抛物方程时间周期问题的有限元多格子动力学迭代

本文我们研究线性周期抛物方程的有限元多格子动力学迭代.多格子动力学迭代又称多重网格波形松弛,它是在函数空间中的一种迭代过程.对于由加速技术得到的多格子动力学迭代算子,我们通过计算周期函数的Fourier系数给出了新的谱表达式.从这些有用的表达式出发,我们推导了时间连续和离散格式的迭代收敛条件.数值实验进一步验证了本文的理论结果.     

Mean-value theorems and extensions of the Elliott-Daboussi theorem on additive arithmetic semigroups

We present more general forms of the mean-value theorems established before for multiplicative functions on additive arithmetic semigroups and prove, on the basis of these new theorems, extensions of the Elliott-Daboussi theorem. Let be an additive arithmetic semigroup with a generating set ℘ of primes p. Assume that the number G(m) of elements a in with “degree” ∂(a)=m satisfies

An asynchronous parallel newton method

A parallel Newton method is described for the minimization of a twice continuously differentiable uniformly convex functionF(x). The algorithm generates a sequence {x _j } which converges superlinearly to the global minimizer ofF(x).     

An approximation algorithm for the generalized assignment problem

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep _ij and incurs a cost ofc _ij ; each machinei is available forT _i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T _i time units.We also extend this result to a variant of the problem where, instead of a fixed processing timep _ij , there is a range of possible processing times for each machine—job pair, and the cost linearly increases as the processing time decreases. We show that these results imply a polynomial-time 2-approximation algorithm to minimize a weighted sum of the cost and the makespan, i.e., the maximum job completion time. We also consider the objective of minimizing the mean job completion time. We show that there is a polynomial-time algorithm that, given valuesM andT, either proves that no schedule of mean job completion timeM and makespanT exists, or else finds a schedule of mean job completion time at mostM and makespan at most 2T. Research partially supported by an NSF PYI award CCR-89-96272 with matching support from UPS, and Sun Microsystems, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.Research supported in part by a Packard Fellowship, a Sloan Fellowship, an NSF PYI award, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

Open shop problems with unit time operations

We show that them-machine open shop problem in which all operations have unit processing times can be polynomially transformed to a special preemptive scheduling problem onm identical parallel machines. Many results published recently as well as some new results are derived by using this transformation. The new results include solutions of open problems mentioned in a recent paper by Kubiak et al. p]A similar relationship is derived between no-wait open shop problems with unit time operations andm-machine problems with jobs having unit processing times.This work was supported by Deutsche Forschungsgemeinschaft (Project JoPTAG).     

线性方程组异步并行迭代法的舍入误差分析

本文对求解大型线性方程组的异步并行迭代法进行了浮点运算的舍入误差分析,给出了算法是向前稳定的充分条件.     

Parallelizing Tabu Search on a Cluster of Heterogeneous Workstations

In this paper, we present the parallelization of tabu search on a network of workstations using PVM. Two parallelization strategies are integrated: functional decomposition strategy and multi-search threads strategy. In addition, domain decomposition strategy is implemented probabilistically. The performance of each strategy is observed and analyzed. The goal of parallelization is to speedup the search in finding better quality solutions. Observations support that both parallelization strategies are beneficial, with functional decomposition producing slightly better results. Experiments were conducted for the VLSI cell placement, an NP-hard problem, and the objective was to achieve the best possible solution in terms of interconnection length, timing performance (circuit speed), and area. The multiobjective nature of this problem is addressed using a fuzzy goal-based cost computation.     

A Mixed Heuristic for Circuit Partitioning

As general-purpose parallel computers are increasingly being used to speed up different VLSI applications, the development of parallel algorithms for circuit testing, logic minimization and simulation, HDL-based synthesis, etc. is currently a field of increasing research activity. This paper describes a circuit partitioning algorithm which mixes Simulated Annealing (SA) and Tabu Search (TS) heuristics. The goal of such an algorithm is to obtain a balanced distribution of the target circuit among the processors of the multicomputer allowing a parallel CAD application for Test Pattern Generation to provide good efficiency. The results obtained indicate that the proposed algorithm outperforms both a pure Simulated Annealing and a Tabu Search. Moreover, the usefulness of the algorithm in providing a balanced workload distribution is demonstrated by the efficiency results obtained by a topological partitioning parallel test-pattern generator in which the proposed algorithm has been included. An extented algorithm that works with general graphs to compare our approach with other state of the art algorithms has been also included.     

Implicit Solution of Hyperbolic Equations with Space-Time Adaptivity

Adaptivity in space and time is introduced to control the error in the numerical solution of hyperbolic partial differential equations. The equations are discretised by a finite volume method in space and an implicit linear multistep method in time. The computational grid is refined in blocks. At the boundaries of the blocks, there may be jumps in the step size. Special treatment is needed there to ensure second order accuracy and stability. The local truncation error of the discretisation is estimated and is controlled by changing the step size and the time step. The global error is obtained by integration of the error equations. In the implicit scheme, the system of linear equations at each time step is solved iteratively by the GMRES method. Numerical examples executed on a parallel computer illustrate the method.