Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Pseudo-marginal algorithms with multiple CPUs

The emergence of pseudo-marginal algorithms has led to improved computational efficiency for dealing with complex Bayesian models with latent variables. Here an unbiased estimator of the likelihood replaces the true likelihood in order to produce a Bayesian algorithm that remains on the marginal space of the model parameter (with latent variables integrated out), with a target distribution that is still the correct posterior distribution. Very efficient proposal distributions can be developed on the marginal space relative to the joint space of model parameter and latent variables. Thus psuedo-marginal algorithms tend to have substantially better mixing properties. However, for pseudo-marginal approaches to perform well, the likelihood has to be estimated rather precisely. This can be difficult to achieve in complex applications. In this paper we propose to take advantage of multiple central processing units (CPUs), that are readily available on most standard desktop computers. Here the likelihood is estimated independently on the multiple CPUs, with the ultimate estimate of the likelihood being the average of the estimates obtained from the multiple CPUs. The estimate remains unbiased, but the variability is reduced. We compare and contrast two different technologies that allow the implementation of this idea, both of which require a negligible amount of extra programming effort. The superior performance of this idea over the standard approach is demonstrated on simulated data from a stochastic volatility model.

Believe it or Not! Multicore CPUs can Match GPUs for FLOP-intensive Applications

In this work, we evaluate performance of a real-world image processing application that uses a cross-correlation algorithm to compare a given image with a reference one. The algorithm processes individual images represented as 2-dimensional matrices of single-precision floating-point values using O(n4) operations involving dot-products and additions. We implement this algorithm on a nVidia GTX 285 GPU using CUDA, and also parallelize it for the Intel Xeon (Nehalem) and IBM Power7 processors, using both manual and automatic techniques. Pthreads and OpenMP with SSE and VSX vector intrinsics are used for the manually parallelized version, while a state-of-the-art optimization framework based on the polyhedral model is used for automatic compiler parallelization and optimization. The performance of this algorithm on the nVidia GPU suffers from: (1) a smaller shared memory, (2) unaligned device memory access patterns, (3) expensive atomic operations, and (4) weaker single-thread performance. On commodity multi-core processors, the application dataset is small enough to fit in caches, and when parallelized using a combination of task and short-vector data parallelism (via SSE/VSX) or through fully automatic optimization from the compiler, the application matches or beats the performance of the GPU version. The primary reasons for better multi-core performance include larger and faster caches, higher clock frequency, higher on-chip memory bandwidth, and better compiler optimization and support for parallelization. The best performing versions on the Power7, Nehalem, and GTX 285 run in 1.02s, 1.82s, and 1.75s, respectively. These results conclusively demonstrate that, under certain conditions, it is possible for a FLOP-intensive structured application running on a multi-core processor to match or even beat the performance of an equivalent GPU version.

Compiler/Runtime Framework for Dynamic Dataflow Parallelization of Tiled Programs

Task-parallel languages are increasingly popular. Many of them provide expressive mechanisms for intertask synchronization. For example, OpenMP 4.0 will integrate data-driven execution semantics derived from the StarSs research language. Compared to the more restrictive data-parallel and fork-join concurrency models, the advanced features being introduced into task-parallelmodels in turn enable improved scalability through load balancing, memory latency hiding, mitigation of the pressure on memory bandwidth, and, as a side effect, reduced power consumption. In this article, we develop a systematic approach to compile loop nests into concurrent, dynamically constructed graphs of dependent tasks. We propose a simple and effective heuristic that selects the most profitable parallelization idiom for every dependence type and communication pattern. This heuristic enables the extraction of interband parallelism (cross-barrier parallelism) in a number of numerical computations that range from linear algebra to structured grids and image processing. The proposed static analysis and code generation alleviates the burden of a full-blown dependence resolver to track the readiness of tasks at runtime. We evaluate our approach and algorithms in the PPCG compiler, targeting OpenStream, a representative dataflow task-parallel language with explicit intertask dependences and a lightweight runtime. Experimental results demonstrate the effectiveness of the approach.

An algorithm for coarse particle sedimentation simulation by Stokesian dynamics

Coarse Particle sedimentation is studied by using an algorithm with no adjustable parameters based on stokesian dynamics. Only inter-particle interactions of hydrodynamic force and gravity are considered. The sedimentation of a simple cubic array of spheres is used to verify the computational results. The scaling and parallelism with OpenMP of the method are presented. Random suspension sedimentation is investigated with Mont Carlo simulation. The computational results are shown in good agreement with experimental fitting at the lower computational cost of O(N In N).

Introducción a los sistemas de cómputo paralelo

Duración (en horas): Más de 50 horas. Destinatario: Estudiante y Docente

Design and analysis of nucleic acid reaction pathways

Nucleic acids are a useful substrate for engineering at the molecular level. Designing the detailed energetics and kinetics of interactions between nucleic acid strands remains a challenge. Building on previous algorithms to characterize the ensemble of dilute solutions of nucleic acids, we present a design algorithm that allows optimization of structural features and binding energetics of a test tube of interacting nucleic acid strands. We extend this formulation to handle multiple thermodynamic states and combinatorial constraints to allow optimization of pathways of interacting nucleic acids. In both design strategies, low-cost estimates to thermodynamic properties are calculated using hierarchical ensemble decomposition and test tube ensemble focusing. These algorithms are tested on randomized test sets and on example pathways drawn from the molecular programming literature. To analyze the kinetic properties of designed sequences, we describe algorithms to identify dominant species and kinetic rates using coarse-graining at the scale of a small box containing several strands or a large box containing a dilute solution of strands.

Implementação paralelizada de métodos de resolução de sistemas algébricos na simulação de reservatórios de gás

Desde a década de 1960, devido à pertinência para a indústria petrolífera, a simulação numérica de reservatórios de petróleo tornou-se uma ferramenta usual e uma intensa área de pesquisa. O principal objetivo da modelagem computacional e do uso de métodos numéricos, para a simulação de reservatórios de petróleo, é o de possibilitar um melhor gerenciamento do campo produtor, de maneira que haja uma maximização na recuperação de hidrocarbonetos. Este trabalho tem como objetivo principal paralelizar, empregando a interface de programação de aplicativo OpenMP (Open Multi-Processing), o método numérico utilizado na resolução do sistema algébrico resultante da discretização da equação que descreve o escoamento monofásico em um reservatório de gás, em termos da variável pressão. O conjunto de equações governantes é formado pela equação da continuidade, por uma expressão para o balanço da quantidade de movimento e por uma equação de estado. A Equação da Difusividade Hidráulica (EDH), para a variável pressão, é obtida a partir deste conjunto de equações fundamentais, sendo então discretizada pela utilização do Método de Diferenças Finitas, com a escolha por uma formulação implícita. Diferentes testes numéricos são realizados a fim de estudar a eficiência computacional das versões paralelizadas dos métodos iterativos de Jacobi, Gauss-Seidel, Sobre-relaxação Sucessiva, Gradientes Conjugados (CG), Gradiente Biconjugado (BiCG) e Gradiente Biconjugado Estabilizado (BiCGStab), visando a uma futura aplicação dos mesmos na simulação de reservatórios de gás. Ressalta-se que a presença de heterogeneidades na rocha reservatório e/ou às não-linearidades presentes na EDH para o escoamento de gás aumentam a necessidade de métodos eficientes do ponto de vista de custo computacional, como é o caso de estratégias usando OpenMP.

地下水流动数值模拟的并行计算方法研究

Numerical modeling of groundwater is very important for understanding groundwater flow and solving hydrogeological problem. Today, groundwater studies require massive model cells and high calculation accuracy, which are beyond single-CPU computer’s capabilities. With the development of high performance parallel computing technologies, application of parallel computing method on numerical modeling of groundwater flow becomes necessary and important. Using parallel computing can improve the ability to resolve various hydro-geological and environmental problems. In this study, parallel computing method on two main types of modern parallel computer architecture, shared memory parallel systems and distributed shared memory parallel systems, are discussed. OpenMP and MPI (PETSc) are both used to parallelize the most widely used groundwater simulator, MODFLOW. Two parallel solvers, P-PCG and P-MODFLOW, were developed for MODFLOW. The parallelized MODFLOW was used to simulate regional groundwater flow in Beishan, Gansu Province, which is a potential high-level radioactive waste geological disposal area in China. 1. The OpenMP programming paradigm was used to parallelize the PCG (preconditioned conjugate-gradient method) solver, which is one of the main solver for MODFLOW. The parallel PCG solver, P-PCG, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. The largest test model has 1000 columns, 1000 rows and 1000 layers. Based on the timing results, execution times using the P-PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree. 2. P-MODFLOW, a domain decomposition–based model implemented in a parallel computing environment is developed, which allows efficient simulation of a regional-scale groundwater flow. The basic approach partitions a large model domain into any number of sub-domains. Parallel processors are used to solve the model equations within each sub-domain. The use of domain decomposition method to achieve the MODFLOW program distributed shared memory parallel computing system will process the application of MODFLOW be extended to the fleet of the most popular systems, so that a large-scale simulation could take full advantage of hundreds or even thousands parallel processors. P-MODFLOW has a good parallel performance, with the maximum speedup of 18.32 (14 processors). Super linear speedups have been achieved in the parallel tests, indicating the efficiency and scalability of the code. Parallel program design, load balancing and full use of the PETSc were considered to achieve a highly efficient parallel program. 3. The characterization of regional ground water flow system is very important for high-level radioactive waste geological disposal. The Beishan area, located in northwestern Gansu Province, China, is selected as a potential site for disposal repository. The area includes about 80000 km2 and has complicated hydrogeological conditions, which greatly increase the computational effort of regional ground water flow models. In order to reduce computing time, parallel computing scheme was applied to regional ground water flow modeling. Models with over 10 million cells were used to simulate how the faults and different recharge conditions impact regional ground water flow pattern. The results of this study provide regional ground water flow information for the site characterization of the potential high-level radioactive waste disposal.

The Shared Memory Parallelisation of an Ocean Modelling Code using an Interactive Parallelisation Toolkit

This paper briefly describes an interactive parallelisation toolkit that can be used to generate parallel code suitable for either a distributed memory system (using message passing) or a shared memory system (using OpenMP). This study focuses on how the toolkit is used to parallelise a complex heterogeneous ocean modelling code within a few hours for use on a shared memory parallel system. The generated parallel code is essentially the serial code with OpenMP directives added to express the parallelism. The results show that substantial gains in performance can be achieved over the single thread version with very little effort.

Using an interactive parallelisation toolkit to parallelise an ocean modelling code

This paper describes an interactive parallelisation toolkit that can be used to generate parallel code suitable for either a distributed memory system (using message passing) or a shared memory system (using OpenMP). This study focuses on how the toolkit is used to parallelise a complex heterogeneous ocean modelling code within a few hours for use on a shared memory parallel system. The generated parallel code is essentially the serial code with OpenMP directives added to express the parallelism. The results show that substantial gains in performance can be achieved over the single thread version with very little effort.

The semi-automatic parallelisation of scientific application codes using a computer aided parallelisation toolkit

The shared-memory programming model can be an effective way to achieve parallelism on shared memory parallel computers. Historically however, the lack of a programming standard using directives and the limited scalability have affected its take-up. Recent advances in hardware and software technologies have resulted in improvements to both the performance of parallel programs with compiler directives and the issue of portability with the introduction of OpenMP. In this study, the Computer Aided Parallelisation Toolkit has been extended to automatically generate OpenMP-based parallel programs with nominal user assistance. We categorize the different loop types and show how efficient directives can be placed using the toolkit's in-depth interprocedural analysis. Examples are taken from the NAS parallel benchmarks and a number of real-world application codes. This demonstrates the great potential of using the toolkit to quickly parallelise serial programs as well as the good performance achievable on up to 300 processors for hybrid message passing-directive parallelisations.

Parallel implementation of the recurrence method for computing the power-spectral density of thin avalanche photodiodes

A simulation program has been developed to calculate the power-spectral density of thin avalanche photodiodes, which are used in optical networks. The program extends the time-domain analysis of the dead-space multiplication model to compute the autocorrelation function of the APD impulse response. However, the computation requires a large amount of memory space and is very time consuming. We describe our experiences in parallelizing the code using both MPI and OpenMP. Several array partitioning schemes and scheduling policies are implemented and tested Our results show that the OpenMP code is scalable up to 64 processors on an SGI Origin 2000 machine and has small average errors.

Parallel bandwidth characteristics calculations for thin avalanche photodiodes on a SGI Origin 2000 supercomputer

An important factor for high-speed optical communication is the availability of ultrafast and low-noise photodetectors. Among the semiconductor photodetectors that are commonly used in today’s long-haul and metro-area fiber-optic systems, avalanche photodiodes (APDs) are often preferred over p-i-n photodiodes due to their internal gain, which significantly improves the receiver sensitivity and alleviates the need for optical pre-amplification. Unfortunately, the random nature of the very process of carrier impact ionization, which generates the gain, is inherently noisy and results in fluctuations not only in the gain but also in the time response. Recently, a theory characterizing the autocorrelation function of APDs has been developed by us which incorporates the dead-space effect, an effect that is very significant in thin, high-performance APDs. The research extends the time-domain analysis of the dead-space multiplication model to compute the autocorrelation function of the APD impulse response. However, the computation requires a large amount of memory space and is very time consuming. In this research, we describe our experiences in parallelizing the code in MPI and OpenMP using CAPTools. Several array partitioning schemes and scheduling policies are implemented and tested. Our results show that the code is scalable up to 64 processors on a SGI Origin 2000 machine and has small average errors.

Ion-Atom/Argon - Calculation of ionization cross sections by fast ion impact for neutral target atoms ranging from hydrogen to argon

A FORTRAN 90 program is presented which calculates the total cross sections, and the electron energy spectra of the singly and doubly differential cross sections for the single target ionization of neutral atoms ranging from hydrogen up to and including argon. The code is applicable for the case of both high and low Z projectile impact in fast ion-atom collisions. The theoretical models provided for the program user are based on two quantum mechanical approximations which have proved to be very successful in the study of ionization in ion-atom collisions. These are the continuum-distorted-wave (CDW) and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations. The codes presented here extend previously published. codes for single ionization of. target hydrogen [Crothers and McCartney, Comput. Phys. Commun. 72 (1992) 288], target helium [Nesbitt, O'Rourke and Crothers, Comput. Phys. Commun. 114 (1998) 385] and target atoms ranging from lithium to neon [O'Rourke, McSherry and Crothers, Comput. Phys. Commun. 131 (2000) 129]. Cross sections for all of these target atoms may be obtained as limiting cases from the present code. Title of program: ARGON Catalogue identifier: ADSE Program summary URL: http://cpc.cs.qub.ac.uk/cpc/summaries/ADSE Program obtainable from: CPC Program Library Queen's University of Belfast, N. Ireland Licensing provisions: none Computer for which the program is designed and others on which it is operable: Computers: Four by 200 MHz Pro Pentium Linux server, DEC Alpha 21164; Four by 400 MHz Pentium 2 Xeon 450 Linux server, IBM SP2 and SUN Enterprise 3500 Installations: Queen's University, Belfast Operating systems under which the program has been tested: Red-hat Linux 5.2, Digital UNIX Version 4.0d, AIX, Solaris SunOS 5.7 Compilers: PGI workstations, DEC CAMPUS Programming language used: FORTRAN 90 with MPI directives No. of bits in a word: 64, except on Linux servers 32 Number of processors used: any number Has the code been vectorized or parallelized? Parallelized using MPI No. of bytes in distributed program, including test data, etc.: 32 189 Distribution format: tar gzip file Keywords: Single ionization, cross sections, continuum-distorted-wave model, continuum- distorted-wave eikonal-initial-state model, target atoms, wave treatment Nature of physical problem: The code calculates total, and differential cross sections for the single ionization of target atoms ranging from hydrogen up to and including argon by both light and heavy ion impact. Method of solution: ARGON allows the user to calculate the cross sections using either the CDW or CDW-EIS [J. Phys. B 16 (1983) 3229] models within the wave treatment. Restrictions on the complexity of the program: Both the CDW and CDW-EIS models are two-state perturbative approximations. Typical running time: Times vary according to input data and number of processors. For one processor the test input data for double differential cross sections (40 points) took less than one second, whereas the test input for total cross sections (20 points) took 32 minutes. Unusual features of the program: none (C) 2003 Elsevier B.V All rights reserved.