Parallel and vector computation for stochastic optimal control applications

A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Learning Parallel Computations with ParaLab

In this paper, we present the ParaLab teachware system, which can be used for learning the parallel computation methods. ParaLab provides the tools for simulating the multiprocessor computational systems with various network topologies, for carrying out the computational experiments in the simulation mode, and for evaluating the efficiency of the parallel computation methods. The visual presentation of the parallel computations taking place in the computational experiments is the key feature of the system. ParaLab can be used for the laboratory training within various teaching courses in the field of parallel, distributed, and supercomputer computations

Performance Analysis of a Novel GPU Computation-to-core Mapping Scheme for Robust Facet Image Modeling

Though the GPGPU concept is well-known in image processing, much more work remains to be done to fully exploit GPUs as an alternative computation engine. This paper investigates the computation-to-core mapping strategies to probe the efficiency and scalability of the robust facet image modeling algorithm on GPUs. Our fine-grained computation-to-core mapping scheme shows a significant performance gain over the standard pixel-wise mapping scheme. With in-depth performance comparisons across the two different mapping schemes, we analyze the impact of the level of parallelism on the GPU computation and suggest two principles for optimizing future image processing applications on the GPU platform

Number partitioning as random energy model

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local random energy'' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.Comment: 8+2 pages, 9 figures, PDF onl

Particle methods parallel implementations by GP-GPU strategies

This paper outlines the problems found in the parallelization of SPH (Smoothed Particle Hydrodynamics) algorithms using Graphics Processing Units. Different results of some parallel GPU implementations in terms of the speed-up and the scalability compared to the CPU sequential codes are shown. The most problematic stage in the GPU-SPH algorithms is the one responsible for locating neighboring particles and building the vectors where this information is stored, since these specific algorithms raise many dificulties for a data-level parallelization. Because of the fact that the neighbor location using linked lists does not show enough data-level parallelism, two new approaches have been pro- posed to minimize bank conflicts in the writing and subsequent reading of the neighbor lists. The first strategy proposes an efficient coordination between CPU-GPU, using GPU algorithms for those stages that allow a straight forward parallelization, and sequential CPU algorithms for those instructions that involve some kind of vector reduction. This coordination provides a relatively orderly reading of the neighbor lists in the interactions stage, achieving a speed-up factor of x47 in this stage. However, since the construction of the neighbor lists is quite expensive, it is achieved an overall speed-up of x41. The second strategy seeks to maximize the use of the GPU in the neighbor's location process by executing a specific vector sorting algorithm that allows some data-level parallelism. Al- though this strategy has succeeded in improving the speed-up on the stage of neighboring location, the global speed-up on the interactions stage falls, due to inefficient reading of the neighbor vectors. Some changes to these strategies are proposed, aimed at maximizing the computational load of the GPU and using the GPU texture-units, in order to reach the maximum speed-up for such codes. Different practical applications have been added to the mentioned GPU codes. First, the classical dam-break problem is studied. Second, the wave impact of the sloshing fluid contained in LNG vessel tanks is also simulated as a practical example of particle method

GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.Comment: 21 pages, 5 figures; Comput. Phys. Commun., accepted, 201

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed