Speedup Ratio Research Articles

A novel MapReduce-based deep convolutional neural network algorithm

Deep convolutional neural networks (DCNNs), with their complex network structure and powerful feature learning and feature expression capabilities, have been remarkable successes in many large-scale recognition tasks. However, with the expectation of memory overhead and response time, along with the increasing scale of data, DCNN faces three non-rival challenges in a big data environment: excessive network parameters, slow convergence, and inefficient parallelism. To tackle these three problems, this paper develops a deep convolutional neural networks optimization algorithm (PDCNNO) in the MapReduce framework. The proposed method first pruned the network to obtain a compressed network in order to effectively reduce redundant parameters. Next, a conjugate gradient method based on modified secant equation (CGMSE) is developed in the Map phase to further accelerate the convergence of the network. Finally, a load balancing strategy based on regulate load rate (LBRLA) is proposed in the Reduce phase to quickly achieve equal grouping of data and thus improving the parallel performance of the system. We compared the PDCNNO algorithm with other algorithms on three datasets, including SVHN, EMNIST Digits, and ISLVRC2012. The experimental results show that our algorithm not only reduces the space and time overhead of network training but also obtains a well-performing speed-up ratio in a big data environment.

Multi-GPU implementation of a cellular automaton model for dendritic growth of binary alloy

A parallel three-dimensional (3D) cellular automaton (CA) model is developed for dendritic growth simulation during solidification of binary alloy. The CA model is implemented using the graphic processing unit (GPU). Compute Unified Device Architecture (CUDA) is combined with Message Passing Interface (MPI) to perform large-scale simulation on the multi-GPU architecture. A CUDA-Aware OpenMPI is used to reduce the communication cost between different GPU cards. The accuracy and the speedup ratio of the CA model are investigated. First, the simulated steady-state tip velocity under different undercooling is compared with the LGK analytical solution. Then, dendritic growth during directional solidification and equiaxed multi-dendrite growth are simulated. Dendritic growth simulation with a domain size up to 453 million grids is performed. Finally, the speedup ratio of the CA model using four GPUs is compared with that using four CPU processes via MPI, which leads to a maximal speedup ratio of 152.19. The developed CA model achieves high parallel performance compared with the MPI-based parallel model. The developed CA model is capable of predicting the columnar to equiaxed transition (CET) event during directional solidification. The results indicate that increasing cooling rate promotes the occurrence of the equiaxed dendrites in the melt ahead of the solidification front, and equiaxed dendrites are prone to nucleate in the columnar dendrite groove zone when a middle cooling rate is applied.

Three-dimensional discontinuous deformation analysis with explicit contact formulation and block-wise multicore CPU acceleration

In this study, an explicit three-dimensional discontinuous deformation analysis (3D-DDA) is parallelized. Using explicit contact force circumvents the open-close iteration and makes the global stiffness matrix block-diagonal. Post-judgment of contacts is split into two parts to unify the data access pattern, constant acceleration Newmark method is adopted to guarantee unconditional stability of time integration, and square-root-free Cholesky decomposition is adopted to solve small linear equations efficiently. To exploit the multicore CPU with few changes in code and achieve good modularity, block-wise parallelization is adopted, which can realize the full-stage parallelization with just several lines of OpenMP directives. There is no need to modify block specific algorithms, such as contact detection and block information update, for the proposed parallelization, which results in the most efficient parallelization scheme to date. Correctness and efficiency are validated using several numerical examples. The speed-up ratio of 5.0–6.5 is achieved on an 8-core CPU.

A Parallel Processing Approach to Dynamic Simulation of Ethylbenzene Process

Parallel computing has been developed for many years in chemical process simulation. However, existing research on parallel computing in dynamic simulation cannot take full advantage of computer performance. More and more applications of data-driven methods and increasing complexity in chemical processes need faster dynamic simulators. In this research, we discuss the upper limit of speed-up for dynamic simulation of the chemical process. Then we design a parallel program considering the process model solving sequence and rewrite the General dynamic simulation & optimization system (DSO) with two levels of parallelism, multithreading parallelism and vectorized parallelism. The dependency between subtasks and the characteristic of the hottest subroutines are analyzed. Finally, the accelerating effect of the parallel simulator is tested based on a 500 kt·a−1 ethylbenzene process simulation. A 5-hour process simulation shows that the highest speed-up ratio to the original program is 261%, and the simulation finished in 70.98 s wall clock time.

Architecture design and performance analysis of a novel memory system for high-bandwidth onboard switching fabric

The development of the space–air–ground integration has put higher demands on satellite network. It needs to support high-bandwidth, large-capacity and various quality of service guarantees. However, the satellite onboard switching is facing the problem of resource constraints and special requirements of hardware complexity and scheduling efficiency. For this, this paper proposes a novel memory architecture for high-bandwidth onboard switching fabric. To reduce hardware complexity, multiplexer is used in the input side to merge k input ports into one internal bus, while the output demultiplexer splits an internal bus into k output links. Shared memory architecture is adopted in the input module to improve the memory efficiency, and a buffered crossbar is used to interconnect the input modules to the output modules. A discrete-time queuing model is formulated, and an iterative approach is used to quantitatively analyze the performance of the proposed architecture. The throughput and delay are calculated under different switch size, input load, and buffer capacity. The numerical results can serve as a guidance on deciding the required buffer size and appropriate speedup ratio. This work is validated by both simulations and FPGA implementations. Synthesize result show that using the state-of-the-art Xilinx VU13P FPGA, a switching fabric with 48 ports can be implemented and the peak throughput of the proposed architecture can reach 480 Gbps. Compared with existing combined input-crosspoint queuing, the proposed architecture can significantly reduce the packet delay and the memory resource cost.

A novel GPGPU-parallelized contact detection algorithm for combined finite-discrete element method

This paper presents a novel algorithm for contact detection for the three-dimensional combined finite-discrete element method (3D FDEM). The contact detection consists of two phases, neighbor search and fine search. Both phases are fully parallelized with Compute Unified Device Architecture (CUDA). In contrast to the non-binary search (NBS) algorithm, the proposed neighbor search algorithm is not sensitive to the element size distribution. To avoid the algorithm being performed at every step, an efficient GPGPU (general purpose graphic processing unit) -parallelized velocity reduction algorithm is employed. For the fine search, the concepts of “positive faces” and “positive edges” are proposed, and the process is considerably simplified and runs faster than the 3D separation axis algorithm. Numerical tests are performed to validate the efficiency and effectiveness of the proposed algorithms. The result shows that for both phases, the computation time is linearly proportional to the number of potential contact pairs regardless of the element size distribution. Furthermore, by using NVIDIA Telsa V100, the resultant overall speed-up ratios of the proposed contact detection algorithms relative to the original Y3D version for uniform and non-uniform element size distributions can reach up to 1982.6 and 13,894.7, respectively. For both quasi-static and dynamic problems, the simulated fracture patterns are in good agreement with the results generated by the NBS algorithm. The proposed methodology can be also employed for 2D FDEM and discrete element method (DEM).

An automatic partition-based parallel algorithm for grid-based distributed hydrological models

Parallel computing is a primary way to increase computing efficiency of grid-based distributed hydrological models. This study proposed an automatic partition-based parallel algorithm (APPA) to approach the theoretical maximum speedup ratio (TMSR). Through a combination of flexible partition for the domain decomposition and the load balance of parallel simulation, APPA optimizes the parallelization of hillslope and channel flow routing processes at sub-basin and channel unit level, respectively. To illustrate APPA's performance, we embedded it in a distributed ecohydrological model, and then applied the updated model to three watersheds at different spatial scales. The results indicate that APPA effectively promoted parallel performance. The estimated speedup ratio approached 93–97% of the TMSR for simulating hillslope processes and 91–98% of the TMSR for simulating channel processes using 26-threads in all three watersheds. These improvements justify that APPA is effective in accelerating model simulation and thus benefits future model-based research.

Parallel computing efficiency of SWAN 40.91

Abstract. Effective and accurate ocean and coastal wave predictions are necessary for engineering, safety and recreational purposes. Refining predictive capabilities is increasingly critical to reduce the uncertainties faced with a changing global wave climatology. Simulating WAves in the Nearshore (SWAN) is a widely used spectral wave modelling tool employed by coastal engineers and scientists, including for operational wave forecasting purposes. Fore- and hindcasts can span hours to decades, and a detailed understanding of the computational efficiencies is required to design optimized operational protocols and hindcast scenarios. To date, there exists limited knowledge on the relationship between the size of a SWAN computational domain and the optimal amount of parallel computational threads/cores required to execute a simulation effectively. To test the scalability, a hindcast cluster of 28 computational threads/cores (1 node) was used to determine the computation efficiencies of a SWAN model configuration for southern Africa. The model extent and resolution emulate the current operational wave forecasting configuration developed by the South African Weather Service (SAWS). We implemented and compared both OpenMP and the Message Passing Interface (MPI) distributing memory architectures. Three sequential simulations (corresponding to typical grid cell numbers) were compared to various permutations of parallel computations using the speed-up ratio, time-saving ratio and efficiency tests. Generally, a computational node configuration of six threads/cores produced the most effective computational set-up based on wave hindcasts of 1-week duration. The use of more than 20 threads/cores resulted in a decrease in speed-up ratio for the smallest computation domain, owing to the increased sub-domain communication times for limited domain sizes.

DRAC: a delta recurrent neural network-based arithmetic coding algorithm for edge computing

This paper develops an arithmetic coding algorithm based on delta recurrent neural network for edge computing devices called DRAC. Our algorithm is implemented on a Xilinx Zynq 7000 Soc board. We evaluate DRAC with four datasets and compare it with the state-of-the-art compressor DeepZip. The experimental results show that DRAC outperforms DeepZip and achieves 5X speedup ratio and 20X power consumption saving.

Research and application of SPH parallel algorithm based on particle decomposition

Smoothed Particle Hydrodynamics (SPH), as a typical meshless numerical method, has it advantage in modeling free surface flows. However, this method is computationally time-consuming. To resolve this problem, we propose a SPH parallel algorithm based on particle decomposition, which evenly distributes all particles to each process for calculation. In this circumstance, the functions including send, receive, and broadcast are called only once for each time step of communication, which is easy to implement and also has a good scalability. To verify the effectiveness of the proposed algorithm, we perform the numerical simulations of 2D dam-break flow and 3D droplet impact onto a liquid film. It is demonstrated that the proposed SPH parallel algorithm can significantly reduce the simulation time and has a massive advantage on 3D large-scale computation; the maximum speed-up ratio can up to 30 when the number of particles is more than million.

DBWGIE-MR: A density-based clustering algorithm by using the weighted grid and information entropy based on MapReduce

The main target of this paper is to design a density-based clustering algorithm using the weighted grid and information entropy based on MapReduce, noted as DBWGIE-MR, to deal with the problems of unreasonable division of data gridding, low accuracy of clustering results and low efficiency of parallelization in big data clustering algorithm based on density. This algorithm is implemented in three stages: data partitioning, local clustering, and global clustering. For each stage, we propose several strategies to improve the algorithm. In the first stage, based on the spatial distribution of data points, we propose an adaptive division strategy (ADG) to divide the grid adaptively. In the second stage, we design a weighted grid construction strategy (NE) which can strengthen the relevance between grids to improve the accuracy of clustering. Meanwhile, based on the weighted grid and information entropy, we design a density calculation strategy (WGIE) to calculate the density of the grid. And last, to improve the parallel efficiency, core clusters computing algorithm based on MapReduce (COMCORE-MR) are proposed to parallel compute the core clusters of the clustering algorithm. In the third stage, based on disjoint-set, we propose a core cluster merging algorithm (MECORE) to speed-up ratio the convergence of merged local clusters. Furthermore, based on MapReduce, a core clusters parallel merging algorithm (MECORE-MR) is proposed to get the clustering algorithm results faster, which improves the core clusters merging efficiency of the density-based clustering algorithm. We conduct the experiments on four synthetic clusters. Compared with H-DBSCAN, DBSCAN-MR and MR-VDBSCAN, the experimental results show that the DBWGIE-MR algorithm has higher stability and accuracy, and it takes less time in parallel clustering.

Supercritical Jet Modeled by a Hybrid Extended Corresponding States Method

In the framework of large eddy simulation, a supercritical jet has been modeled by using the extended corresponding states (ECS) method, the cubic Peng–Robinson (PR) equation of state, as well as the ideal gas law. The accuracy of ECS and PR was first verified for a binary mixture against the standard data. A zone-adaptive hybrid ECS/ideal method was developed to efficiently model the supercritical jet while maintaining accuracy, because most of the flow region can be approximately described by the ideal gas law. Quick expansion and local speedup driven by the drastic heating were observed during the development of the supercritical jet. By using the hybrid ECS method, the predictions are consistent with those calculated by the original ECS method, with a speedup ratio of 5–10 achieved. The hybrid ECS method was generalized by defining the expression formulas that describe the isosurface in the pressure–temperature–composition space for typical fuel mixtures.

Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project’ approach

AbstractA novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This ‘discretize‐then‐project’ approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the ROM level). These are two main advantages compared to existing approaches. The fully discrete FOM is obtained by a finite volume discretization of the incompressible Navier‐Stokes equations on a collocated grid, with a forward Euler time discretization. Two variants of the time discretization method, the inconsistent and consistent flux method, have been investigated. The latter leads to divergence‐free velocity fields, also on the ROM level, whereas the velocity fields are only approximately divergence‐free in the former method. For both methods, accurate results have been obtained for test cases with different types of boundary conditions: a lid‐driven cavity and an open‐cavity (with an inlet and outlet). The ROM obtained with the consistent flux method, having divergence‐free velocity fields, is slightly more accurate but also slightly more expensive to solve compared to the inconsistent flux method. The speedup ratio of the ROM and FOM computation times is the highest for the open cavity test case with the inconsistent flux method.

Machine learning tabulation of thermochemistry in turbulent combustion: An approach based on hybrid flamelet/random data and multiple multilayer perceptrons

A new machine learning methodology is proposed for speeding up thermochemistry computations in simulations of turbulent combustion. The approach is suited to a range of methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and the computation of laminar flames. In these methods, the chemical source term must be evaluated at every time step, and is often the most expensive element of a simulation. The proposed methodology has two main objectives: to offer enhanced capacity for generalisation and to improve the accuracy of the ANN prediction. To accomplish the first objective, we propose a hybrid flamelet/random data (HFRD) method for generating the training set. The random element endows the resulting ANNs with increased capacity for generalisation. Regarding the second objective, a multiple multilayer perceptron (MMP) approach is developed where different multilayer perceptrons (MLPs) are trained to predict states that result in smaller or larger composition changes, as these states feature different dynamics. It is shown that the multiple MLP method can greatly reduce the prediction error, especially for states yielding small composition changes. The approach is used to simulate flamelets of varying strain rates, one-dimensional premixed flames with differential diffusion and varying equivalence ratio, and finally the Large Eddy Simulation (LES) of CH4/air piloted flames Sandia D, E and F, which feature different levels of local extinction. The simulation results show very good agreement with those obtained from direct integration, while the range of problems simulated indicates that the approach has great capacity for generalisation. Finally, a speed-up ratio of 12 is attained for the reaction step.

An Efficient Time-Domain Electromagnetic Algorithm Based on LSTM Neural Network

Although neural networks have been applied in many fields since they were first introduced, the feasibility of applying it to predict the solution of Maxwell's equations remains open. In this letter, we investigate the feasibility of utilizing the long- and short-term memory (LSTM) neural network to solve the time-domain electromagnetic (TDEM) forward problems. With ground truth datasets being generated from the finite-difference time-domain (FDTD) method, a novel LSTM-TDEM model structure is proposed, and trained by a new feasible algorithm specifically designed for time-domain simulation. The strong approximation ability of the LSTM-TDEM method can accurately predict the electromagnetic field distributions for topologies of different geometries, materials, and excitations at different locations. The effectiveness of the proposed LSTM-TDEM method has been validated by several numerical experiments. The average relative error can be as small as 0.63% for 2-D case and 0.35% for 3-D case. It is worth noting that the training data are only 5% (198/4087) and 30% (660/2189) in 2-D and 3-D cases, respectively. Meanwhile, compared with the traditional FDTD method, the proposed method greatly reduces the calculation time, with its speedup ratio more than 1800 and 44 000 times over the FDTD method in 2-D and 3-D cases, respectively.

Exploiting sequential dilution of precision for a general framework of PPP convergence period evaluation

The convergence period is of critical significance in Precise Point Positioning (PPP) applications. Current criterion for determining PPP convergence period is by comparing the positioning error to the ground truth. This experiment-based criterion can be influenced by many factors like the accuracy of ephemeris and the test area. One can hardly get a consistent result of the convergence period without abundant experiments. Consequently, the criterion is not suitable for global-wide PPP specification determination and relevant GNSS service design. In response, we build a new framework of PPP convergence period evaluation based on statistical analysis, with the definition of an indicator, Sequential Dilution of Precision (SDOP). The SDOP represents the propagation from measurement errors to the filter-derived positioning errors. And the framework is established based on SDOP to connect the measurement error, confidential probability, and PPP convergence period. Furthermore, the impact factors of PPP convergence are classified into three parts, satellite geometry, satellite movement, and un-modeled measurement error, which enables researchers to focus on a specific property for analysis. Specifically, the satellite movement can be described by DOP, and we further define the Speed-Up Ratio (SUR) to represent satellite movement. The SDOP is influenced by both DOP and SUR. The proposed framework and relevant variables are examined with both real data and simulated GNSS and Low Earth Orbit (LEO) data. The results are in good agreement with public recognition. Moreover, as an example usage, the global maps of PPP convergence period are presented using the new framework, which are almost impossible to be given with traditional experiment-based criterion. The variation of PPP convergence period through latitude, longitude, and positioning directions is clearly exhibited. The plots can play a significant part in PPP analysis and GNSS service design.

A high-order implicit least square-based finite difference-finite volume method for incompressible flows on unstructured grids

In this study, a high-order implicit least squares-based finite difference-finite volume (ILSFD-FV) method with a lattice Boltzmann flux solver is presented for the simulation of two-dimensional incompressible flows on unstructured grids. In this method, a high-order polynomial based on Taylor series expansion is applied within each control cell, where the unknown spatial derivatives at each cell center are approximated by the least squares-based finite difference scheme. The volume integral of the high-order polynomial over the control cell results in a pre-multiplied coefficient matrix in the time-dependent term. This makes the high-order method be implicit in nature. With this feature, a high-order implicit Runge–Kutta time integration scheme, namely, the explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) scheme, is applied to obtain the time-accurate solutions for flow problems. The non-linear system of equations arising from each ESDIRK stage except for the first explicit stage is solved by a dual time stepping approach. A matrix-free lower-upper symmetric Gauss–Seidel solver is then used to efficiently march the solution in the pseudo time. The present high-order ILSFD-FV method is verified and validated by both steady and unsteady 2D incompressible flow problems. Numerical results indicate that the developed implicit method outperforms its explicit counterpart in terms of the convergence property and computational efficiency. The speedup ratio of the computational effort is about 3–22.

Optimization based on LLVM global instruction selection

Instruction selection is a key component of code generation. High-quality instruction selection has a great impact on the size and quality of the generated code. The existing instruction selection technology is mostly limited to a single statement or a single basic block, and the global instruction selection based on LLVM degrades the entire function in the form of SSA. Global instruction selection optimization based on LLVM is implemented on Shenwei platform, including global instruction merge optimization based on cost model, register bank selection optimization and instruction locality optimization. Through the test of SPEC CPU2006, Experimental results show that the average speed-up ratio before and after the optimization of global instruction selection based on LLVM is 1.08, and the maximum speed-up ratio is 1.36. In addition, when the quality of the generated code is equivalent, the global instruction selection is compared with the default instruction selection, the LLC compilation speed is increased by an average of 20%, and the entire compilation cycle is increased by an average of 6%-8%.

Research on GPU parallel algorithm for direct numerical solution of two-dimensional compressible flows

In this paper, a novel parallel algorithm is proposed to solve the problems of heavy computation and long simulation time in the field of compressible flows. In this algorithm, a third-order upwind scheme and a fourth-order central difference scheme are employed, with a third-order Runge-Kutta method for time stepping. Considering the powerful floating-point computing ability of the Graphics Processing Unit (GPU), this paper establishes the algorithm on the basis of GPU. Moreover, the direct numerical simulation method is adopted in this algorithm to improve the solution accuracy of the simulation results. To further enhance the efficiency of the algorithm, several optimization strategies are explored in the design of the algorithm as well. Both accuracy and feasibility of the algorithm are verified by a classical two-dimensional example. Compared with solving this example on the Central Processing Unit platform, the experimental results demonstrate that the maximum speedup ratio achieved by our approach is 18.03 times.

Improvement of Superconducting Linear Acceleration System for Pellet Injection: Optimization of Current Profile

The improvement of the acceleration performance of a superconducting linear acceleration (SLA) system for injecting the pellet container into the helical fusion reactor has been investigated numerically. To this end, a numerical code used in the finite element method and the non-dominated sorting genetic algorithms-II has been developed for analyzing both the shielding current density in an HTS film and the dynamic motion of the film. In addition, the current profile of the acceleration coil is optimized by the normalized Gaussian network (NGnet) method. The results of the computations show that when the current profile of the outer coil is optimized by using the NGnet method, the pellet velocity is greatly faster than that for the homogeneous current profile. Moreover, the speedup ratio decreases monotonously as the coil length increases. If the length of the outer coil is more than twice that of the inner coil, the number of the filaments outside the inner coil reduces extremely. This result means that the amount of the filament and the energy consumption can be reduced compared with the homogeneous current profile.