直接数值模拟／大涡模拟中数值误差影响的研究

通过比较湍流的能谱和总动能,对数值误差(包括混淆误差、离散截断误差)、亚格子模型以及它们之间相互作用对直接数值模拟和大涡模拟的影响进行了系统研究.算例采用了三维各向均匀同性湍流.为了研究复杂几何形状,数值格式采用了谱方法和Pade紧致格式.大涡模型采用了truncated Navior-Stokes(TNS)模型结合Pade离散滤波器.结果表明直接数值模拟中离散误差对结果有很大影响,低阶格式会导致计算发散.而大涡模拟中亚格子模型不仅能表征小尺度对大尺度的影响,而且还缓解了数值误差对计算结果的影响.因而低精度格式也可取得不错的结果.     

High speed computation of group characters

This paper describes a practical procedure for computing the ordinary irreducible characters of finite groups (of orders up to 1000 or so). The novelty of the method consists of transposing the problem from the field of complex numbers into the field of integers modulop for a suitable primep. It is much easier to compute the modular characters in the latter field, and from these characters we can calculate the ordinary irreducible characters in algebraic form.     

DNS Curves in a Production/Inventory Model

In this paper, we investigate the bifurcation behavior of an inventory/production model close to a Hamilton-Hopf bifurcation. We show numerically that two different types of DNS curves occur: If the initial states are far from the bifurcating limit cycle, the limit cycle can be approached along different trajectories with the same cost. For a subcritical bifurcation scenario, the hyperbolic equilibrium state and the hyperbolic limit cycle coexist for some parameter range. When both the long term states yield approximately the same cost, a second DNS curve separates their domains of attraction. At the intersection of these two DNS curves, a threefold Skiba point in the state space is found. The acronym DNS stands for Dechert, Nishimura, and Skiba (Ref. 1)     

Convex hull-based multi-objective evolutionary computation for maximizing receiver operating characteristics performance

The receiver operating characteristics (ROC) analysis has gained increasing popularity for analyzing the performance of classifiers. In particular, maximizing the convex hull of a set of classifiers in the ROC space, namely ROCCH maximization, is becoming an increasingly important problem. In this work, a new convex hull-based evolutionary multi-objective algorithm named ETriCM is proposed for evolving neural networks with respect to ROCCH maximization. Specially, convex hull-based sorting with convex hull of individual minima (CH-CHIM-sorting) and extreme area extraction selection (EAE-selection) are proposed as a novel selection operator. Empirical studies on 7 high-dimensional and imbalanced datasets show that ETriCM outperforms various state-of-the-art algorithms including convex hull-based evolutionary multi-objective algorithm (CH-EMOA) and non-dominated sorting genetic algorithm II (NSGA-II).     

A subspace preconditioning algorithm for eigenvector/eigenvalue computation

We consider the problem of computing a modest number of the smallest eigenvalues along with orthogonal bases for the corresponding eigenspaces of a symmetric positive definite operatorA defined on a finite dimensional real Hilbert spaceV. In our applications, the dimension ofV is large and the cost of invertingA is prohibitive. In this paper, we shall develop an effective parallelizable technique for computing these eigenvalues and eigenvectors utilizing subspace iteration and preconditioning forA. Estimates will be provided which show that the preconditioned method converges linearly when used with a uniform preconditioner under the assumption that the approximating subspace is close enough to the span of desired eigenvectors.     

Remarks on coupled multi-scale simulations and high performance computation

To describe material behaviour more precisely than nowadays, tomorrows simulation software will include multi-scale homogenisation techniques. State of the art are various scale bridging strategies, like FE-ODE, FE-Phasefield or FE²-Method. We are dealing with the FE²-Method, see [3], [4], which gives us the possibility to take the geometric, discrete micro-structure of a material into account. Furthermore, it allows to integrate enhanced continuum mechanical models. Here, we are researching on two-scale approach with poro-mechanical coupling based on the Theory of Porous Media (TPM), for more details see [1] or [2]. The framework is demanding and need a lot of computational effort. In order to receive industrial recognition, it is necessary to decrease the computation runtime. One way to go is definitely using high performance cluster. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discretization effects on approximate deconvolution modeling for LES

We study the applicability of low‐order schemes with the approximate deconvolution model (ADM) for large‐eddy simulation. As a test case compressible decaying isotropic turbulence is considered. Results obtained with low‐order finite difference schemes and a pseudospectral scheme are compared with filtered well‐resolved direct numerical simulation (DNS) data. It is found that even for low‐order schemes very good results can be obtained if the cutoff wavenumber of the filter is adjusted to the modified wavenumber of the differentiation scheme.     

A GPU-based algorithm for efficient LES of high Reynolds number flows in heterogeneous CPU/GPU supercomputers

Αn optimized MPI+OpenACC implementation model that performs efficiently in CPU/GPU systems using large-eddy simulation is presented. The code was validated for the simulation of wave boundary-layer flows against numerical and experimental data in the literature. A direct Fast-Fourier-Transform-based solver was developed for the solution of the Poisson equation for pressure taking advantage of the periodic boundary conditions. This solver was optimized for parallel execution in CPUs and outperforms by 10 times in computational time a typical iterative preconditioned conjugate gradient solver in GPUs. In terms of parallel performance, an overlapping strategy was developed to reduce the overhead of performing MPI communications using GPUs. As a result, the weak scaling of the algorithm was improved up to 30%. Finally, a large-scale simulation (Re = 2 × 10⁵) using a grid of 4 × 10⁸ cells was executed, and the performance of the code was analyzed. The simulation was launched using up to 512 nodes (512 GPUs + 6144 CPU-cores) on one of the current top 10 supercomputers of the world (Piz Daint). A comparison of the overall computational time showed that the GPU version was 4.2 times faster than the CPU one. The parallel efficiency of this strategy (47%) is competitive compared with the state-of-the-art CPU implementations, and it has the potential to take advantage of modern supercomputing capabilities.     

Pseudorandom generators for space-bounded computation

Pseudorandom generators are constructed which convertO(SlogR) truly random bits toR bits that appear random to any algorithm that runs inSPACE(S). In particular, any randomized polynomial time algorithm that runs in spaceS can be simulated using onlyO(Slogn) random bits. An application of these generators is an explicit construction of universal traversal sequences (for arbitrary graphs) of lengthn ^O(logn).The generators constructed are technically stronger than just appearing random to spacebounded machines, and have several other applications. In particular, applications are given for deterministic amplification (i.e. reducing the probability of error of randomized algorithms), as well as generalizations of it.This work was done in the Laboratory for Computer Science, MIT, supported by NSF 865727-CCR and ARO DALL03-86-K-017     

Optimum computation of p bilinear forms

We wish to answer the following question: p matrices B_i, of the same dimension, being given, what is the minimum number of multiplications we have to perform to obtain the p values X^tB_iY, for arbitrary vectors X and Y? We will give first a precise definition of the class of algorithms we consider to evaluate these p bilinear forms, and of our optimization criteria. Then we will characterize an optimal algorithm of this class, and relate the minimum number of multiplications used to the tensorial rank of the p matrices B_i. Properties of this number are given. Finally, the paper will conclude with a proof of the optimality of Strassen's algorithm to perform the product of two 2×2 matrices.     

Improving shock-free compressible RANS solvers for LES on unstructured meshes

Standard numerical methods used to solve the Reynolds averaged Navier–Stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model. A possible solution is to resort to non-dissipative central schemes. Unfortunately, these schemes are in general unstable. A way to reach stability is to select a central scheme that conserves the discrete kinetic energy. To that purpose, a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock-free flows on unstructured grids. A direct numerical simulation of the flow past a sphere at a Reynolds number of 300 and a large eddy simulation at a Reynolds number of 10,000 are performed to validate the methodology.     

一种邻近性的计算方法

邻近律是Gestalt定律的基本定律之一,然而迄今为止,如何在图像处理中计算元素之间的邻近性程度还没有具体方法提出．以点元素作为抽象载体提出了一种邻近性的计算方法,该方法借鉴基于最小支撑树（MST）的聚类思想,引入三角剖分和Prim算法计算元素之间的MST邻近性测度和加权MST邻近性测度用于度量元素之间的邻近性．实验结...     

Numerical approaches for computation of fronts

Moving fronts and pulses appear in many engineering applications like flame propagation and a falling liquid film. Standard computation methods are inappropriate since the problem is defined over an infinite domain and a steady-state solution exists only for a certain front velocity. This work presents a transformation that converts the original problem into a boundary-value problem within a finite domain, in a way that preserves the behavior at the boundaries. Good low-order approximations can be obtained as demonstrated by two examples. In another approach, a central element of adjustable length is incorporated into a three-element structure where the edge-elements obey known asymptotic solutions. That yields multiplicity of travelling fronts in an infinite domain but it successfully approximates standing wave solutions in a finite domain. The approximate solutions are shown to obey the qualitative features known for the exact solutions, like asymptotic solutions or the bifurcation set–the boundary where a new solution emerges or disappears.     

Algorithms for two-dimensional transfer function computation

Algorithms for the computation of two-dimensional transfer functions from state-space configurations are derived. The principal steps in the programming procedure are provided.     

Homotopies for computation of fixed points

Given a point to set mapf on a simplex with certain conditions, an algorithm for computing fixed points is described. The algorithm operates by following the fixed point as an initially affine function is deformed towardsf. This research was supported in part by Army Research Office Durham Contract DAHC-04-67-C-0028 and in part by NSF Grant GK-5695.     

Newton’s method and high-order algorithms for the nth root computation

Two modifications of Newton’s method to accelerate the convergence of the n$n$th root computation of a strictly positive real number are revisited. Both modifications lead to methods with prefixed order of convergence p∈N,p≥2$p\in \mathbb{N},p\ge 2$. We consider affine combinations of the two modified p$p$th-order methods which lead to a family of methods of order p$p$ with arbitrarily small asymptotic constants. Moreover the methods are of order p+1$p+1$ for some specific values of a parameter. Then we consider affine combinations of the three methods of order p+1$p+1$ to get methods of order p+1$p+1$ again with arbitrarily small asymptotic constants. The methods can be of order p+2$p+2$ with arbitrarily small asymptotic constants, and also of order p+3$p+3$ for some specific values of the parameters of the affine combination. It is shown that infinitely many p$p$th-order methods exist for the n$n$th root computation of a strictly positive real number for any p≥3$p\ge 3$.     

Parallel computation structure for magnetohydrodynamic problems

Translated from Vychislitel'nye Sistemy i Voprosy Prinyatiya Reshenii, pp. 18–27, 1991.