Sustaining a large fraction of single GPU performance in parallel computations is considered to be the major problem of GPU-based clusters. In this article, this topic is addressed in the context of a lattice Boltzmann flow solver that is integrated in the WaLBerla software framework. We propose a multi-GPU implementation using a block-structured MPI parallelization, suitable for load balancing and heterogeneous computations on CPUs and GPUs. The overhead required for multi-GPU simulations is discussed in detail and it is demonstrated that the kernel performance can be sustained to a large extent. With our GPU implementation, we achieve nearly perfect weak scalability on InfiniBand clusters. However, in strong scaling scenarios multi-GPUs make less efficient use of the hardware than IBM BG/P and x86 clusters. Hence, a cost analysis must determine the best course of action for a particular simulation task. Additionally, weak scaling results of heterogeneous simulations conducted on CPUs and GPUs simultaneously are presented using clusters equipped with varying node configurations.
In this paper, we study various parallelization schemes for the Variable Neighborhood Search (VNS) metaheuristic on a CPU-GPU system via OpenMP and OpenACC. A hybrid parallel VNS method is applied to recent benchmark problem instances for the multi-product dynamic lot sizing problem with product returns and recovery, which appears in reverse logistics and is known to be NP-hard. We report our findings regarding these parallelization approaches and present promising computational results.
t-SNE remains one of the most popular embedding techniques for visualizing high-dimensional data. Most standard packages of t-SNE, such as scikit-learn, use the Barnes-Hut t-SNE (BH t-SNE) algorithm for large datasets. However, existing CPU implementations of this algorithm are inefficient. In this work, we accelerate the BH t-SNE on CPUs via cache optimizations, SIMD, parallelizing sequential steps, and improving parallelization of multithreaded steps. Our implementation (Acc-t-SNE) is up to 261x and 4x faster than scikit-learn and the state-of-the-art BH t-SNE implementation from daal4py, re…
We modified a MPI-friendly density functional theory (DFT) source code within hybrid parallelization including CUDA. Our objective is to find out how simple conversions within the hybrid parallelization with mid-range GPUs affect DFT code not originally suitable to CUDA. We settled several rules of hybrid parallelization for numerical-atomic-orbital (NAO) DFT codes. The test was performed on a magnetite material system with OpenMX code by utilizing a hardware system containing 2 Xeon E5606 CPUs and 2 Quadro 4000 GPUs. 3-way hybrid routines obtained a speedup of 7.55 while 2-way hybrid speedup …
The standard RSA relies on multiple big-number modular exponentiation operations and longer key-length is required for better protection. This imposes a hefty time penalty for encryption and decryption. In this study, we analyzed and developed an improved parallel algorithm (PMKRSA) based on the idea of splitting the plaintext into multiple chunks and encrypt the chunks using multiple key-pairs. The algorithm in our new scheme is so natural for parallelized implementation that we also investigated its parallelization in a GPU environment. In the following, the structure of our new scheme is ou…
The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these benefits, it has been necessary to reformulate some of the most fundamental algorithms, including the Verlet list, pair searching and cut-offs. Here, we present the heterogeneous parallelization and acceleration design of molecular dynamics implemented in the GROMACS codebase over the last decade. The setup involves a general cluster-based approach to pair …
We present new algorithms for the parallelization of Eulerian-Lagrangian interaction operations in the immersed boundary method. Our algorithms rely on two well-studied parallel primitives: key-value sort and segmented reduce. The use of these parallel primitives allows us to implement our algorithms on both graphics processing units (GPUs) and on other shared memory architectures. We present strong and weak scaling tests on problems involving scattered points and elastic structures. Our tests show that our algorithms exhibit near-ideal scaling on both multicore CPUs and GPUs.
In this paper, we demonstrate how GPU-accelerated BEM routines can be used in a simple black-box fashion to accelerate fast boundary element formulations based on Hierarchical Matrices (H-Matrices) with ACA (Adaptive Cross Approximation). In particular, we focus on the expensive evaluation of the discrete weak form of boundary operators associated with the Laplace and the Helmholtz equation in three space dimensions. The method is based on offloading the CPU assembly of elements during the ACA assembly onto a GPU device and to use threading strategies across ACA blocks to create sufficient wor…
We investigate and characterize the performance of an important class of operations on GPUs and Many Integrated Core (MIC) architectures. Our work is motivated by applications that analyze low-dimensional spatial datasets captured by high resolution sensors, such as image datasets obtained from whole slide tissue specimens using microscopy image scanners. We identify the data access and computation patterns of operations in object segmentation and feature computation categories. We systematically implement and evaluate the performance of these core operations on modern CPUs, GPUs, and MIC syst…
Triple DES (3DES) is a standard fundamental encryption algorithm, used in several electronic payment applications and web browsers. In this paper, we propose a parallel implementation of 3DES on GPU. Since 3DES encrypts data with 64-bit blocks, our approach considers each 64-bit block a kernel block and assign a separate thread to process each bit. Algorithm's permutation operations, XOR operations, and S-box operations are done in parallel within these kernel blocks. The implementation benefits from the use of constant and shared memory types to optimize memory access. The results show an ave…
To effectively control large-scale distributed systems online, model predictive control (MPC) has to swiftly solve the underlying high-dimensional optimization. There are multiple techniques applied to accelerate the solving process in the literature, mainly attributed to software-based algorithmic advancements and hardware-assisted computation enhancements. However, those methods focus on arithmetic accelerations and overlook the benefits of the underlying system's structure. In particular, the existing decoupled software-hardware algorithm design that naively parallelizes the arithmetic oper…
B-spline based orbital representations are widely used in Quantum Monte Carlo (QMC) simulations of solids, historically taking as much as 50% of the total run time. Random accesses to a large four-dimensional array make it challenging to efficiently utilize caches and wide vector units of modern CPUs. We present node-level optimizations of B-spline evaluations on multi/many-core shared memory processors. To increase SIMD efficiency and bandwidth utilization, we first apply data layout transformation from array-of-structures to structure-of-arrays (SoA). Then by blocking SoA objects, we optimiz…
Currently, multi/many-core CPUs are considered standard in most types of computers including, mobile phones, PCs or supercomputers. However, the parallelization of applications as well as refactoring/design of applications for efficient hardware usage remains restricted to experts who have advanced technical knowledge and who can invest time tuning their software. In this context, the compilation community has proposed different methods for automatic parallelization, but their focus is traditionally on loops and nested loops with the support of polyhedral techniques. In this study, we propose …
Optimizing the performance of stencil algorithms has been the subject of intense research over the last two decades. Since many stencil schemes have low arithmetic intensity, most optimizations focus on increasing the temporal data access locality, thus reducing the data traffic through the main memory interface with the ultimate goal of decoupling from this bottleneck. There are, however, only few approaches that explicitly leverage the shared cache feature of modern multicore chips. If every thread works on its private, separate cache block, the available cache space can become too small, an…
The parallelization, design and scalability of the \sky code to search for periodic gravitational waves from rotating neutron stars is discussed. The code is based on an efficient implementation of the F-statistic using the Fast Fourier Transform algorithm. To perform an analysis of data from the advanced LIGO and Virgo gravitational wave detectors' network, which will start operating in 2015, hundreds of millions of CPU hours will be required - the code utilizing the potential of massively parallel supercomputers is therefore mandatory. We have parallelized the code using the Message Passing …
This paper introduces a novel approach to automatic ahead-of-time (AOT) parallelization and optimization of sequential Python programs for execution on distributed heterogeneous platforms. Our approach enables AOT source-to-source transformation of Python programs, driven by the inclusion of type hints for function parameters and return values. These hints can be supplied by the programmer or obtained by dynamic profiler tools; multi-version code generation guarantees the correctness of our AOT transformation in all cases. Our compilation framework performs automatic parallelization and sophis…
The Atmospheric General Circulation Model (AGCM) has been an important research tool in the study of climate change for decades. As the demand for high-resolution simulation is becoming urgent, the scalability and simulation efficiency is faced with great challenges, especially for the latitude-longitude mesh-based models. In this paper, we propose a highly scalable 3D atmospheric general circulation model based on leap-format, namely AGCM-3DLF. Firstly, it utilizes a 3D decomposition method allowing for parallelism release in all three physical dimensions. Then the leap-format difference comp…
We carry out a comparative performance study of multi-core CPUs, GPUs and Intel Xeon Phi (Many Integrated Core - MIC) with a microscopy image analysis application. We experimentally evaluate the performance of computing devices on core operations of the application. We correlate the observed performance with the characteristics of computing devices and data access patterns, computation complexities, and parallelization forms of the operations. The results show a significant variability in the performance of operations with respect to the device used. The performances of operations with regular…
This paper presents two conceptually simple methods for parallelizing a Parallel Tempering Monte Carlo simulation in a distributed volunteer computing context, where computers belonging to the general public are used. The first method uses conventional multi-threading. The second method uses CUDA, a graphics card computing system. Parallel Tempering is described, and challenges such as parallel random number generation and mapping of Monte Carlo chains to different threads are explained. While conventional multi-threading on CPUs is well-established, GPGPU programming techniques and technologi…
Understanding and optimizing the properties of solar cells is becoming a key issue in the search for alternatives to nuclear and fossil energy sources. A theoretical analysis via numerical simulations involves solving Maxwell's Equations in discretized form and typically requires substantial computing effort. We start from a hybrid-parallel (MPI+OpenMP) production code that implements the Time Harmonic Inverse Iteration Method (THIIM) with Finite-Difference Frequency Domain (FDFD) discretization. Although this algorithm has the characteristics of a strongly bandwidth-bound stencil update schem…
In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several image processing operations. In the IWPP, data elements in the wavefront propagate waves to their neighboring elements on a grid if a propagation condition is satisfied. Elements receiving the propagated waves become part of the wavefront. This pattern results in irregular data accesses and computations. We develop and evaluate strategies for efficient computati…
High fidelity Computational Fluid Dynamics simulations are generally associated with large computing requirements, which are progressively acute with each new generation of supercomputers. However, significant research efforts are required to unlock the computing power of leading-edge systems, currently referred to as pre-Exascale systems, based on increasingly complex architectures. In this paper, we present the approach implemented in the computational mechanics code Alya. We describe in detail the parallelization strategy implemented to fully exploit the different levels of parallelism, tog…
Current AMR simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient parallelization and memory management. We have attempted to employ new techniques to achieve both of these goals. Patch or grid based AMR often employs ghost cells to decouple the hyperbolic advances of each grid on a given refinement level. This decoupling allows each grid to be advanced independently. In AstroBEAR we utilize this independence by threading the grid advances on each le…
The flexible flow shop scheduling problem is an NP-hard problem and it requires significant resolution time to find optimal or even adequate solutions when dealing with large size instances. Thus, this paper proposes a dual island genetic algorithm consisting of a parallel cellular model and a parallel pseudo model. This is a two-level parallelization highly consistent with the underlying architecture and is well suited for parallelizing inside or between GPUs and a multi-core CPU. At the higher level, the efficiency of island GAs is improved by exploring new regions within the search space ut…
Ant Colony Optimisation (ACO) is an effective population-based meta-heuristic for the solution of a wide variety of problems. As a population-based algorithm, its computation is intrinsically massively parallel, and it is there- fore theoretically well-suited for implementation on Graphics Processing Units (GPUs). The ACO algorithm comprises two main stages: Tour construction and Pheromone update. The former has been previously implemented on the GPU, using a task-based parallelism approach. However, up until now, the latter has always been implemented on the CPU. In this paper, we discuss sev…
In this work we use the GPU porting task for the operative Japanese weather prediction model "ASUCA" as an opportunity to examine productivity issues with OpenACC when applied to structured grid problems. We then propose "Hybrid Fortran", an approach that combines the advantages of directive based methods (no rewrite of existing code necessary) with that of stencil DSLs (memory layout is abstracted). This gives the ability to define multiple parallelizations with different granularities in the same code. Without compromising on performance, this approach enables a major reduction in the code c…
We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for \textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search…
Researchers working on the automatic parallelization of programs have long known that too much parallelism can be even worse for performance than too little, because spawning a task to be run on another CPU incurs overheads. Autoparallelizing compilers have therefore long tried to use granularity analysis to ensure that they only spawn off computations whose cost will probably exceed the spawn-off cost by a comfortable margin. However, this is not enough to yield good results, because data dependencies may \emph{also} limit the usefulness of running computations in parallel. If one computation…
Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art deep learning model for representation learning on graphs. It is challenging to accelerate training of GCNs, due to (1) substantial and irregular data communication to propagate information within the graph, and (2) intensive computation to propagate information along the neural network layers. To address these challenges, we design a novel accelerator for training GCNs on CPU-FPGA heterogeneous systems, by incorporating multiple algorithm-architecture co-optimizations. We first analyze the computation and communication c…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient parallelization and memory management. We have attempted to employ new techniques to achieve both of these goals. Patch or grid based AMR often employs ghost cells to decouple the hyperbolic advances of each grid on a given refinement level. This decoupling allows each grid to be advanced independently. In AstroBEAR we utilize this independence by threading t…
Convolutional Neural Networks (CNNs) have shown to be powerful classification tools in tasks that range from check reading to medical diagnosis, reaching close to human perception, and in some cases surpassing it. However, the problems to solve are becoming larger and more complex, which translates to larger CNNs, leading to longer training times that not even the adoption of Graphics Processing Units (GPUs) could keep up to. This problem is partially solved by using more processing units and distributed training methods that are offered by several frameworks dedicated to neural network traini…
Similarity search in high-dimentional spaces is a pivotal operation found a variety of database applications. Recently, there has been an increase interest in similarity search for online content-based multimedia services. Those services, however, introduce new challenges with respect to the very large volumes of data that have to be indexed/searched, and the need to minimize response times observed by the end-users. Additionally, those users dynamically interact with the systems creating fluctuating query request rates, requiring the search algorithm to adapt in order to better utilize the un…
Prony's method is a standard tool exploited for solving many imaging and data analysis problems that result in parameter identification in sparse exponential sums $$f(k)=\sum_{j=1}^{T}c_{j}e^{-2πi\langle t_{j},k\rangle},\quad k\in \mathbb{Z}^{d},$$ where the parameters are pairwise different $\{ t_{j}\}_{j=1}^{M}\subset [0,1)^{d}$, and $\{ c_{j}\}_{j=1}^{M}\subset \mathbb{C}\setminus \{ 0\}$ are nonzero. The focus of our investigation is on a Prony's method variant based on a multivariate matrix pencil approach. The method constructs matrices $S_{1}$, \ldots , $S_{d}$ from the sampling values,…
In this project, the goal was to use the Julia programming language and parallelization to write a fast map reduce algorithm to count word frequencies across large numbers of documents. We first implement the word frequency counter algorithm on a CPU using two processes with MPI. Then, we create another implementation, but on a GPU using the Julia CUDA library, though not using the in built map reduce algorithm within FoldsCUDA.jl. After doing this, we apply our CPU and GPU algorithms to count the frequencies of words in speeches given by Presidents George W Bush, Barack H Obama, Donald J Trum…
Manufacturers have been developing new graphics processing unit (GPU) nodes with large capacity, high bandwidth memory and very high bandwidth intra-node interconnects. This enables moving large amounts of data between GPUs on the same node at low cost. However, small packet bandwidths and latencies have not decreased which makes global dot products expensive. These characteristics favor a new kind of problem decomposition called "equation decomposition" rather than traditional domain decomposition. In this approach, each GPU is assigned one equation set to solve in parallel so that the freque…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In addition to that significant computational efficiency in memory requirement has been achieved using homogenization strategy. The algorithm has been integrated with versitile computing platform of MATLAB for ease of use and customization. The bottlenecking repetitive solution of the state equation has been solved using an optimized geometric multigrid approach along…
We study the factors affecting training time in multi-device deep learning systems. Given a specification of a convolutional neural network, our goal is to minimize the time to train this model on a cluster of commodity CPUs and GPUs. We first focus on the single-node setting and show that by using standard batching and data-parallel techniques, throughput can be improved by at least 5.5x over state-of-the-art systems on CPUs. This ensures an end-to-end training speed directly proportional to the throughput of a device regardless of its underlying hardware, allowing each node in the cluster to…
The clustering coefficient and the transitivity ratio are concepts often used in network analysis, which creates a need for fast practical algorithms for counting triangles in large graphs. Previous research in this area focused on sequential algorithms, MapReduce parallelization, and fast approximations. In this paper we propose a parallel triangle counting algorithm for CUDA GPU. We describe the implementation details necessary to achieve high performance and present the experimental evaluation of our approach. Our algorithm achieves 8 to 15 times speedup over the CPU implementation and is c…
In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used at the top level and graphic processors for massive computing. For solving problems of cluster analysis on GPUs the nearest neighbor method (NNM) is developed. This algorithm allows us to handle up to 2 millions records with number of features up to 25. Since sequential and parallel algorithms are fundamentally different, it is difficult to compare the comput…
The High Energy Physics (HEP) experiments, such as those at the Large Hadron Collider (LHC), traditionally consume large amounts of CPU cycles for detector simulations and data analysis, but rarely use compute accelerators such as GPUs. As the LHC is upgraded to allow for higher luminosity, resulting in much higher data rates, purely relying on CPUs may not provide enough computing power to support the simulation and data analysis needs. As a proof of concept, we investigate the feasibility of porting a HEP parameterized calorimeter simulation code to GPUs. We have chosen to use FastCaloSim, t…
