OpenMP Approach Research Articles

Fast and Accurate Solution of Integral Formulations of Large MQS Problems Based on Hybrid OpenMP–MPI Parallelization

This paper proposes an optimal strategy to parallelize the solution of large 3D magneto-quasi-static (MQS) problems, by combining the MPI and OpenMP approaches. The studied numerical problem comes from a weak-form integral formulation of a MQS problem and is finally cast in terms of a large linear system to be solved by means of a direct method. For this purpose, two main tasks are identified: the assembly and the inversion of the matrices. The paper focuses on the optimization of the resources required for assembling the matrices, by exploiting the feature of a hybrid OpenMP–MPI approach. Specifically, the job is shared between clusters of nodes in parallel by adopting an OpenMP paradigm at the node level and a MPI one at the process level between nodes. Compared with other solutions, such as pure MPI, this hybrid parallelization optimizes the available resources, with respect to the speed, allocated memory, and the communication between nodes. These advantages are clearly observed in the case studies analyzed in this paper, coming from the study of large plasma fusion machines, such as the fusion reactor ITER. Indeed, the MQS problems associated with such applications are characterized by a huge computational cost that requires parallel computing approaches.

A parallel wavelet adaptive WENO scheme for 2D conservation laws

PurposeThe current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws.Design/methodology/approachThe serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax–Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge–Kutta method.FindingsThe parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach.Research limitations/implicationsThe resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value.Practical implicationsSo far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used.Social implicationsThis work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term experience in applied mathematics for industrial applications and the other in a starting process of international academic insertion. In this way, this scientific partnership has the potential of promoting further knowledge exchange, involving students and other collaborators.Originality/valueThe proposed methodology (use of OpenMP programming model for the wavelet adaptive splitting scheme) is original and contributes to a very active research area in the past years, namely, adaptive methods for conservation laws and their parallel formulations, which is of great interest for the entire scientific community.

ISPH modelling of an oscillating wave surge converter using an OpenMP-based parallel approach

Fluid–structure interactions occurring between a wave train and an oscillating wave surge converter (OWSC) are studied in this paper using smoothed particle hydrodynamics (SPH). SPH is an alternative numerical method to conventional computational fluid dynamics for studying complex free surface flows. A new open multi-processing (OpenMP)-based parallel SPH code is developed and tested on a wave impacting an OWSC. An incompressible SPH (ISPH) method is implemented here to avoid spurious pressure oscillations, and an OpenMP approach is employed due to its relative ease of coding. The simulation results show good agreement with the experimental data. The performance of the new parallel SPH code is also reported for the water surge from a canonical dam break impinging on a tall square structure.

Fast 2-D ultrasound strain imaging: the benefits of using a GPU

Deformation of tissue can be accurately estimated from radio-frequency ultrasound data using a 2-dimensional normalized cross correlation (NCC)-based algorithm. This procedure, however, is very computationally time-consuming. A major time reduction can be achieved by parallelizing the numerous computations of NCC. In this paper, two approaches for parallelization have been investigated: the OpenMP interface on a multi-CPU system and Compute Unified Device Architecture (CUDA) on a graphics processing unit (GPU). The performance of the OpenMP and GPU approaches were compared with a conventional Matlab implementation of NCC. The OpenMP approach with 8 threads achieved a maximum speed-up factor of 132 on the computing of NCC, whereas the GPU approach on an Nvidia Tesla K20 achieved a maximum speed-up factor of 376. Neither parallelization approach resulted in a significant loss in image quality of the elastograms. Parallelization of the NCC computations using the GPU, therefore, significantly reduces the computation time and increases the frame rate for motion estimation.

Fast 2-D ultrasound strain imaging: the benefits of using a GPU

Deformation of tissue can be accurately estimated from radio-frequency ultrasound data using a 2-dimensional normalized cross correlation (NCC)-based algorithm. This procedure, however, is very computationally time-consuming. A major time reduction can be achieved by parallelizing the numerous computations of NCC. In this paper, two approaches for parallelization have been investigated: the OpenMP interface on a multi-CPU system and Compute Unified Device Architecture (CUDA) on a graphics processing unit (GPU). The performance of the OpenMP and GPU approaches were compared with a conventional Matlab implementation of NCC. The OpenMP approach with 8 threads achieved a maximum speed-up factor of 132 on the computing of NCC, whereas the GPU approach on an Nvidia Tesla K20 achieved a maximum speed-up factor of 376. Neither parallelization approach resulted in a significant loss in image quality of the elastograms. Parallelization of the NCC computations using the GPU, therefore, significantly reduces the computation time and increases the frame rate for motion estimation.

Massively parallel regularized 3D inversion of potential fields on CPUs and GPUs

We have recently introduced a massively parallel regularized 3D inversion of potential fields data. This program takes as an input gravity or magnetic vector, tensor and Total Magnetic Intensity (TMI) measurements and produces 3D volume of density, susceptibility, or three dimensional magnetization vector, the latest also including magnetic remanence information. The code uses combined MPI and OpenMP approach that maps well onto current multiprocessor multicore clusters and exhibits nearly linear strong and weak parallel scaling. It has been used to invert regional to continental size data sets with up to billion cells of the 3D Earth's volume on large clusters for interpretation of large airborne gravity and magnetics surveys. In this paper we explain the features that made this massive parallelization feasible and extend the code to add GPU support in the form of the OpenACC directives. This implementation resulted in up to a 22x speedup as compared to the scalar multithreaded implementation on a 12 core Intel CPU based computer node. Furthermore, we also introduce a mixed single–double precision approach, which allows us to perform most of the calculation at a single floating point number precision while keeping the result as precise as if the double precision had been used. This approach provides an additional 40% speedup on the GPUs, as compared to the pure double precision implementation. It also has about half of the memory footprint of the fully double precision version.

Hybrid MPI-OpenMP Parallelization of Image Reconstruction

Perceptual coding should take full advantage of the results from human visual system (HVS) studies. In this paper, we exploit an image reconstruction algorithm, which can simply and reliably represent images using regional shape and texture information and effectually eliminate perceptual redundancy. But real-time application of the algorithm is limited due to its inherent complex and intensive computation. Therefore, we implement image reconstruction with a hybrid message passing interface (MPI) and OpenMP approach on the basis of a standard MPI implementation. Experimental results confirm our image reconstruction algorithm can get optimal restoration results. Compared with JPEG and JPEG2000 compression, this algorithm can not only get more coding gain but remain most information people care. Our hybrid MPI-OpenMP approach can significantly improve time performance of image reconstruction algorithm.

Performance Analysis of MatrixVector Multiplication in Hybrid 'MPI + OpenMP'

g of multiple tasks simultaneously on multiple processors is called Parallel Computing. The parallel program consists of multiple active processes simultaneously solving a given problem. Parallel computers can be roughly classified as Multi-Processor and Multi-Core. In both these classifications the hardware supports parallelism with computer node having multiple processing elements in a single machine, either in single chip pack or on more than one distinct chip respectively. Parallel programming is the ability of program to run on this infrastructure which is still quite difficult and complex task to achieve. Out of many two different approaches used in parallel environment are MPI and OpenMP, each one of them having their own merits and demerits. Hybrid model combines both approaches in the pursuit of reducing the weaknesses in individual. In proposed approach takes a pair of, Matrices produces another matrix by using Matrix-Vector Multiplication Algorithm. The resulting matrix agrees with the result of composition of the linear transformations represented by the two original matrices. This algorithm is implemented in MPI, OpenMP, and Hybrid mode. The algorithm is tested for number of nodes with different number of matrix size. The results indicates that the Hybrid approach out performs the MPI and OpenMP approach.

Hybrid MPI + OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

This work is devoted to the development of efficient parallel algorithms for the direct numerical simulation (DNS) of incompressible flows on modern supercomputers. In doing so, a Poisson equation needs to be solved at each time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is the part of the algorithm that is most difficult to parallelize. The Poisson solver presented here is restricted to problems with one uniform periodic direction. It is a combination of a block preconditioned Conjugate Gradient (PCG) and an FFT diagonalization. The latter decomposes the original system into a set of mutually independent 2D systems that are solved by means of the PCG algorithm. For the most ill-conditioned systems, that correspond to the lowest Fourier frequencies, the PCG is replaced by a direct Schur-complement based solver. The previous version of the Poisson solver was conceived for single-core (also dual-core) processors and therefore, the distributed memory model with message-passing interface (MPI) was used. The irruption of multi-core architectures motivated the use of a two-level hybrid MPI + OpenMP parallelization with the shared memory model on the second level. Advantages and implementation details for the additional OpenMP parallelization are presented and discussed in this paper. Numerical experiments show that, within its range of efficient scalability, the previous MPI-only parallelization is slightly outperformed by the MPI + OpenMP approach. But more importantly, the hybrid parallelization has allowed to significantly extend the range of efficient scalability. Here, the solver has been successfully tested up to 12800 CPU cores for meshes with up to 10 9 grid points. However, estimations based on the presented results show that this range can be potentially stretched up until 200,000 cores approximately. Finally, several examples of DNS simulations are briefly presented to illustrate some potential applications of the solver.

Performance Evaluation of a Multi-Zone Application in Different OpenMP Approaches

We describe a performance study of a multi-zone application benchmark implemented in several OpenMP approaches that exploit multi-level parallelism and deal with unbalanced workload. The multi-zone application was derived from the well-known NAS Parallel Benchmarks (NPB) suite that involves flow solvers on collections of loosely coupled discretization meshes. Parallel versions of this application have been developed using the Subteam concept and Workqueuing model as extensions to the current OpenMP. We examine the performance impact of these extensions to OpenMP and compare with hybrid and nested OpenMP approaches on several large parallel systems.

Hybrid MPI-OpenMP Programming for Parallel OSEM PET Reconstruction

To improve the parallel efficiency (PE) of the ordered-subsets expectation-maximization (OSEM) algorithm for three-dimensional (3-D) positron emission tomography (PET) image reconstruction, we focused on reducing the computational imbalance among parallel processes and interprocess data exchange time which were the dominant limiting factors of PE when a large number of networked compute nodes were used. As clusters with multiple processors on each compute node have become increasingly common, we have aimed to take advantage of the load-balancing mechanism and the inherently lower latency of shared memory threads across processors within a single node. We, therefore, implemented the OSEM algorithm with a hybrid message passing interface (MPI) and OpenMP approach on the basis of a standard MPI implementation. The contributing components to the total reconstruction time for the hybrid technique were quantified and compared to that using only MPI. The hybrid MPI-OpenMP technique achieved a consistent PE improvement of approximately 7% to 17% compared to the pure MPI approach on the same number of compute nodes. As clusters of larger shared-memory multiprocessor (SMP) machines continue to become more cost effective, we expect this hybrid MPI-OpenMP approach to be increasingly valuable

Parallelization and performance tuning of molecular dynamics code with OpenMP

An OpenMP approach was proposed to parallelize the sequential molecular dynamics (MD) code on shared memory machines. When a code is converted from the sequential form to the parallel form, data dependence is a main problem. A traditional sequential molecular dynamics code is anatomized to find the data dependence segments in it, and the two different methods, i. e., recover method and backward mapping method were used to eliminate those data dependencies in order to realize the parallelization of this sequential MD code. The performance of the parallelized MD code was analyzed by using some performance analysis tools. The results of the test show that the computing size of this code increases sharply form 1 million atoms before parallelization to 20 million atoms after parallelization, and the wall clock during computing is reduced largely. Some hot-spots in this code are found and optimized by improved algorithm. The efficiency of parallel computing is 30% higher than that of before, and the calculation time is saved and larger scale calculation problems are solved.