基于并行预处理算法的三维重力快速反演

随着地球物理设备和探测技术的不断发展,快速处理大规模地球物理数据的需求也随之增长。为了解决三维重力数据密度反演的耗时问题,提出一种并行的预处理共轭梯度算法来提高计算效率。本文分别采用两种不同的预处理算子通过组合模型数据反演进行测试比较,并利用迭代残差和计算用时共同评价其加速效果。结果表明：对称逐次超松弛预处理方法比对角预处理方法反演计算速度快,密度结果更贴近实际模型;与传统串行的共轭梯度算法相比,本文并行预处理快速算法可以获得近19倍的加速比。将该算法应用于美国Vinton盐丘的实测重力数据中,反演结果能够很好地圈定出岩体的位置,验证了本文并行预处理共轭梯度法在三维重力数据快速反演中的高效性和可行性。     

油藏精细地质模型网格粗化算法及其效果

在前人研究基础上, 根据DP(Dykstra-Parsons)系数能定量评价储层非均质性, 微网格块的渗透率值粗化后, 其等效渗透率的上、下限(C_min、C_max)能反映渗透率的各向异性的特点, 提出了一种运算速度快和相对有效的网格粗化算法。该算法能考虑到储层非均质性对不同方向渗透率值的影响, 且求解过程相对简单。应用该方法对鄂尔多斯盆地中部某油藏的陆相储层的精细地质模型进行了网格粗化计算, 然后在粗化后的模型上进行油藏数值模拟研究, 同时针对研究区地质背景和产出流体微可压缩的物性特征, 首次利用流线模拟器对精细地质模型进行了油藏数值模拟研究, 并以此结果为标准, 对该网格粗化算法时效性进行了系统评价。分析表明, 该算法具有较快的计算速度和较高的可靠性, 是解决储层非均质强、物性差的陆相成因油藏精细油藏数值模拟的一种行之有效的手段。      

大地电磁三维正演聚集多重网格算法

为了加快大地电磁三维正演的求解速度,本文将一种新型的代数多重网格算法——聚集多重网格（aggregation-based algebraic multigrid, AGMG）算法引入大地电磁三维正演模拟中。首先从准静态条件下的麦克斯韦方程出发,利用交错网格有限体积法进行离散,并采用第一类Dirichlet边界条件形成大型稀疏复线性方程组;然后阐述AGMG算法的粗化策略和套迭代技术,并实施3种不同的AGMG求解算法：1）传统的V循环AGMG算法;2）AGMG预处理共轭梯度（AGMG-CG）;3）AGMG预处理广义共轭残差法（AGMG-GCR）。最终实现大地电磁法三维正演模拟。对典型地电模型进行正演模拟,并与已有的大地电磁三维正反演程序（ModEM）进行结果对比,以验证本文算法的准确性。另外,不同剖分网格和极化方式正演模拟结果与准残量最小化（QMR）迭代算法的对比表明,AGMG预处理求解算法（AGMG-CG、AGMG-GCR）不仅能够改善算法的稳定性,而且能够快速有效地求解正演问题;其中AGMG-GCR迭代次数更少,求解速度更快,误差衰减曲线更光滑,在144×152×104网格剖分情况下,相对于现有ModEM程序能够提高十几倍的计算速度,尤其适合大规模大地电磁三维正演问题。     

二维输运方程高精度数值模拟

采用剖开算子法,把二维输运问题剖分为两个子初值问题(对流分步、扩散分步)。在任意三角形网格中,分别对不同性质的算子采用各自适合的算法,即采用特征线法求解对流分步,采用半隐式有限元法求解扩散分步。重点探讨了对流插值问题,给出了一种完全对称三次插值模式,有效地减少了数值阻尼。为了克服高阶插值数值震荡问题,计算中保证了函数及其一阶偏导数连续。算例表明,数值方法模拟结果与精确解吻合较好。该算法在求解输运方程(包括纯对流输运方程)时,既能有效减少数值阻尼,也能保证计算中不出现数值震荡。     

缓坡地形上非线性波浪变形的并行计算

基于椭圆型缓坡方程和消息传递接口机制,提出了缓坡地形上非线性波浪变形的一种并行数值模拟方法,并在微机群集并行系统上进行了数值实现.对一种典型缓坡地形上的非线性波浪传播变形进行了数值模拟,数值结果与实验数据的比较表明,在椭圆型缓坡方程中应用非线性波色散关系可有效考虑波浪的非线性效应,同时从获得的并行效率和并行加速比来看,并行数值方法可有效提高数值模拟效率.     

复杂地表起伏多重变加密网格有限差分法波动方程数值模拟

常规变加密网格有限差分波动方程数值模拟方法采用水平分层加密网格,该网格剖分策略在适应地形起伏和近地表速度结构变化特征方面效果较差。针对该问题,提出一种起伏多重变加密网格有限差分波动方程数值模拟方法。该方法根据地形起伏和近地表低速层到高速层的速度分布特征进行网格加密;采用不同网格中的变系数差分格式离散声波方程,在保证波场模拟精度的同时兼顾计算效率;同时,为了进一步保障地表附近波场模拟的精度,地表附近最细网格中的差分格式不做降阶处理,针对位于地表以上的虚像点的波场值,提出一种融入自由地表边界条件的法向虚像外推法。算例分析验证该算法对速度模型不同区域进行的网格多次加密显著提高了计算效率,以黄土塬实际模型为例,耗时为常规1 m×1 m网格耗时的43.3%,并可达到和细网格基本一致的模拟精度,模拟误差控制在10^-12范围内,同时表现出很好的近地表散射压制和边界吸收效果,且算法能稳定地适应实际复杂地表介质。     

无网格法中节点非均匀自动布置及背景网格生成

针对形状复杂的区域,提出了一种基于节点间距函数的非均匀节点自动布置和背景网格的生成算法。该算法对不规则区域适应能力强,节点可任意加密,无需人工干预,且有实现简单、耗时少等特点。这些自动布置的离散节点可直接用于无网格数值计算。用所布置的节点进一步生成背景网格简单易行且高效,生成的背景网格还可直接用来进行后置处理。     

基于MPI+OpenMP的时间域航空电磁快速正演算法

时间域有限元算法已被广泛应用于航空电磁三维正演模拟当中,然而由于航空电磁测区面积大,且采样密集,造成正演计算量巨大,传统的串行算法已经无法满足计算效率要求,为此,开展了并行加速算法研究以解决计算效率不足的问题。基于航空电磁系统的影响范围有限,采用局部网格技术将计算任务划分成多个子网格,即每个发射源一套网格,各网格的正演计算相互独立,不存在数据依赖性,具有很好的可并行性;利用MPI技术对多个子网格正演任务进行分配,在各个进程上进行并行计算;针对每个正演子网格,在进行时间域有限元算法正演模拟过程中,采用OpenMP技术对单元矩阵进行并行计算。典型地电模型的数值模拟结果表明本文开发的MPI+OpenMP并行正演算法可以有效提高正演速度,最高加速比可达10倍。     

基于高性能并行计算的隧道开挖数值模拟

随着岩土工程规模的不断扩大、复杂性的增加以及计算参数的多样化和计算精度的提高, 人们对于计算机计算能力的要求越来越高, 然而单处理器无法满足这类大规模计算.从数据输入、区域分解、线性方程组的迭代求解、后处理等方面详细阐述高性能计算平台上并行有限元求解大规模岩土工程的关键问题.提出了利用MPI2的新特性进行海量数据的分段并行读入, 采用ParMetis软件并行地进行区域分解, 实现了前处理过程的完全并行化; 采用基于Jacobi预处理技术的预处理共轭梯度法(PCG)进行线性方程组的并行迭代求解; 采用Paraview软件实现了后处理的并行可视化.在深腾7000系统上对某隧道工程的三维开挖过程进行了数值模拟, 对其并行性能进行了分析和评价, 验证了采用的区域分解算法和系统方程组的求解方法的可行性, 并且具有较高的加速比和并行效率.      

二维水动力模型的并行计算研究

建立了二维水动力并行模型;针对MPI不能实现进程迁移现状,自主开发了并行通讯平台,平台机群负载平衡采用基于蚁群算法的人工智能算法,并根据模型需要制定了相关通讯协议;对长江内江段进行数值模拟,结果表明当网格数一定时,存在一最优客户端数,当客户端数小于最优客户端数时,并行算法所需时间小于串行算法时间,并随着客户端数增加,所需时间也逐渐减少;反之,所需时间则逐渐增大。     

Parallel inexact constraint preconditioning for ill-conditioned consolidation problems

Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward because of their inherent sequentiality. The present paper describes a novel parallel inexact constraint preconditioner (ParICP) for the efficient solution of linear algebraic systems arising from the FE discretization of the coupled poro-elasticity equations. The ParICP implementation is based on the use of the block factorized sparse approximate inverse incomplete Cholesky preconditioner, which is a very recent and effective development for the parallel preconditioning of symmetric positive definite matrices. The ParICP performance is experimented with in real 3D coupled consolidation problems, proving a scalable and efficient implementation of the constraint preconditioning for high-performance computing. ParICP appears to be a very robust algorithm for solving ill-conditioned large-size coupled models in a parallel computing environment.     

基于EBE方法的三维有限元并行计算

在水利工程中,施工过程的模拟、动力的时域分析、开裂计算等,都对大规模并行计算提出了迫切的需求。然而,基于高斯消去的有限元直接解法,通常会占用大量的内存,并花费大量的CPU时间。而水利工程中的问题多为大带宽问题,这些问题更为突出。基于EBE-PCG方法的有限元方法,可以避免形成整体刚度矩阵,进而,显著减少内存的需求。而且,这种方法可以有效地并行实现,为大规模数值计算提供了可能。采用基于EBE策略的Jacobi预处理共轭梯度法,编制了有限元计算程序,并成功应用于溪洛渡、锦屏等工程的大规模数值分析。结果表明,对水利工程中的大带宽问题,该方法是一种很有效的并行计算方法。     

大型洞室群软岩置换方案优化的并行实现

并行计算己成为求解大规模岩土工程问题的一种强大趋势 。 以水布娅大型洞室群软岩置换方案优化为例 , 探讨了方案优化中的并行计算问题,分析了并行计算中的编程模式 、 任务划分 、负载平衡和编程方法等问题,在 W id n o w s 环境下的 PC 机群上成功实现了软岩置换方案优化的并行计算,并获得了近乎线性的加速比 , 从而大大提高了方案优化的计算速度和效率 , 为岩土工程计算并行化思路提供了重要参考 。     

Modelling transient heat and moisture transfer in unsaturated soil using a parallel computing approach

A parallel numerical model, employing a finite difference explicit scheme for the analysis of coupled heat and moisture transfer in unsaturated soil, is employed to simulate a laboratory experiment of heating of medium sand. The model, written in a two-dimensional polar co-ordinate formulation, is programmed in the concurrent language Occam and executed on a parallel computing network of transputers. Parallelization is adopted as a means of overcoming computing difficulties, which limited numerical solutions to those at steady state, to enable transient behaviour to be simulated. The parallel algorithm was found to be very efficient, enabling a full solution of transient behaviour to be obtained. An investigation of the ability of the model to accurately simulate the complex, interrelated coupled nature of both two-dimensional transient and steady-state behaviour yielded very good correlation between experimental and numerical results. It can therefore be concluded that overall the results obtained provide confidence in the validity of the approach proposed.     

Efficient solution for matrix-fracture flow with multiple interacting continua

An efficient numerical procedure for implementing the multiple interacting continua (MINC) method for fractured porous media in a general-purpose multiphase simulator is presented. This procedure is substantially faster, requires less memory, is amenable to any n-component, multiphase non-isothermal package, and is readily adaptable for parallel processing computers. The present procedure results in a reduction of the computing time by a factor of the order of NMINC³ as compared to the band algorithm, where NMINC is the number of nested continua into which each matrix block is further discretized. The memory requirement approaches a reduction factor of the order of NMINC² for larger problems compared to the band algorithm. The code for the algorithm was structured so as to set up the time consuming, but independent, computations for each matrix block in a subroutine that was parallelized and tested using a Sequent machine accessed under a UNIX environment. For NMINC=10, total computing time was reduced by 33 per cent for the use of two versus one processor, with the savings increasing for increasing NMINC. The proposed procedure can be implemented with the same ease and efficiency in conjunction with any iterative or direct method, and the grid-blocks can be ordered in any non-standard manner such as in D-4, D-2, and others. Copyright © 1999 John Wiley & Sons, Ltd.     

A fine-granularity scheduling algorithm for parallel XDraw viewshed analysis

Viewshed analysis is widely used in many terrain applications such as siting problem, path planning problem, and etc. But viewshed computation is very time-consuming, in particular for applications with large-scale terrain data. Parallel computing as a mainstream technique with the tremendous potential has been introduced to enhance the computation performance of viewshed analysis. This paper presents a revised parallel viewshed computation approach based on the existing serial XDraw algorithm in a distributed parallel computing environment. A layered data-dependent model for processing data dependency in the XDraw algorithm is built to explore scheduling strategy so that a fine-granularity scheduling strategy on the process-level and thread-level parallel computing model can be accepted to improve the efficiency of the viewshed computation. And a parallel computing algorithm, XDraw-L, is designed and implemented taken into account this scheduling strategy. The experimental results demonstrate a distinct improvement of computation performance of the XDraw-L algorithm in this paper compared with the coarse-partition algorithm, like XDraw-E which is presented by Song et al. (Earth Sci Inf 10(5):511–523, 2016), and XDraw-B that is the basic algorithm of serial XDraw. Our fine-granularity scheduling algorithm can greatly improve the scheduling performance of the grid cells between the layers within a triangle region.     

边坡稳定可靠度分析的并行随机有限元方法

将Monte-Carlo随机方法与并行有限元方法结合,设计了基于PC机群的并行随机有限元算法,每一次随机模拟产生一个随机场,作为一个样本,代入有限元进行稳定性计算,发挥并行有限元计算量大、计算速度快的特点,克服了Monte-Carlo方法计算时间长的缺点。用C++语言结合MPI消息传递接口开发了相应的计算软件,计算了1 000个随机样本的边坡可靠度问题,验证了程序的可靠性及高效性。     

基于MPI的快速富里叶变换并行算法

随着并行计算技术的快速发展 ,数据处理、信息处理等应用领域处理问题规模的日益增大 ,对并行计算的需求也越来越迫切。这里给出一种基于可移植消息传递界面 (MPI)标准的一维快速富里叶变换并行算法 ,可应用于分布式存储并行计算机系统     

Quasi-Monte Carlo integration on the grid for sensitivity studies

In this paper we present error and performance analysis of quasi-Monte Carlo algorithms for solving multidimensional integrals (up to 100 dimensions) on the grid using MPI. We take into account the fact that the Grid is a potentially heterogeneous computing environment, where the user does not know the specifics of the target architecture. Therefore parallel algorithms should be able to adapt to this heterogeneity, providing automated load-balancing. Monte Carlo algorithms can be tailored to such environments, provided parallel pseudorandom number generators are available. The use of quasi-Monte Carlo algorithms poses more difficulties. In both cases the efficient implementation of the algorithms depends on the functionality of the corresponding packages for generating pseudorandom or quasirandom numbers. We propose efficient parallel implementation of the Sobol sequence for a grid environment and we demonstrate numerical experiments on a heterogeneous grid. To achieve high parallel efficiency we use a newly developed special grid service called Job Track Service which provides efficient management of available computing resources through reservations.     

FORTRANM在重磁数据处理中的应用

介绍了ＦｏｒｔｒａｎＭ的基本概念和特点。ＦｏｒｔｒａｎＭ是一个支持分布式环境中并行计算的Ｆｏｒｔｒａｎ语言新成员，它在Ｆｏｒｔｒａｎ７７上扩充而成，不仅能支持数据并行程序设计，而且能支持任务并行程序设计。在重磁数据处理中，常常要进行大计算量的运算，如果采用并行计算方法，可以大大提高低档机器的运算能力，降低运算费用，缩短处理周期。本文用ＦｏｒｔｒａｎＭ把ＧＭＰＳ改造成并行计算系统ＧＭＰＳ－ＦＭ，经实际运行，效果良好，最后对测试结果作了分析。