Parallel Algorithm For Computing Research Articles

Data-driven fluid simulations using regression forests

Traditional fluid simulations require large computational resources even for an average sized scene with the main bottleneck being a very small time step size, required to guarantee the stability of the solution. Despite a large progress in parallel computing and efficient algorithms for pressure computation in the recent years, realtime fluid simulations have been possible only under very restricted conditions. In this paper we propose a novel machine learning based approach, that formulates physics-based fluid simulation as a regression problem, estimating the acceleration of every particle for each frame. We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a large time step setting on yet unseen test videos. We used a regression forest to approximate the behaviour of particles observed in the large training set of simulations obtained using a traditional solver. Our GPU implementation led to a speed-up of one to three orders of magnitude compared to the state-of-the-art position-based fluid solver and runs in real-time for systems with up to 2 million particles.

A New Parallel Computing Algorithm to Get the Cubic Subgraph for a Simple Graph

A New Parallel Computing Algorithm to Get the Cubic Subgraph for a Simple Graph

Enhanced fixed-size parallel speedup with the Muskingum method using a trans-boundary approach and a large subbasins approximation

This study presents a new algorithm for parallel computation of river flow that builds on recent work demonstrating the relative independence of distant river reaches in the update step of the Muskingum method. The algorithm is designed to achieve enhanced fixed-size parallel speedup and uses a mathematical approximation applied at the boundaries of large subbasins. In order to use such an algorithm, a balanced domain decomposition method that differs from the traditional classifications of river reaches and subbasins and based on network topology is developed. An application of the algorithm and domain decomposition method to the Mississippi River Basin results in an eightfold decrease in computing time with 16 computing cores which is unprecedented for Muskingum-type algorithms applied in classic parallel-computing paradigms having a one-to-one relationship between cores and subbasins. An estimated 300 km between upstream and downstream reaches of subbasins guarantees the applicability of the algorithm in our study and motivates further investigation of domain decomposition methods.

Parallel PPI Prediction Performance Study on HPC Platforms

STRIKE is an algorithm which predicts protein–protein interactions (PPIs) and determines that proteins interact if they contain similar substrings of amino acids. Unlike other methods for PPI prediction, STRIKE is able to achieve reasonable improvement over the existing PPI prediction methods. Although its high accuracy as a PPI prediction method, STRIKE consumes a large execution time and hence it is considered to be a compute-intensive application. In this paper, we develop and implement a parallel STRIKE algorithm for high-performance computing (HPC) systems. Using a large-scale cluster, the execution time of the parallel implementation of this bioinformatics algorithm was reduced from about a week on a serial uniprocessor machine to about 16.5 h on 16 computing nodes, down to about 2 h on 128 parallel nodes. Communication overheads between nodes are thoroughly studied.

Fault-tolerant parallel computing for DEM data blocks with layered dependent relationships based on redundancy mechanism

The objective of this paper is to build a quantitative method of data partition in parallelisation of digital terrain analysis DTA so as to guide the design of algorithms in parallel computing. According to the data-intensive characteristics of the digital elevation model DEM, a data dependency model is proposed to describe the hierarchical relationships of data blocks. The parallel schedule policies and algorithms for the DEM are built according to the model. With the increase of computing scale in data or tasks, the reliability of the calculation must also be considered in parallel computing. A fault-tolerant parallel computing method is proposed based on the data dependence graph. Respectively, this paper puts forward parallel computing algorithms of two times redundant, three times redundant and partially redundant, with a discussion of their respective advantages. Finally, a visibility algorithm in DTA as an example is used to verify the validity of the strategies and methods.

Modeling of elastic waves in a blocky medium based on equations of the Cosserat continuum

Based on the equations of the dynamics of piecewise-homogeneous elastic material, parallel computational algorithms are developed to simulate the process of stress and strain wave propagation in a medium consisting of a large number of blocks interacting through compliant interlayers. Computations of waves caused by localized impulse perturbations show that such a medium can be considered as isotropic only in the case of sufficiently thin interlayers. In the case of relatively thick interlayers, the anisotropy effects are observed which consist in the appearance of elongated wave fronts along the coordinate directions and characteristic oscillations of velocities and stresses because of the rotational motion of blocks. For the description of waves in a blocky medium with thin interlayers, the equations of the isotropic Cosserat continuum are applicable. As the thickness of interlayers increases, the orthotropic Cosserat continuum theory which takes into account the symmetry of elastic properties relative to the coordinate planes can be applied. By comparing the elastic wave velocities in the framework of piecewise-homogeneous model and continuum model, a simple method is obtained to estimate the mechanical parameters of the orthotropic Cosserat continuum modeling a blocky medium. In two-dimensional formulation of the orthotropic model the computational algorithm and the program system are worked out for the analysis of propagation of elastic waves. The comparison showed good qualitative agreement between the results of computations of waves caused by localized impulses, in the framework of the model of a blocky medium with compliant interlayers and the model of orthotropic Cosserat continuum.

Large-scale parallel computation of the phonon Boltzmann Transport Equation

Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In this article, strategies and algorithms for large-scale parallel computation of the phonon BTE are presented. An unstructured finite volume method for spatial discretization is coupled with the control angle discrete ordinates method for angular discretization. The single-time relaxation approximation is used to treat phonon–phonon scattering. Both dispersion and polarization of the phonons are accounted for. Three different parallelization strategies are explored: (a) band-based, (b) direction-based, and (c) hybrid band/cell-based. Subsequent to validation studies in which silicon thin-film thermal conductivity was successfully predicted, transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral cells. The angular space was discretized using 400 angles, and the spectral space was discretized into 40 spectral intervals (bands). This resulted in ∼9.7 × 109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-based and hybrid band/cell-based parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy—about 88%—was found to be superior to that of the direction-based strategy, and is recommended as the preferred strategy for even larger scale computations.

GPU Parallel Computing Algorithm in Target Tracking of Space

Article careful analysis of existing processes and target tracking algorithm and part of the video image processing algorithm that consume large amount of data based CPU. Each algorithm for image pre-processing module and tracking module algorithm designed operational processes. Several studies algorithm for image pre-processing module, and each was carried out in parallel GPU accelerated processing, and were tested in a unified CUDA computing device. Experimental data show that some parts of the algorithm can be improved after the adoption of CUDA target tracking algorithm optimized overall efficiency, has some practical significance.

Imitation Monte Carlo methods for problems of the Boltzmann equation with small Knudsen numbers, parallelizing algorithms with splitting

The talk examines a system of pairwise interaction particles, which models a rarefied gas in accordance with the nonlinear Boltzmann equation, the master equations of Markov evolution of this system and corresponding numerical Monte Carlo methods. Selection of some optimal method for simulation of rarefied gas dynamics depends on the spatial size of the gas flow domain. For problems with the Knudsen number Kn of order unity "imitation", or "continuous time", Monte Carlo methods ([2]) are quite adequate and competitive. However if Kn ≤ 0.1 (the large sizes), excessive punctuality, namely, the need to see all the pairs of particles in the latter, leads to a significant increase in computational cost(complexity). We are interested in to construct the optimal methods for Boltzmann equation problems with large enough spatial sizes of the flow. Speaking of the optimal, we mean that we are talking about algorithms for parallel computation to be implemented on high-performance multi-processor computers. The characteristic property of large systems is the weak dependence of sub-parts of each other at a sufficiently small time intervals. This property is taken into account in the approximate methods using various splittings of operator of corresponding master equations. In the paper, we develop the approximate method based on the splitting of the operator of master equations system "over groups of particles" ([7]). The essence of the method is that the system of particles is divided into spatial subparts which are modeled independently for small intervals of time, using the precise"imitation" method. The type of splitting used is different from other well-known type "over collisions and displacements", which is an attribute of the known Direct simulation Monte Carlo methods. The second attribute of the last ones is the grid of the "interaction cells", which is completely absent in the imitation methods. The main of talk is parallelization of the imitation algorithms with splitting using the MPI library. New constructed algorithms are applied to solve the problems: on propagation of the temperature discontinuity and on plane Poiseuille flow in the field of external forces. In particular, on the basis of numerical solutions, comparative estimates of the computational cost are given for all algorithms under consideration.

Volumetric fibular transfer planning with shape-based indicators in mandibular reconstruction.

In preoperative planning for mandibular reconstructive surgery, it is necessary to determine the osteotomy lines for fibular shaping and the proper placement of fibular segments in the mandible. Although virtual surgical planning has been utilized in preoperative decision making, current software designs require manual operation and a trial-and-error process to refine the reconstruction plan. We have developed volumetric fibular transfer simulation software that can quickly design a preoperative plan based on direct volume manipulation and quantitative comparison with the patient's original mandible. We propose three quantitative shape indicators-volume ratio, contour error, and maximum projection-for symmetrical lesions of the mandible, and have implemented a parallel computation algorithm for the semiautomatic placement of fibular segments. Using this virtual planning software, we conducted a retrospective study of the computed tomography data from nine patients. We found that combining direct volume manipulation with real-time local search of placement improved the applicability of the planning system to optimize mandibular reconstruction.

Research on the Algorithm for Parallel Computing Based on Lifting Wavelet Transform

In this paper we proposed the new method of a lifting wavelet transform accoding to the characteristics of the parallel computing hardware units in practial application. We improved the mode of integer to construct a new 5/3 wavelet transform scheme .In order to validate the effectiveness of the proposed method applying the new method to the image and compare the result obtained using the traditional transform by the MSE evaluation. Experimental results show that the proposed method is superior and reducing the number of computations and the large capacity storage that restrict the implementation of algorithm for hardware.

Polynomial Basis Multiplier Using Cellular Systolic Architecture

ABSTRACTIn this study, we present a polynomial basis multiplication architecture based on cellular systolic hardware architecture for Montgomery multiplication over Galois fields by adopting a qualified Montgomery factor which is highly suitable for the design on our structures. At first, we propose a parallel computation algorithm which operates two independent computations. The algorithm is efficiently designed by reordering the sequence of the terms on the polynomial. Second, we construct an ideal architecture which is composed of two independent parts. Our architecture is possible to compute two parts simultaneously. Each part is composed of same cell structures so that it is easy to be generalized and scalable. Finally, we obtain a time-saved architecture in a large degree with high scalability.

MIXED VOLUME COMPUTATION IN PARALLEL

Efficient algorithms for computing mixed volumes, via the computation of mixed cells, have been implemented in DEMiCs [18] and MixedVol-2.0 [13]. While the approaches in those two packages are somewhat different, they follow the same theme and are both highly serial. To fit the need for the parallel computing, a reformulation of the algorithms is inevitable. This article proposes a reformulation of the algorithm for the mixed volume computation rooted from algorithms in graph theory, making it much more fine-grained and scalable. The resulting parallel algorithm can be readily adapted to both distributed and shared memory computing systems. Illustrated by the numerical results on several different architectures, the speedups of our parallel algorithms for the mixed volume computation are remarkable.

Complex Modeling of Matrix Parallel Algorithms

Parallel principles are the most effective way how to increase performance in parallel computing (parallel computers and algorithms too). In this sense the paper is devoted to a complex performance evaluation of matrix parallel algorithms (MPA). At first the paper describes the typical matrix parallel algorithms and then it summarizes common properties of them to complex performance modeling of MPA. To complex performance analysis we are able to take into account all overheads influence performance of parallel algorithms (parallel computer architecture, parallel computation, communication etc.). To be le to analyze MPA in their abstract form we have defined needed decomposition models of MPA. For these decomposition strategies we derived analytical relation for defined complex performance criterions including isoefficiency functions, which allow us to predict performance although for hypothetical parallel computer. In its experimental part the paper considers the achieved results using defined complex performance criterions including issoefficiency function for performance prediction also for hypothetical future parallel computers. Such idea of common abstract analysis could be very useful in deriving complex performance criterions for groups of other similar parallel algorithms (PA) as for example numerical integration PA, optimization PA etc.

Modeling of Communication Complexity in Parallel Computing

Parallel principles are the most effective way how to increase parallel computer performance and parallel algorithms (PA) too. Parallel using of more computing nodes (processors, cores), which have to cooperate each other in solving complex problems in a parallel way, opened imperative problem of modeling communication complexity so in symmetrical multiprocessors (SMP) based on motherboard as in other asynchronous parallel computers (computer networks, cluster etc.). In actually dominant parallel computers based on NOW and Grid (network of NOW networks) [31] there is necessary to model communication latency because it could be dominant at using massive (number of processors more than 100) parallel computers [17]. In this sense the paper is devoted to modeling of communication complexity in parallel computing (parallel computers and algorithms). At first the paper describes very shortly various used communication topologies and networks and then it summarized basic concepts for modeling of communication complexity and latency too. To illustrate the analyzed modeling concepts the paper considers in its experimental part the results for real analyzed examples of abstract square matrix and its possible decomposition models. These illustration examples we have chosen first due to wide matrix application in scientific and engineering fields and second from its typical exemplary representation for any other PA.

Параллельные вычисления автоматами на прямом и обратном остовах графа

The paper presents a parallel computation algorithm of an arbitrary function value on a multiset of values distributed on directed graph vertices. The computation is performed by message passing executed by automata distributed on the graph vertices. The key idea of the algorithm is to use a structural information on the graph that can be extracted by its parallel exploration and encoded into structures of direct and back spanning trees of the graph, which require only finite number of bits in each graph vertex, and to represent the function calculated as a composition of so called aggregate function and another one. Aggregate functions are characterized by possibility to calculate their value on a union of multisets by aggregating their values on separate multisets, that makes them easy for parallel computation.

Multiprocessor technologies of design for tasks of Monte – Karlo

The process of mathematical modeling of applied Monte-Carlo problems based on the use of multiprocessor computation system found further development in the paper. Operating experience of the first parallel systems has shown that their efficiency requires radical change of the structure of numerical methods. In this connection, the corresponding distributed algorithms were developed, the features of modeling applied problems based on multi-processor systems were identified and shown. Application of the developed approach provides a new way to consider the idea of computation parallelization and the use of cluster computation technologies. A modified algorithm for parallel computation using the Monte-Carlo method is proposed in the paper. Here, each computer has its own random number generator. In this case, the intermediate computations are carried out independently on different, individual cluster blades - “computers”, and the results are processed at any individual master-blade - “analyzer”. This allows to get rid of the indispensable presence of routercommunicator between the random number generator and “computer”. Obviously, this solution allows speeding up the computational process. The computational schemes that enhance the productivity and performance are given. The effectiveness of the proposed approach is illustrated by a comparative analysis of solution of some class of problems

Parallel algorithm for computation of second-order sequential best rotations

Algorithms for computing an approximate polynomial matrix eigenvalue decomposition of para-Hermitian systems have emerged as a powerful, generic signal processing tool. A technique that has shown much success in this regard is the sequential best rotation (SBR2) algorithm. Proposed is a scheme for parallelising SBR2 with a view to exploiting the modern architectural features and inherent parallelism of field-programmable gate array (FPGA) technology. Experiments show that the proposed scheme can achieve low execution times while requiring minimal FPGA resources.

Optimal control of switched systems and its parallel optimization algorithm

In this paper, a class of optimal switching control problems is considered in which the mode sequence of active subsystems and the number of mode switchings are not pre-specified, and both the switching sequence and the control inputs are to be chosen such that the cost functional is minimized. For solving this problem, we discuss the necessary conditions for optimality and the construction method for suboptimal solutions, and develop a few sufficient conditions of judgment on the optimal or suboptimal solutions of the switched system. According to the sufficient conditions, a parallel computational algorithm is constructed to find optimal or suboptimal solutions. For illustration, two examples are solved using the proposed algorithm.

Massively parallel Monte Carlo for many-particle simulations on GPUs

Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little attention because of the inherent serial nature of the statistical sampling. In this paper, we present a massively parallel method that obeys detailed balance and implement it for a system of hard disks on the GPU. We reproduce results of serial high-precision Monte Carlo runs to verify the method. This is a good test case because the hard disk equation of state over the range where the liquid transforms into the solid is particularly sensitive to small deviations away from the balance conditions. On a Tesla K20, our GPU implementation executes over one billion trial moves per second, which is 148 times faster than on a single Intel Xeon E5540 CPU core, enables 27 times better performance per dollar, and cuts energy usage by a factor of 13. With this improved performance we are able to calculate the equation of state for systems of up to one million hard disks. These large system sizes are required in order to probe the nature of the melting transition, which has been debated for the last forty years. In this paper we present the details of our computational method, and discuss the thermodynamics of hard disks separately in a companion paper.