声学Burton-Miller方程边界元法GPU并行计算

基于GPU,对声学Burton-Miller积分方程的边界元解法进行并行计算.提出并行计算格式和程序实现方法,以及Burton-Miller方程中各类奇异(包括强奇异、超奇异)积分的GPU计算和局部修正方法.典型算例结果表明,在特征频率处可获得正确的解,具有较高精度,可在普通个人计算机上快速完成自由度超过2×10⁵的声学边界元分析.为计算声学及相关工程领域的中、大规模声场分析问题提供一种快速、高效、简便的数值计算工具.     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势,     

LBM伪势MRT三维模型GPU并行计算的性能优化

格子Boltzmann方法伪势模型算法中的格点间计算未完全局部化,因此在并行计算时需要更多次的全局内存读写、使用更多数量的寄存器和线程同步操作,从而导致GPU并行计算效率下降.本文针对伪势模型并行计算的局限性,基于三维十五速格子结构的多松弛时间伪势模型,以气液相分离为算例,通过合并访问的方式提高全局内存的读写效率;并提出一种"定向转移"算法,提高格子边界格点获取邻居格点数据的效率;最后探索不同资源分配中各种因素对计算效率的影响,总结最优资源分配的方法.     

新的对角形式快速多极边界元法求解声学Helmholtz方程

传统外部声学Helmholtz边界积分方程无法在个人计算机上求解大规模工程问题. 为了有效解决这个问题, 将快速多极方法引入到边界积分方程中, 加速系统矩阵方程组的迭代求解. 由于在边界积分方程中引入基本解的对角形式多极扩展, 新的快速多极边界元法的计算效率与传统边界元相比显著提高, 计算量和存储量减少到O(N)量级(N为问题的自由度数). 包括含有420000个自由度的大型潜艇模型数值算例验证了快速多极边界元法的准确性和高效性, 清楚表明新算法在求解大规模声学问题中的优势, 具有良好的工程应用前景.     

气体动力学直接模拟Monte Carlo的高效GPU并行计算

实现了基于计算统一设备架构(CUDA)的直接模拟Monte Carlo(DSMC)并行算法,改进了原有多图形处理器(GPU)数据之间传输并行算法,数值模拟计算二维Couette流和二维顶盖驱动方腔流,定量比较了CPU、单GPU和多GPU并行计算的结果和计算时间.结果表明单GPU并行计算相对CPU计算的加速效果可以达到10~30倍,双GPU并行计算加速效果可以达到40~60倍,多GPU并行计算的加速效率接近100%,且计算精度能够得到良好保证.     

新型快速多极边界元法求解电荷任意分布的二维静电场

在初始快速多极边界元法(FMM)基础上提出一种适合位势问题的新型快速多极边界元格式,并用于求解静电场问题.新型算法引入对角化概念,减少了形成局部展开系数的时间,提高计算效率.最后给出数值算例,证明了新型算法的计算精度及处理大规模问题的速度优势.     

MRM-BEM本征值计算中波数k初始值的预估算法

利用基于多重互易的边界元法计算二维声学谐振腔的本征值和本征频率.通过搜索包含未知波数k的高阶行列式值的0点,来确定系统的本征值.基于波的传播原理,提出一种波数k初始值的粗略估计算法.计算了几种模型的估计算法的效率.研究多重互易边界元法基本解的阶数对结果精度的影响,发现基本解至少采用七重互易结果才收敛.数值结果与解析解和文献符合的很好,证明了方法的有效性和可靠性.     

消声器声学性能预测的子结构快速多极子边界元法

鉴于快速多极子边界元法的应用主要局限于单区域声学问题计算,发展基于子结构技术的快速多极子边界元法以计算多区域声场问题,介绍基本原理、具体实施过程以及优缺点.以带有插进口管的膨胀腔消声器为例,应用子结构快速多极子边界元法和传统边界元法计算其传递损失,通过与实验测量结果的比较,验证方法的有效性和计算精度.研究表明,快速多极子边界元法与传统边界元法相比,节点数越多,其在节省计算时间,减少计算量等方面的优势越明显.     

边界元奇异与近奇异数值积分方法及其应用于大规模声学问题

提出了综合处理Burton-Miller方法所导致的奇异积分与近奇异积分问题的数值求积方法,以此改进了基于常量元素的常规边界元和低频快速多极边界元方法。对于奇异积分问题,利用Hadamard有限积分方法进行解决;对于近奇异积分问题,则采用极坐标变换法和PART方法(Projection and Angular&;Radial Transformation)进行克服。与解析解和LMS Virtual.Lab商业软件的结果比较验证了方法的正确性,并对比分析了奇异积分与近奇异积分对计算精度的影响。采用低频快速多极子方法以加速常规边界元法的计算效率,计算分析了计算复杂度,并成功实现了34万自由度大规模问题的计算。结果表明,近奇异积分问题主要由超奇异核函数引起,对计算精度的影响不容忽略;快速多极边界元法的精度与常规边界元法一致,但计算复杂度要远低于后者。      

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

基于等几何分析的边界元法求解Helmholtz问题

将基于一类局部双变量B样条函数的等几何分析方法和Burton-Miller方法相结合,分析三维Helmholtz问题.对于某些从二维参数域映射到三维空间具有奇异点的参数曲面,该方法可以有效地避免奇异点处大量奇异与近奇异积分的计算.数值算例表明该方法具有较好的计算精度和计算效率.复杂问题的分析表明,该方法具有良好的工程应用前景.     

Implementation of Multi-GPU Based Lattice Boltzmann Method for Flow Through Porous Media

The lattice Boltzmann method (LBM) can gain a great amount of performance benefit by taking advantage of graphics processing unit (GPU) computing, and thus, the GPU, or multi-GPU based LBM can be considered as a promising and competent candidate in the study of large-scale fluid flows. However, the multi-GPU based lattice Boltzmann algorithm has not been studied extensively, especially for simulations of flow in complex geometries. In this paper, through coupling with the message passing interface (MPI) technique, we present an implementation of multi-GPU based LBM for fluid flow through porous media as well as some optimization strategies based on the data structure and layout, which can apparently reduce memory access and completely hide the communication time consumption. Then the performance of the algorithm is tested on a one-node cluster equipped with four Tesla C1060 GPU cards where up to 1732 MFLUPS is achieved for the Poiseuille flow and a nearly linear speedup with the number of GPUs is also observed.     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.     

Fast multipole accelerated boundary element method for the Helmholtz equation in acoustic scattering problems

We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficultie...     

Multilevel fast multipole algorithm for acoustic wave scattering by truncated ground with trenches

The multilevel fast multipole algorithm (MLFMA) is extended to solve for acoustic wave scattering by very large objects with three-dimensional arbitrary shapes. Although the fast multipole method as the prototype of MLFMA was introduced to acoustics early, it has not been used to study acoustic problems with millions of unknowns. In this work, the MLFMA is applied to analyze the acoustic behavior for very large truncated ground with many trenches in order to investigate the approach for mitigating gun blast noise at proving grounds. The implementation of the MLFMA is based on the Nystrom method to create matrix equations for the acoustic boundary integral equation. As the Nystrom method has a simpler mechanism in the generation of far-interaction terms, which MLFMA acts on, the resulting scheme is more efficient than those based on the method of moments and the boundary element method (BEM). For near-interaction terms, the singular or near-singular integrals are evaluated using a robust technique, which differs from that in BEM. Due to the enhanced efficiency, the MLFMA can rapidly solve acoustic wave scattering problems with more than two million unknowns on workstations without involving parallel algorithms. Numerical examples are used to demonstrate the performance of the MLFMA with report of consumed CPU time and memory usage.     

消声器传递损失预测的边界元模态展开混合方法

将边界元法和解析方法结合形成一种混合方法用于计算消声器的传递损失,消声器被划分成若干个子结构,解析方法和边界元方法被分别用于计算规则结构和不规则结构的阻抗矩阵,不同子结构之间通过阻抗矩阵连接起来。为减少计算时间,采用一种基于模态配点法的简化方法。对单级膨胀腔、双级膨胀腔和穿孔管阻性消声器的传递损失进行了计算,混合方法计算结果与解析方法和三维数值方法计算结果吻合良好。分析了混合方法的计算效率并与传统子结构方法进行了比较,混合方法能明显节省计算时间。