Stabilization of infinite-dimensional semilinear second-order systems by position feedback

In this paper stabilization of infinite-dimensional undampedsemilinear second-order systems is considered in the case whereany velocity feedback is not available. For such a case parallelcompensators are effective. For the systems with collocatedinput and output operators the stabilizer is constructed bya P-controller for the augmented system which consists of thecontrolled system and a parallel compensator. The asymptoticstability of the closed-loop system is proved by LaSalle's invarianceprinciple under compactness of the resolvent.     

A General Decomposition Algorithm for Parallel Queues with Correlated Arrivals

Queueing with correlated arrivals occurs when customers arrive at a set of queues simultaneously. The difficulty in analyzing systems with correlated arrivals is due to the fact that the individual queueing systems are stochastically dependent. Exact methods for analyzing these systems are computationally intensive and are limited to only a few special cases. In this paper, we consider a system of parallel queues with bulk service and correlated arrivals. We show how the matrix-geometric approach can be used to obtain the performance measures of the system. We also develop an algorithm for large systems that efficiently approximates the performance measures by decomposing it into individual queueing systems. Finally, we describe how the principles of our decomposition algorithm can be extended to analyze a variety of different parallel queueing systems with correlated arrivals. We then evaluate the accuracy of our algorithm through a numerical study.     

A parallel approach to improvement and estimation of the approximate optimal control

In this paper the method for computing a priori estimates of the approximate optimal control is considered. These estimates provide us with information about the quality of the approximate optimal solution obtained by applying the improvement control procedure. The method is implemented in the form of a parallel algorithm. This algorithm is an essential part of the developed software package intended for optimization of controllable dynamical systems. We also consider the scalability of the parallel algorithm in the OpenTS parallel programming system for chemical and biochemical engineering problems.     

五对角线性方程组求解的并行算法

引理。设 P_i=F_iF_(i-1)…F_1g,i=1,2,…,n,(16)其中F_i(i=1,2,…,n)为k阶矩阵,g为k维向量,则由(16)计算所有P_i(i=1,2,…,n),[T_klog_2(n+1)]步完成.所用处理机台数不超过[s_k(n+1)/2],这里T_k表     

Efficiency measurement for parallel production systems

In the real world there are systems which are composed of independent production units. The conventional data envelopment analysis (DEA) model uses the sum of the respective inputs and outputs of all component units of a system to calculate its efficiency. This paper develops a parallel DEA model which takes the operation of individual components into account in calculating the efficiency of the system. A property owned by this parallel model is that the inefficiency slack of the system can be decomposed into the inefficiency slacks of its component units. This helps the decision maker identify inefficient components and make subsequent improvements. Another property is that the efficiency calculated from this model is smaller than that calculated from the conventional DEA model. Few systems will have perfect efficiency score; consequently, a stronger discrimination power is gained. In addition to theoretical derivations, a case of the national forests of Taiwan is used as an example to illustrate the whole idea.     

Problem of checking the functional completeness in the class of piecewise parallel functions

The author showed previously that it is possible to implement an arbitrary piecewise parallel function by circuits of linear elements and one nonlinear element implementing the θ-function. Thus, the functional completeness of a particular system of functions in the class of piecewise parallel functions was established. In this paper we consider the same class and study its completeness property for a system of functions whose closures contain all linear functions. We formulate and prove a criterion of functional completeness for such systems in terms of precomplete classes.     

A simulation tool for the performance evaluation of parallel branch and bound algorithms

Parallel computation offers a challenging opportunity to speed up the time consuming enumerative procedures that are necessary to solve hard combinatorial problems. Theoretical analysis of such a parallel branch and bound algorithm is very hard and empirical analysis is not straightforward because the performance of a parallel algorithm cannot be evaluated simply by executing the algorithm on a few parallel systems. Among the difficulties encountered are the noise produced by other users on the system, the limited variation in parallelism (the number of processors in the system is strictly bounded) and the waste of resources involved: most of the time, the outcomes of all computations are already known and the only issue of interest is when these outcomes are produced.We will describe a way to simulate the execution of parallel branch and bound algorithms on arbitrary parallel systems in such a way that the memory and cpu requirements are very reasonable. The use of simulation has only minor consequences for the formulation of the algorithm.     

Block s‐step Krylov iterative methods

Block (including s‐step) iterative methods for (non)symmetric linear systems have been studied and implemented in the past. In this article we present a (combined) block s‐step Krylov iterative method for nonsymmetric linear systems. We then consider the problem of applying any block iterative method to solve a linear system with one right‐hand side using many linearly independent initial residual vectors. We present a new algorithm which combines the many solutions obtained (by any block iterative method) into a single solution to the linear system. This approach of using block methods in order to increase the parallelism of Krylov methods is very useful in parallel systems. We implemented the new method on a parallel computer and we ran tests to validate the accuracy and the performance of the proposed methods. It is expected that the block s‐step methods performance will scale well on other parallel systems because of their efficient use of memory hierarchies and their reduction of the number of global communication operations over the standard methods. Copyright © 2009 John Wiley & Sons, Ltd.     

A communication-less parallel algorithm for tridiagonal Toeplitz systems

Diagonally dominant tridiagonal Toeplitz systems of linear equations arise in many application areas and have been well studied in the past. Modern interest in numerical linear algebra is often focusing on solving classic problems in parallel. In McNally [Fast parallel algorithms for tri-diagonal symmetric Toeplitz systems, MCS Thesis, University of New Brunswick, Saint John, 1999], an m processor Split & Correct algorithm was presented for approximating the solution to a symmetric tridiagonal Toeplitz linear system of equations. Nemani [Perturbation methods for circulant-banded systems and their parallel implementation, Ph.D. Thesis, University of New Brunswick, Saint John, 2001] and McNally (2003) adapted the works of Rojo [A new method for solving symmetric circulant tri-diagonal system of linear equations, Comput. Math. Appl. 20 (1990) 61–67], Yan and Chung [A fast algorithm for solving special tri-diagonal systems, Computing 52 (1994) 203–211] and McNally et al. [A split-correct parallel algorithm for solving tri-diagonal symmetric Toeplitz systems, Internat. J. Comput. Math. 75 (2000) 303–313] to the non-symmetric case. In this paper we present relevant background from these methods and then introduce an m processor scalable communication-less approximation algorithm for solving a diagonally dominant tridiagonal Toeplitz system of linear equations.     

一类非线性代数方程组的并行算法——适用于MIMD系统

为连续对角映射.而A=(a_(ij)∈L(R~n)是单调矩阵,B∈L(R~n)为非负矩阵,b∈R~n为已知向量. 方程组(1.1)具有丰富的实际背景,许多非线性微分方程的求解问题,经过有限元或差分离散,均可归纳为(1.1)的求解.特别,如[7],[10]以及[11]讨论的弱非线性椭圆方程和Stefan问题等,均可作为(1.1)的特例.     

A domain-decomposing parallel sparse linear system solver

The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few examples of the application areas in which large sparse linear systems need to be solved effectively. In this paper, we introduce a new parallel hybrid sparse linear system solver for distributed memory architectures that contains both direct and iterative components. We show that by using our solver one can alleviate the drawbacks of direct and iterative solvers, achieving better scalability than with direct solvers and more robustness than with classical preconditioned iterative solvers. Comparisons to well-known direct and iterative solvers on a parallel architecture are provided.     

多态系统部件维修成本评估分析

多态系统是可靠性理论中的一种重要系统,是指部件和系统具有多个状态。随着部件的劣化,系统的性能随之下降。为了提高系统的性能,部件需要进行一定的维修。本文考虑部件状态转移率与停留时间的关系,利用重要度理论来分析部件维修成本的变化规律,得出对系统维修成本影响最大的部件。首先,基于维修成本的函数关系,给出了重要度的表达式;其次,针对典型串联系统和并联系统,随着时间推移,给出维修成本的变化规律;最后算例仿真验证了提出方法的有效性和正确性。     

A domain-decomposing parallel sparse linear system solver

The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few examples of the application areas in which large sparse linear systems need to be solved effectively. In this paper, we introduce a new parallel hybrid sparse linear system solver for distributed memory architectures that contains both direct and iterative components. We show that by using our solver one can alleviate the drawbacks of direct and iterative solvers, achieving better scalability than with direct solvers and more robustness than with classical preconditioned iterative solvers. Comparisons to well-known direct and iterative solvers on a parallel architecture are provided.     

一类刚性大系统的并行组合方法

本文针对一类分解的刚性大系统提出一种并行组合方法（ＰＣＭ）,该方法将系统分割的并行化方法与并行化方法相结合,采用并行显式Ｒｕｎｇｅ－ｋｕｔｔａ（ＲＫ）方法求解非刚性子系统,采用并行Ｒｏｓｅｎｂｒｏｃｋ方法求解刚性子系统,文中讨论了方法的相容阶、并对方法的收敛性进行了分析,数值结果表明该方法对于分解的刚性大系统的求解是实用和有效的。     

Waveform relaxation methods for implicit differential equations

We apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems increases linearly with the number of stages of the underlying Runge-Kutta method, resulting in high linear algebra costs in the iterative process for high-order Runge-Kutta methods. In our earlier investigations of iterative solvers for implicit initial-value problems, we designed an iteration method in which the linear algebra costs are almost independent of the number of stages when implemented on a parallel computer system. In this paper, we use this parallel iteration process in the Runge-Kutta waveform relaxation method. In particular, we analyse the convergence of the method. The theoretical results are illustrated by a few numerical examples.     

A parallel balance scheme for banded linear systems

A parallel algorithm is proposed for the solution of narrow banded non‐symmetric linear systems. The linear system is partitioned into blocks of rows with a small number of unknowns common to multiple blocks. Our technique yields a reduced system defined only on these common unknowns which can then be solved by a direct or iterative method. A projection based extension to this approach is also proposed for computing the reduced system implicitly, which gives rise to an inner–outer iteration method. In addition, the product of a vector with the reduced system matrix can be computed efficiently on a multiprocessor by concurrent projections onto subspaces of block rows. Scalable implementations of the algorithm can be devized for hierarchical parallel architectures by exploiting the two‐level parallelism inherent in the method. Our experiments indicate that the proposed algorithm is a robust and competitive alternative to existing methods, particularly for difficult problems with strong indefinite symmetric part. Copyright © 2001 John Wiley & Sons, Ltd.     

Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers

Model reduction is an area of fundamental importance in many modeling and control applications. In this paper we analyze the use of parallel computing in model reduction methods based on balanced truncation of large-scale dense systems. The methods require the computation of the Gramians of a linear-time invariant system. Using a sign function-based solver for computing full-rank factors of the Gramians yields some favorable computational aspects in the subsequent computation of the reduced-order model, particularly for non-minimal systems. As sign function-based computations only require efficient implementations of basic linear algebra operations readily available, e.g., in the BLAS, LAPACK, and ScaLAPACK, good performance of the resulting algorithms on parallel computers is to be expected. Our experimental results on a PC cluster show the performance and scalability of the parallel implementation.     

Safety of structural systems with correlated resistances

In this paper, the reliability of basic structural systems is examined. For elementary chain and ductile parallel systems, the effects of equal correlation between element strengths is established assuming normality. A special case involving a choice between statically determinate and indeterminate structural systems is examined and an ‘optimum’ design approach is presented. In this optimal solution, the correlation structure between elements is controlled so as to maximize the system reliability for given element safety. Reliability analysis is based on a two moment safety index.     

三状态串、并联系统的优化分配方法

给出了单目标、单约束下三状态串联、并联系统中由选取重要度来提高系统可靠度的有效优化模型及算法,并进行了实例验证.     

Strategic defense and attack for series and parallel reliability systems

A system of independent components is defended by a strategic defender and attacked by a strategic attacker. The reliability of each component depends on how strongly it is defended and attacked, and on the intensity of the contest. In a series system, the attacker benefits from a substitution effect since attacker benefits flow from attacking any of the components, while the defender needs to defend all components. Even for a series system, when the attacker is sufficiently disadvantaged with high attack inefficiencies, and the intensity of the contest is sufficiently high, the defender earns maximum utility and the attacker earns zero utility. The results for the defender (attacker) in a parallel system are equivalent to the results for the attacker (defender) in a series system. Hence, the defender benefits from the substitution effect in parallel systems. With budget constraints the ratio of the investments for each component, and the contest success function for each component, are the same as without budget constraints when replacing the system values for the defender and attacker with their respective budget constraints.