发表机构
Eastern Institute of Technology; Shanghai Jiao Tong University（东方理工大学; 上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对高频亥姆霍兹方程，提出一种基于IOFD离散的大规模并行三网格预条件子，在多类速度模型上实现稳健收敛与可扩展并行性能，64个A100 GPU可18.1秒求解340波长跨度的问题。
AI 中文摘要
对三维时谐波在多个波长上的传播进行精确模拟，需要控制相位误差并高效求解大型不定方程组。我们开发了一种基于紧凑27点插值优化有限差分（IOFD）离散格式的三网格求解器。该方法的波数相关模板支持每最短波长6个点的精细网格分辨率，且在2h网格上的未偏移物理校正仅需每最短波长3个点。该方法在h和2h网格上保留未偏移的IOFD算子，而复偏移的2h-4h辅助循环则为粗网格逆的无分解迭代近似提供预条件。将偏移量限制在该辅助循环内，可保留粗网格校正的传播特性。与出射格林函数的比较证实，在最大达6144³的一系列网格上，相位和相对振幅精度均符合要求，最大问题在每个坐标方向上跨度约为1024个波长。相同的固定求解器配置在光滑、不连续、高对比度及地球物理速度模型上均保持稳健收敛，并展现出可扩展的并行性能。具体而言，在仅64个NVIDIA A100 GPU上，求解每个坐标方向跨度约340个波长的问题仅需18.1秒。
英文摘要
Accurate simulation of three-dimensional time-harmonic wave propagation over many wavelengths requires control of phase error and efficient solution of large indefinite systems. We develop a three-grid solver based on the compact 27-point interpolated optimized finite-difference (IOFD) discretization. Its wavenumber-dependent stencil supports a fine-grid resolution of six points per shortest wavelength and an unshifted physical correction on the \(2h\) grid at only three points per shortest wavelength. The method retains unshifted IOFD operators on the \(h\) and \(2h\) grids, while a complex-shifted \(2h\)--\(4h\) auxiliary cycle preconditions a factorization-free iterative approximation of the coarse inverse. Restricting the shift to this auxiliary cycle preserves the propagative character of the coarse correction. Comparison with the outgoing Green function confirms phase and relative-amplitude accuracy on a sequence of meshes up to \revision{\(10240^3\)}, \revision{exceeding one trillion unknowns,} with the largest problem spanning approximately \revision{1704} wavelengths per coordinate. The same fixed solver configuration retains robust convergence across smooth, discontinuous, high-contrast, and geophysical velocity models and exhibits scalable parallel performance. In particular, a \revision{\(2560^3\)} problem spanning approximately \revision{425} wavelengths in each coordinate direction is solved in \revision{43.8 seconds} on just 64 NVIDIA A100 GPUs.
