The Fast Multipole Boundary Element Method (FMBEM) reduces the [Formula: see text] computational and memory complexity of the conventional BEM discretized with [Formula: see text] boundary unknowns, to [Formula: see text] and [Formula: see text], respectively. A number of massively parallel FMBEM models have been developed in the last decade or so for CPU, GPU and heterogeneous architectures, which are capable of utilizing hundreds of thousands of CPU cores to treat problems with billions of degrees of freedom (dof). On the opposite end of this spectrum, small-scale parallelization of the FMBEM to run on the typical workstation computers available to many researchers allows for a number of simplifications in the parallelization strategy. In this paper, a novel parallel broadband Helmholtz FMBEM model is presented, which utilizes a simple columnwise distribution scheme, element reordering and rowwise compression of data, to parallelize all stages of the fast multipole method (FMM) algorithm with a minimal communication overhead. The sparse BEM near-field and sparse approximate inverse preconditioner are also constructed and executed in parallel, while the flexible generalized minimum residual (fGMRES) solver has been modified to apply the FMBEM matrix-vector products and corresponding minimum residual convergence within the parallel environment. The algorithmic and memory complexities of the resulting parallel FMBEM model are shown to reaffirm the above estimates for both the serial and parallel configurations. The parallel efficiency (PE) of the FMBEM matrix-vector products and fGMRES solution for the present model is shown to be satisfactory; achieving PEs up to [Formula: see text] and [Formula: see text] in the fGMRES solution using 3 and 6 CPU cores respectively, when applied to models having [Formula: see text] dof per CPU core. The PE of the precalculation stages of the FMBEM — in particular the FMM precomputation stage which is largely unparallelized — reduces the overall PE of the FMBEM model; resulting in average efficiencies of [Formula: see text] and [Formula: see text] for the 3-core and 6-core models when treating problems with [Formula: see text] dof per CPU core. The present model is able to treat large-scale acoustic scattering problems involving up to [Formula: see text] dof on a workstation computer equipped with 128[Formula: see text]GB of RAM, while acoustic target strength (TS) results calculated up to 3[Formula: see text]kHz for the BeTSSi II submarine model demonstrate its capabilities for large-scale TS modeling.

中文翻译：

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用于大规模目标强度建模的并行宽带亥姆霍兹 FMBEM 模型

快速多极边界元法 (FMBEM) 将使用 [公式：参见文本] 边界未知数离散化的传统 BEM 的 [公式：参见文本] 计算和存储复杂度降低到 [公式：参见文本] 和 [公式：参见文本] ， 分别。在过去十年左右的时间里，针对 CPU、GPU 和异构架构开发了许多大规模并行 FMBEM 模型，它们能够利用数十万个 CPU 内核来处理数十亿自由度 (dof) 的问题。在这个范围的另一端，在许多研究人员可用的典型工作站计算机上运行 FMBEM 的小规模并行化允许在并行化策略中进行许多简化。在本文中，提出了一种新颖的并行宽带亥姆霍兹 FMBEM 模型，它利用简单的列分布方案、元素重新排序和数据的行压缩，以最小的通信开销并行化快速多极方法 (FMM) 算法的所有阶段。稀疏 BEM 近场和稀疏近似逆预处理器也被并行构建和执行，而灵活的广义最小残差 (fGMRES) 求解器已被修改为在并行环境中应用 FMBEM 矩阵向量积和相应的最小残差收敛。所得到的并行 FMBEM 模型的算法和内存复杂性被证明再次证实了上述对串行和并行配置的估计。本模型的 FMBEM 矩阵向量乘积和 fGMRES 解决方案的并行效率 (PE) 令人满意；在分别使用 3 个和 6 个 CPU 内核的 fGMRES 解决方案中实现高达 [公式：见文本] 和 [公式：见文本] 的 PE，当应用于每个 CPU 内核具有 [公式：见文本] 自由度的模型时。FMBEM 预计算阶段的 PE——特别是在很大程度上是无与伦比的 FMM 预计算阶段——降低了 FMBEM 模型的整体 PE；在处理每个 CPU 核心的 [公式：参见文本] 自由度问题时，导致 3 核和 6 核模型的 [公式：参见文本] 和 [公式：参见文本] 的平均效率。本模型能够在配备 128 [公式：参见文本]GB RAM 的工作站计算机上处​​理高达 [公式：参见文本] 自由度的大规模声散射问题，同时计算出声目标强度 (TS) 结果至 3 [公式：