Regular Algebra Applied to Path-finding Problems

In an earlier paper, one of the authors presented an algebrafor formulating and solving extremal path problems. There arestriking similarities between that algebra and the algebra ofregular languages, which lead one to consider whether the previousresults can be generalized—for instance to path enumerationproblems—and whether the algebra of regular languagescan itself be profitably used for the general study of path-findingproblems. This paper gives affirmative answers to both thesequestions.     

Dynamic Sampling Applied to Problems in Optimal Control

Dynamic sampling utilizes the option of varying the sampling rates according to the situation of the systems, thus obtaining procedures with improved efficiencies. In this paper, the technique is applied to a typical problem in optimal control theory, that of tracking and controlling the position of an object. It is shown that the dynamic sampling results in a significantly improved procedure for this case, even when applying a suboptimal policy which can be analyzed in closed form.     

Minimization of Energy Functionals Applied to Some Inverse Problems

We consider a general class of problems of the minimization of convex integral functionals subject to linear constraints. Using Fenchel duality, we prove the equality of the values of the minimization problem and its associated dual problem. This equality is a variational criterion for the existence of a solution to a large class of inverse problems entering the class of generalized Fredholm integral equations. In particular, our abstract results are applied to marginal problems for stochastic processes. Such problems naturally arise from the probabilistic approaches to quantum mechanics. Accepted 26 March 2001. Online publication 19 July 2001.     

Massively Parallel Particle Simulations on Graphics Processing Units with CUDA

Particle methods are a powerful tool to model dynamic systems. Thereby, the system is discretized by a large number of particles, which are interacting via local, predefined particle-particle interaction laws. The resulting computational effort includes neighborhood search, computation of interaction forces and state update via time integration. Particle methods are used in a lot of different fields of applications like computer science, physics and engineering sciences. As the analyzed systems' number of particles constantly grow, performance enhancement has become an important part of present algorithm development. Besides the well-established approach of algorithm parallelization on multi-core CPUs or CPU clusters, modern graphics processing units (GPUs) present a different and trend-setting possibility for massive parallelization even on desktop computers. Among the top four supercomputers of the world, three are already using NVIDIA GPUs. In late 2006, NVIDIA introduced the first GPUs optimized for general purpose calculations. This was followed by the introduction of a new computing architecture differing from the standard graphics user-interface like OpenGL. This architecture is called Compute Unified Device Architecture (CUDA). It enables the user to program the GPU using standard C commands with few additional runtime functions. The differences in architecture between CPU and GPU result in a completely different algorithm implementation. So, a performance evaluation of different types of particle systems implemented on a GPU using CUDA and on a standard CPU is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

同伦算法在并联机器人运动学中的应用

讨论同伦算法求解并联机器人运动学正问题.通过参系数同伦法大大减少了跟踪路径的数目,从而提高了同伦算法的效率使之对求解一般非线性代数方程组更为可行.采用这一算法,求出了中科院沈阳自动化研究所机器人开放研究实验室的新型并联机器人模型的全部正解.为新模型的机构分析和实时控制提供了理论依据.     

Parallel FE approximation of the even/odd-parity form of the linear Boltzmann equation

A novel solution method has been developed to solve the linear Boltzmann equation on an unstructured triangular mesh. Instead of tackling the first-order form of the equation, this approach is based on the even/odd-parity form in conjunction with the conventional multigroup discrete-ordinates approximation. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, and the method is well suited for massively parallel computers.     

Parallel Algorithms for Orthotropic Problems

Finite element meshes and node-numberings suitable for parallel solution with equally loaded processors are presented for linear orthotropic elliptic partial differential equations. These problems are of great importance, for instance in the oil and airfoil industries. The linear systems of equations are solved by the conjugate gradient method preconditioned by modified incomplete factorization, MIC. The basic method presented, is based on fronts of uncoupled nodes and unlike earlier methods it has the advantage of no requirement of a specific orientation of the mesh. This method is however, in general, restricted to small degree of anisotropy in the differential equation. Another method, which does not suffer from this limitation, uses rotation of the differential equation and spectral equivalence. The rotation is made in such a way that in the new co-ordinate system, the basic method is applicable. The spectral equivalence property is used for estimation of the condition number of the preconditioned system. Both methods are suitable for implementation on parallel computers. The computer architecture could be single instruction multiple data (SIMD) as well as multiple instruction multiple data (MIMD) with shared or distributed memory. Implementation of the basic method on a shared memory parallel computer shows a significant improvement by use of the MIC method compared with the diagonal scaling preconditioning method.     

Parallel Computing for Long-Time Simulations of Calcium Waves in a Heart Cell

Calcium waves are modeled by parabolic partial differential equations, whose simulation codes contain Krylov subspace methods as computational kernels. This paper presents GPU-based parallel computations for the conjugate gradient method applied to the finite difference discretization of a Poisson equation as prototype problem for the computational kernel. The CUDA algorithm tests the three memory systems of global memory, texture memory, and shared memory of a CUDA-enabled GPU. Due to the caching mechanism and coalesced read/write operations, the CUDA algorithm using global memory and single precision floating point numbers outperforms algorithms accessing texture memory and the shared memory. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy

In this paper, we develop an infinite dimensional Lagrangian duality framework for modeling and analyzing the evolutionary pollution control problem. Specifically, we examine the situation in which different countries aim at determining the optimal investment allocation in environmental projects and the tolerable pollutant emissions, so as to maximize their welfare. We state the equilibrium conditions underlying the model, and provide an equivalent formulation in terms of an evolutionary variational inequality. Moreover, by means of infinite dimensional duality tools, we prove the existence of Lagrange multipliers that play a fundamental role in order to describe countries’ decision-making processes.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

Neighborhood Portfolio Approach for Local Search Applied to Timetabling Problems

A recent trend in local search concerns the exploitation of several different neighborhoods so as to increase the ability of the algorithm to navigate the search space. In this work we investigate a hybridization technique, that we call Neighborhood Portfolio Approach, that consists in the interleave of local search techniques based on various combinations of neighborhoods. In particular, we are able to select the most effective search technique through a systematic analysis of all meaningful combinations built upon a set of basic neighborhoods. The proposed approach is applied to two practical problems belonging to the timetabling family, and systematically tested and compared on real-world instances. The experimental analysis shows that our approach leads to automatic design of new algorithms that provide better results than basic local search techniques.     

PSE在可压缩边界层转捩问题中的应用

提出了用抛物化稳定性方程（PSE）预测层流-湍流转捩的一种新的概念．它被试用于平板可压缩边界层转捩位置的预测问题中,并将结果与直接数值模拟（DNS）所得进行比较．结果二者符合情况令人满意．二者符合的原因在于PSE方法准确地再现了层流-湍流转捩中导致breakdown过程的机理,即平均流剖面的修正导致其稳定性特性的明显改变．     

最优化问题的并行算法

本文对求解非线性最优化问题的几种主要并行思想，即按变量分裂的并行算法，函数值、梯度值的并行计算，计算步骤并行的算法等，作了简要的综述，并介绍了近几年在这方面取得的进展．     

A Study on Mixed Finite Element Formulations Applied to Diffusion Problems

The objective of this contribution is to study various mixed finite element schemes applied to classical and non-classical diffusion problems. The Fickean diffusion is considered using a three-field formulation where the concentration gradient and the diffusive flux are additionally chosen as independent variables. Furthermore, the non-classical diffusion model given by the Cahn–Hilliard equation is discussed where mixed finite elements are used to cast the fourth-order PDE into two second-order PDEs. A penalized version of a mixed formulation for the underlying second gradient model is given by specific micromorphic models. Another approach is a classical second order splitting method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Problems in Determining Bidding Strategies

A methodology for estimating the bidding strategy of a collaborating company in an apparently complex market, as exemplified by a heating and ventilating contractor, has been developed. In the absence of sufficient detailed price data on all identified competitors, the market lowest bid strategy was determined sufficiently accurately to allow possible strategy changes to be simulated.     

PSE在超音速边界层二次失稳问题中的应用

用抛物化稳定性方程（PSE）研究超音速边界层中的二次失稳问题．结果显示无论二维基本扰动是第一模态还是第二模态的T-S波,二次失稳机制都起作用．三维亚谐波的放大率随其展向波数和二维基本波幅值的变化关系与不可压缩边界层中所得类似．但是,即使二维波的幅值大到2％的量级,三维亚谐波的最大放大率仍远小于最不稳定的第二模态二维T-S波的放大率．因此,二次失稳应该不是导致超音速边界层转捩的主要因素．     

A Computer Simulation Model Applied to Design Problems of a Petrochemical Complex

This paper describes a computer simulation model which was developed by BP Chemicals International and applied to some of the design problems of a petrochemical complex. The individual plants in this type of complex are closely interlinked in terms of input and output of raw materials, usage from common storage tanks and utilities requirements. Thus decisions taken within a particular area can have serious effects on overall site performance. The simulation model was constructed to assist management in evaluating the consequences of alternative design decisions.The structure and data requirements of the model are described and special mention is made of the decision rules used to arrive at a feasible mass balance. Limitations of the model are discussed and some sample applications are presented, including the problem of the sizing of storage tanks.     

求极限中的解题策略

通过实例介绍求极限的解题策略,旨在帮助学生在解题过程中效仿与拓展,从而强化其创新意识,使其灵活掌握所学基础知识.     

弹性动力问题的有限元与特解边界元耦合的数值方法

导出了特解边界元法与有限元法的耦合方程。并应用自由度缩减技术,使耦合方程的自由度缩减到有限元域及其和边界元域的耦合边界上。这样得到的耦合方程不增加原有限元方程的带宽和阶数。耦合方程的求解可以引用求解有限元方程的所有方法,易于程序实现。数值算例结果表明,本文所提出的方法是正确的,是一种较为理想的耦合方法。