SOLVING DISCRETE-TIME LYAPUNOV EQUATIONS FOR THE CHOLESKY FACTOR ON A SHARED MEMORY MULTIPROCESSOR

The four points modified explicit group (MEG) method for solving 2D Poisson equation was introduced by Othman and Abdullah [“An efficient Four Points Modified Explicit Group Poisson Solver”, Int. J. Comput. Math., 76 (2000) 203–217], which was shown to be superior to the four points-explicit decoupled group (EDG) and explicit group (EG) methods due to Abdullah [“The Four Explicit Decoupled Group (EDG) Method: A Fast Poisson Solver”, Int. J. Comput. Math., 38 (1991) 60–70] and Evans and Biggins [“The solution of elliptic partial differential equations by A New Block Over-Relaxation Technique”, Int. J. Comput. Math., 10 (1982) 269–282], respectively. These methods were found to be suitable for parallel implementation [see Evans, D.J. and Yousif, W.S. “The implementation of the Explicit Block Iterative Methods on the balance 8000 parallel computer”, Parallel Computing, 16 (1990) 81–97; Yousif, W.S. and Evans, D.J. “Explicit De-coupled Group Iterative Methods and their parallel implementations”, Parallel Algorithms and Applications, 7 (1995) 53–71]. In this paper, the implementation of the parallel four points MEG algorithm with the red black and four colors ordering strategies for solving the same equation on shared memory multiprocessors are presented. The experiment results of the test problem are included and compared with the parallel four points- EG and EDG algorithms.

Rockburst disaster is one of the prominent problems faced by deep underground engineering. In this study, rockburst in four elliptical holes with different axial ratios in sandstone under biaxial loading is studied as an analogue for underground roadways. Video and acoustic emission (AE) equipment is used to monitor the biaxial loading tests. Experimental results indicate that each of the elliptical holes goes through four stages: quiet period, small particle ejection, spalling, and rockburst. The duration of quiet and spalling periods increased with increasing axial ratio of ellipse. The duration of the ejection and rockburst periods remains unchanged. All the four elliptical holes have V-shaped pits after rockburst occurs. The fragments produced during rockburst are divided into coarse, medium, fine, and micro grains. The quantity of coarse and medium grains increases with increasing axial ratio. The mass ratio of coarse and medium grains increases and that of fine and micro grains decreases. The depth, angle, and area of the V-shaped pits decrease with increasing axis ratio. Tensile cracks play an important role in rockburst failure. Tensile cracks are the dominant crack types formed during rockburst and account for over 70% of all cracks in the samples. The number of tensile cracks increased and the number of shear cracks decreased. This paper has some reference value for practical engineering design and prevention of rockburst.

Dynamic programming is an efficient technique to solve combinatorial search and optimization problem. There have been many parallel dynamic programming algorithms. The purpose of this paper is to study a family of dynamic programming algorithm where data dependence appear between non-consecutive stages, in other words, the data dependence is non-uniform. This kind of dynnamic programming is typically called nonserial polyadic dynamic programming. Owing to the non-uniform data dependence, it is harder to optimize this problem for parallelism and locality on parallel architectures. In this paper, we address the chanllenge of exploiting fine grain parallelism and locality of nonserial polyadic dynamic programming on a multi-core architecture. We present a programming and execution model for multi-core architectures with memory hierarchy. In the framework of the new model, the parallelism and locality benifit from a data dependence transformation. We propose a parallel pipelined algorithm for filling the dynamic programming matrix by decomposing the computation operators. The new parallel algorithm tolerates the memory access latency using multi-thread and is easily improved with tile technique. We formulate and analytically solve the optimization problem determing the tile size that minimizes the total execution time. The experiments on a simulator give a validation of the proposed model and show that the fine grain parallel algorithm achieves sub-linear speedup and that a potential high scalability on multi-core arichitecture.

Recurrence solution of a block tridiagonal matrix equation with Neumann, Dirichlet, mixed or periodic boundary conditions

A new method to retrieve aerosol optical thickness from satellite images on a parallel system

The parallelizing compiler for the B-HIVE loosely-coupled multiprocessor system uses a medium grain model to minimize the communication overhead. A medium grain model is shown to be an optimum way of merging fine grain operations into parallel tasks such that the parallelism obtained at the grain level is retained and communication overhead is decreased. A new communication model is introduced in this paper, allowing additional overlap between computation and communication. Simulation results indicate that the medium grain communication model shows promise for automatic parallelization for a loosely-coupled multiprocessor system.

An efficient parallel sorting algorithm for shared memory multiprocessors

Parallel algorithms for reduction of a general matrix to upper Hessenberg form on a shared memory multiprocessor

We present a parallel algorithm for solving the dual transshipment problem. The traditional dual simplex method does not offer much scope for parallelization, because it moves from one basic feasible solution to another, performing one pivot operation at a time. We present a new method called modified network dual simplex method which uses concurrent pivots. This departure from the traditional LP approach raises several issues such as the need to convert a non-basic feasible solution to a basic feasible solution. We present our strategies to handle these issues as well as the corresponding parallel algorithms. We also present results of testing this algorithm on large graphs to solve the integrated layout compaction and wire balancing problem. >

A parallel algorithm is presented for the efficient numerical solution of the stochastic collection equation. It is based on Bott flux method for numerical solution of the stochastic collection equation. The algorithm of Bott has been chosen as one of the most popular algorithms intended for calculation of the evolution of cloud particle spectra. The optimized algorithm makes it possible to use multiple CPU cores for computation acceleration without significant accuracy loss and remains free from mass defect. Acceleration is achieved at the cost of reduced accuracy, because the steps of strictly sequential algorithm are executed in parallel. Tests showed a 3.5 time speedup on PC with four CPU cores. Results of the numerical tests show that the parallel algorithm is very promising to be used in the numerical models of convective clouds for calculating the spectra of cloud particles, such as water drops and various types of ice crystals. Stochastic collection equation presents the most computationally expensive part of such models aimed at forecasting thunderstorms, heavy rains and hails. Thus elaborated parallel algorithm can become an efficient instrument in the hardware and software systems designed for operational forecast of dangerous weather phenomena.KeywordsStochastic collection equationEfficient algorithmMeteorologyNumerical modelingMultithreading

Designing irregular parallel algorithms with mutual exclusion and lock-free protocols

The authors provide optimal parallel solutions to several fundamental link distance problems set in trapezoided rectilinear polygons. All parallel algorithms are deterministic, run in logarithmic time, have an optimal time-processor product and are designed to run on EREW PRAM. The authors develop techniques (e.g. rectilinear window partition) for solving link distance problems in parallel which are expected to find applications in the design of other parallel computational geometry algorithms. They employ these parallel techniques for example to compute the link diameter, link center, and central diagonal of a rectilinear polygon. Their results also imply an optimal linear-time sequential algorithm for constructing a data structure to support rectilinear link distance queries between points.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parallel asynchronous subdomain algorithms with flexible communication for the numerical solution of nonlinear diffusion problems are presented. The discrete maximum principle is considered and the Schwarz alternating method and multisplitting methods are studied. A connection is made with M-functions for a classical nonlinear diffusion problem. Finally, computational experiments carried out on a shared memory multiprocessor are presented and analyzed.

Physical map reconstruction in the presence of errors is a central problem in genetics of high computational complexity. A parallel genetic algorithm for a maximum likelihood estimation-based approach to physical map reconstruction is presented. The estimation procedure entails gradient descent search for determining the optimal spacings between probes for a given probe ordering. The optimal probe ordering is determined using a genetic algorithm. A two-tier parallelization strategy is proposed wherein the gradient descent search is parallelized at the lower level and the genetic algorithm is simultaneously parallelized at the higher level. Implementation and experimental results on a network of shared-memory symmetric multiprocessors (SMPs) are presented. The genetic algorithm is seen to result in physical maps with fewer contig breaks when compared to simulated Monte Carlo algorithms such as simulated annealing and the large-step Markov chain algorithm.

A parallelizable and vectorizable algorithm for solving linear algebraic systems arising from two-point boundary value ODEs is described. The method is equivalent to Gaussian elimination, with row partial pivoting, applied to a certain row- and column-reordered version of the usual almost block-diagonal coefficient matrix. Analytical and numerical evidence is presented to show that the algorithm is stable. Results from implementation on a shared-memory multiprocessor and a vector processor are given. The approach can be extended to handle problems with multipoint and integral conditions or algebraic parameters.