非连续变形分析（DDA）线性方程组的高效求解算法

非连续变形分析(DDA)方法对大规模工程问题的数值模拟耗时太长,其中线性方程组求解耗时可占总计算时间的70%以上,因此,高效的线性方程组解法是重要研究课题。首先,阐述了适用于DDA方法的基于块的行压缩法和基于试验-误差迭代格式的非0位置记录;然后,针对DDA的子矩阵技术,将块雅可比迭代法 (BJ)、预处理的块共轭梯度法 (PCG,包括Jacobi-PCG、SSOR-PCG) 引入DDA方法,重点研究了线性方程组求解过程中的关键运算;最后,通过两个洞室开挖算例,分析了各线性方程组求解算法在DDA中的计算效率。研究表明：与迭代法相比,直解法无法满足大规模工程计算需要;BJ迭代法与块超松弛迭代法(BSOR)的效率差别不大,但明显不如PCG迭代法。因此,建议采用PCG迭代法求解DDA线性方程组,特别是SSOR-PCG值得推广;如果开展并行计算研究,Jacobi-PCG是较好的选择,当刚度矩阵惯性优势明显时,BJ迭代法同样有效。     

GPU-based parallel computation for discontinuous deformation analysis (DDA) method and its application to modelling earthquake-induced landslide

Graphic Processing Unit (GPU), as a computing device, has upgraded from single-subject graphical processors to multi-core processors with tremendous computational horsepower. This paper proposes to accelerate the DDA using parallel Jacobi Preconditioned Conjugate Gradient (JPCG) technique on GPUs. Based on the results of two numerical examples, the calculation accuracies of the DDA with serial and parallel solvers are validated, and we found that the DDA with parallel solvers exhibits a much higher execution efficiency. The movement process of Daguangbao landslide triggered by the Wenchuan earthquake is replicated and the modeled deposit pattern coincides well with the actual topography after earthquake.     

Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method

Large‐scale engineering computing using the discontinuous deformation analysis (DDA) method is time‐consuming, which hinders the application of the DDA method. The simulation result of a typical numerical example indicates that the linear equation solver is a key factor that affects the efficiency of the DDA method. In this paper, highly efficient algorithms for solving linear equations are investigated, and two modifications of the DDA programme are presented. The first modification is a linear equation solver with high efficiency. The block Jacobi (BJ) iterative method and the block conjugate gradient with Jacobi pre‐processing (Jacobi‐PCG) iterative method are introduced, and the key operations are detailed, including the matrix‐vector product and the diagonal matrix inversion. Another modification consists of a parallel linear equation solver, which is separately constructed based on the multi‐thread and CPU‐GPU heterogeneous platforms with OpenMP and CUDA, respectively. The simulation results from several numerical examples using the modified DDA programme demonstrate that the Jacobi‐PCG is a better iterative method for large‐scale engineering computing and that adoptive parallel strategies can greatly enhance computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

基于OpenMP的非连续变形分析并行计算方法

非连续变形分析（DDA）方法严格满足平衡要求和能量守恒,具有完全的运动学及数值可靠性,但对大规模岩土工程问题的数值模拟耗时太长,尤其是线性方程组求解,并行计算可以很好地解决该问题。首先基于DDA方法的基本理论,阐述了适用于DDA方法中的基于块的行压缩法和基于“试验-误差”迭代格式的非零位置记录;其次,引入块雅可比迭代法并行求解DDA方法的线性方程组,并改进了相应的非零存储方法;最后,基于OpenMP实现了DDA线性方程组求解并行计算,并将其应用于地下洞室群的破坏过程分析,以加速比为并行效率的指标评价,结果表明,该并行计算策略可以极大提高DDA的计算效率,而且适合各种规模的问题。     

井—地三维激发极化数据快速反演

为实现井—地激发极化数据的快速反演,分析三维有限元正演四面体网格剖分形成的系数矩阵的元素规律,应用MSR非零元素压缩存储和SSOR-PCG方程求解技术,提高了正演执行效率。在正演基础上,利用Jacobian矩阵与正演方程的简单关系,采用共轭梯度法求解最小二乘目标函数的模型修改量,避开Jacobian矩阵的直接计算和存储,实现了三维井-地激电数据的分钟级快速反演。模型正演合成数据的反演结果表明,能基本再现已知的模型。     

Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

基于GPU的并行条件模拟算法及其在储量估算中的应用

条件模拟是一种计算非常耗时的高精度三维插值算法。针对串行条件模拟算法计算时间过长的问题,提出基于GPU的并行条件模拟算法,并进行储量估算。对条件模拟算法进行并行分析,利用GPU的高度并行性,构建CUDA通用计算开发环境,实现串行条件模拟算法到并行条件模拟算法的转换,使条件模拟算法的时间复杂度从O(n)降至O(logn)。并对西藏甲玛铜矿进行了储量估算。实验结果表明,在安装普通NVIDIA显卡的计算机以及估算精度不下降的情况下,GPU并行条件模拟的计算效率比CPU串行条件模拟的计算效率提高了60倍以上。     

Cache-efficient parallel eikonal solver for multicore CPUs

Numerical solution of the eikonal equation is frequently used to compute first-arrival travel times for a given velocity model in seismic applications. Computations for large three-dimensional models become expensive requiring the use of efficient parallel solvers. We present new parallel implementations of the fast sweeping and locking sweeping methods optimized for shared memory systems such as multicore CPUs; we call them block fast sweeping method (BFSM) and block locking sweeping method (BLSM). Proposed methods are based on the domain decomposition approach with a special attention paid to high efficiency of the cache utilization and task execution synchronization. Performance tests on realistic models show high parallel efficiency of 85–95% on modern multicore CPUs and require the same number of iterations to converge as do the serial sweeping methods. We also highlight the importance of properly selecting the stopping criterion in the iterative sweeping methods aiming for a balance between computational time and accuracy of the result required by an application. In particular, we show that in seismic applications one can reach reasonable accuracy of computed travel times while dramatically reducing the number of iterations compared to the case of using the full convergence stopping criterion.     

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.     

GPU提速叠前时间体偏移技术

为了进一步提高叠前时间体偏移的计算效率,实现了在GPU＼CPU协同并行计算模式下Kirchhoff叠前时间体偏移技术,并进行优化。经在Nvida Tesla C1060GPU上的测试表明,GPU（Graphic Processing Unit）的处理速度是CPU（单核）的四十倍左右。同时表明,CUDA（Cornpute Unified Device Architectarc）编程为CPU向GPU的转化提供了一个较为方便的语言环境。     

基于GPU实现汉克尔变换并行计算

地球物理勘探技术日新月异,地球物理勘探数据的处理和解释对高性能计算机的要求越来越高.相比于地震勘探,重力、磁法、电法勘探中的并行计算研究还都处于起步阶段.基于GPU的并行计算能够提供强大的计算能力和存储器带宽,同时具有良好的可编程性、较低的成本和较短的开发周期.这里实现了瞬变电磁法一维正演计算中汉克尔变换基于GPU的并行计算,比较了汉克尔变换串行算法和并行算法的计算耗时,基于GPU技术的并行计算相比串行计算,获得了很高的加速比.     

A one-dimensional local discontinuous Galerkin Richards’ equation solution with dual-time stepping

We present a compact, high-order Richards’ equation solver using a local discontinuous Galerkin finite element method in space and a dual-time stepping method in time. Dual-time stepping methods convert a transient problem to a steady state problem, enabling direct evaluation of residual terms and resolve implicit equations in a step-wise manner keeping the method compact and amenable to parallel computing. Verification of our solver against an analytical solution shows high-order error convergence and demonstrates the solvers ability to maintain high accuracy using low spatial resolution; the method is robust and accurately resolves numerical solutions with time steps that are much larger than what is normally required for lower-order implicit schemes. Resilience of our solver (in terms of nonlinear convergence) is demonstrated in ponded infiltration into homogeneous and layered soils, for which HYDRUS-1D solutions are used as qualitative references to gauge performance of two slope limiting schemes.

     

GPU-accelerated iterative solutions for finite element analysis of soil–structure interaction problems

Soil–structure interaction problems are commonly encountered in engineering practice, and the resulting linear systems of equations are difficult to solve due to the significant material stiffness contrast. In this study, a novel partitioned block preconditioner in conjunction with the Krylov subspace iterative method symmetric quasiminimal residual is proposed to solve such linear equations. The performance of these investigated preconditioners is evaluated and compared on both the CPU architecture and the hybrid CPU–graphics processing units (GPU) computing environment. On the hybrid CPU–GPU computing platform, the capability of GPU in parallel implementation and high-intensity floating point operations is exploited to accelerate the iterative solutions, and particular attention is paid to the matrix–vector multiplications involved in the iterative process. Based on a pile-group foundation example and a tunneling example, numerical results show that the partitioned block preconditioners investigated are very efficient for the soil–structure interaction problems. However, their comparative performances may apparently depend on the computer architecture. When the CPU computer architecture is used, the novel partitioned block symmetric successive over-relaxation preconditioner appears to be the most efficient, but when the hybrid CPU–GPU computer architecture is adopted, it is shown that the inexact block diagonal preconditioners embedded with simple diagonal approximation to the soil block outperform the others.     

Discontinuous deformation analysis with second‐order finite element meshed block

The discontinuous deformation analysis (DDA) with second‐order displacement functions was derived based on six‐node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second‐order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright © 2006 John Wiley & Sons, Ltd.     

基于显式时间积分的球颗粒DDA计算方法

非连续变形分析方法（DDA）是一种平行于有限元法的新型数值计算方法,该方法基于最小势能原理,把每个离散块体的变形、运动和块体之间的接触统一到平衡方程中进行隐式求解。然而,传统DDA方法在计算过程中需组装整体刚度矩阵并联立求解方程组,在用于大型岩土工程问题的三维数值模拟时占用内存较大、耗时较长、计算效率极低。因此,提出一种基于显式时间积分的三维球颗粒DDA方法。该方法在求解过程中不需要组装整体刚度矩阵,在求解加速度时,由于质量矩阵为对角矩阵,可存储为一维向量占用内存较少,且可分块逐自由度求解,效率较高,在接触判断上采用最大位移准则简化了接触算法,采用较小的时步,保证了计算的精确性;通过几个典型算例验证了该方法的准确性及计算效率。     

Boundary setting method for the seismic dynamic response analysis of engineering rock mass structures using the discontinuous deformation analysis method

Large deformations and discontinuous problems can be calculated using the discontinuous deformation analysis (DDA) method by solving time steps, and this method is suitable for simulating the seismic dynamic response of engineering rock mass structures. However, the boundary setting must be carefully analyzed. In this paper, four boundary settings for the DDA method are investigated. First, the contributions to the DDA equations for nonreflecting boundaries (including the viscous boundary and the viscoelastic boundary) are deduced based on the Newmark method. Second, a free‐field boundary is introduced in the DDA method with boundary grid generation and coupling calculation algorithms to accurately simulate external source wave motion, such as earthquakes. Third, seismic input boundary treatments are intensively examined, and the force input method is introduced based on nonreflecting boundaries. Finally, the static‐dynamic unified boundary is implemented to ensure consistent boundary transformation. The boundary setting method in the DDA method is discussed, and the suggested treatments are used to analyze the seismic dynamic response of underground caverns. Copyright © 2015 John Wiley & Sons, Ltd.     

Validating the ability of the discontinuous deformation analysis method to model normal P‐wave propagation across rock fractures

The effects of fractures on wave propagation problems are increasingly abstracting the attention of scholars and engineers in rock engineering field. This study aims to fully validate the ability of discontinuous deformation analysis (DDA) to model normal P‐wave propagation across rock fractures. The effects of a single fracture and multiple parallel fractures are all tested. The results indicate that DDA can accurately reflect the fracture effects, including the fractures stiffness, the fracture spacing and the fracture number, and the effects of incident wave frequency on one‐dimensional P‐wave propagation problems. Thus, DDA is able to deal well with normal incident P‐wave propagation problems. Copyright © 2017 John Wiley & Sons, Ltd.     

大地电磁三维正、反演多核并行计算的设计与实现

首先以频点为并行粒度,完成了MT三维正演并行计算,然后将该算法引入共轭梯度法MT三维反演过程中的正演求数据的残差、反演方程右端项的求取、共轭梯度求解模型增量这三个计算环节中,使得MT三维反演中的主要计算量实现并行化。对编制的MT三维正、反演并行计算程序,在多核工作站上通过理论地电模型进行了正演试算和反演验证,并在串行和并行两种计算方式下进行了计算效率对比。     

Comparison of linear solvers for equilibrium geochemistry computations

Equilibrium chemistry computations and reactive transport modelling require the intensive use of a linear solver under very specific conditions. The systems to be solved are small or very small (4 × 4 to 20 × 20, occasionally larger) and are very ill-conditioned (condition number up to 10¹⁰⁰). These specific conditions have never been investigated in terms of the robustness, accuracy, and efficiency of the linear solver. In this work, we present the specificity of the linear system to be solved. Several direct and iterative solvers are compared using a panel of chemical systems, including or excluding the formation of mineral species. We show that direct and iterative solvers can be used for these problems and propose computational keys to improve the chemical solvers.     

DDA数值方法及工程应用研究

基于 DD A计算模型 ,补充和发展了 D DA计算程序 ,分析了边坡大位移问题和地下开挖引起地面变形的工程实例 ,并与离散元计算结果进行了比较研究。计算分析结果表明 ,该模型的计算结果基本符合实际 ,适合于不连续块体系统岩体的情况 ,可用于大规模工程问题的应用和分析。