evolution described by the governing differential equations (GDEs) i.e. the IVP, (b) the solutions are admissible in the non‐discretized form of the GDEs in the pointwise sense (i.e. anywhere and everywhere) in the entire space–time domain, and hence in the integrated sense as well, (c) the numerical approximations progressively approach the same global differentiability in space and time as the theoretical solutions, (d) it is possible to time march the solutions (this is essential for efficiency as well as ensuring desired accuracy of the computed solution for the current increment of time, i.e. to minimize the error build up in the time marching process), (e) the computational process is unconditionally stable and non‐degenerate regardless of the choice of discretization, nature of approximations and their global differentiability and the dimensionless parameters influencing the physics of the process, (f) there are no issues of stability, CFL number limitations and (g) the mathematical and computational methodology is independent of the nature of the space–time differential operators. We consider one‐dimensional compressible flow in a viscous and conducting medium with shocks as model problems to illustrate various features of the general mathematical and computational framework used here and to demonstrate that the proposed framework is general and is applicable to all IVP. The Riemann shock tube with a single diaphragm serves as a model problem. The specific details presented in the paper discuss: (1) Choice of the form of the GDEs, i.e. strong form or weak form. (2) Various choices of variables. The paper establishes and considers density, velocity and temperature as variables of choice. (3) Details of the space–time least squares (LS) integral forms (meritorious over all others in all aspects) are presented and choice of approximation spaces are discussed. (4) In all numerical studies we consider a viscous and conducting medium with ideal gas law, however results are also presented for non‐conducting medium. Extension of this work to real gas models will be presented in a separate paper. It is worth noting that when the medium is viscous and conducting, the solutions of gas dynamics equations are analytic. (5) It is also significant to note that upwinding methods based on addition of artificial diffusion such as SUPG, SUPG/DC, SUPG/DC/LS and their many variations are neither needed nor used in this present work. (6) Numerical studies are aimed at resolving the localized details of the shock structure, i.e. shock relations, shock width, shock speed, etc. as well as the over all global behaviour of the solution in the entire space–time domain. (7) Numerical studies are presented for Riemann shock tube for high Mach number flows with special emphasis also on time accuracy of the evolution which is ensured by requiring that the approximations for each increment of time satisfy non‐discretized form of the GDEs in the pointwise sense, and hence in the integrated sense as well. (8) Comparisons are made with published results as well as theoretical solutions (when possible). It is established that space–time least squares processes are the only processes that yield variationally consistent space–time integral forms, and hence unconditionally non‐degenerate space–time computational processes, which when considered in higher‐order scalar product spaces provide the desired mathematical framework in which progressively higher‐order global differentiability solutions in space and time yield the same characteristics as the theoretical solutions of the IVP in all aspects. Copyright © 2006 John Wiley & Sons, Ltd.     

An analysis of dam-break flow on slope

The one-dimensional steep slope shallow water equations are used to model the dam-break flow down a uniform slope with arbitrary inclination, and analytical solutions are derived by the hodograph transformation and the Riemann＇s method in terms of evaluated integrals. An implicit analytical solution is obtained to evaluate the spatio-temporal distributions of dam-break flood hydrographs along the slope. For convenience, the solution for representative wave profiles and velocity distributions is shown in charts. Comparing with the Dressler＇s solution and WES experimental data, the analytical solution is seen reasonable.     

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.     

Numerical computations of resistance of high speed catamaran in calm water

In this paper, the in-house multifunction solver naoe-FOAM-SJTU is applied to study the resistance and wave-making performance of a high-speed catamaran sailing at different velocity in calm water. The volume of fluid（VOF） method is used to capture the free interface and the finite volume method（FVM） is adopted as the discretization scheme. The hull model is fixed with initial trim and sinkage. The numerical results of the presented paper agree very well with the measurement data of model test. Wave making and vortex field are well simulated to analyze the hydrodynamic performance of a catamaran.     

Weak Schur numbers and the search for G.W. Walker’s lost partitions

A set A of integers is weakly sum-free if it contains no three distinct elements x,y,z such that x+y=z. Given k≥1, let WS(k) denote the largest integer n for which {1,…,n} admits a partition into k weakly sum-free subsets. In 1952, G.W. Walker claimed the value WS(5)=196, without proof. Here we show WS(5)≥196, by constructing a partition of {1,…,196} of the required type. It remains as an open problem to prove the equality. With an analogous construction for k=6, we obtain WS(6)≥572. Our approach involves translating the construction problem into a Boolean satisfiability problem, which can then be handled by a SAT solver.     

新疆开都河小山口二级水电站吊车梁设计

水电站厂房的吊车主要用于吊装水轮机与发电机。承受吊车荷载的吊车梁是厂房上部承重的重要结构之一,必须严格按照要求进行设计,以保证吊车梁的质量和使用效果。采用理正结构求解器对新疆开都河小山口二级水电站吊车粱进行了设计和结构计算分析,得出吊车梁的结构与配筋满足设计要求。此吊车梁设计的成功为今后类似工程提供了很好的参考。     

A parallel algorithm solving a tridiagonal Toeplitz linear system

A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver first decomposes an n-dimensional strictly diagonally dominant TTLS equation into a number of m-dimensional subsystems employing a modified Gaussian elimination method. An analytic solution of a continued fraction is obtained to derive the solver. The solver based on the modified Gaussian elimination method fully exploits parallelism. Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).     

矿井通风网络解算软件研究综述

通过对国内外网络通风软件资料研究,围绕网络解算软件的理论基础、功能模块、主要研究方向等进行了综述.阐述了通风网络软件的发展现状及完善过程,总结了网络解算的发展特点,为矿井通风网络解算软件设计人员提供了一定参考.     

基于IDDES方法的模型尺度和实尺度VLCC阻力预报与流场分析

随着CFD技术的发展和计算机运算能力的提高,CFD在船舶设计中发挥着越来越重要的作用。目前CFD对于船舶阻力的计算基本集中在模型尺度,一方面因为实尺度缺乏相关的实验数据,导致缺乏对实尺度高雷诺数下近壁面湍流模型和壁面函数的探索;另一方面也是因为在实尺度计算中,非定常特征更加明显,数值计算的复杂性会大大增加,传统的RANS方法处理起来较为困难。该文应用基于OpenFOAM开发的船舶与海洋工程水动力求解器naoe-FOAMSJTU,应用改进的DES模型—IDDES,采用CFD方法同时对模型尺度和实尺度的32万吨VLCC进行阻力预报,并分别与RANS的计算结果、实验结果/三因次换算结果进行比较分析。在实尺度计算中考虑到表面粗糙度的影响,采用带粗糙度补贴的壁面函数进行近壁面处理。该文探讨了采用IDDES方法在船模和实船阻力预报中的可行性,同时也对实尺度和模型尺度下的流场进行了讨论与对比分析。