We present an accelerated and hardware parallelized integral-equation solver for the problem of acoustic scattering by a two-dimensional surface in three-dimensional space. The approach is based, in part, on the novel Interpolated Factored Green Function acceleration method (IFGF) that, without recourse to the Fast Fourier Transform (FFT), evaluates the action of Green function-based integral operators for an $N$-point surface discretization at a complexity of $\Ord(N\log N)$ operations instead of the $\Ord(N^2)$ cost associated with nonaccelerated methods. The IFGF algorithm exploits the slow variations of factored Green functions to enable the fast evaluation of fields generated by groups of sources on the basis of a recursive interpolation scheme. In the proposed approach, the IFGF method is used to account for the vast majority of the computations, while, for the relatively few singular, nearly-singular and neighboring non-singular integral operator evaluations, a high-order rectangular-polar quadrature approach is employed instead. Since the overall approach does not rely on the FFT, it is amenable to efficient shared- and distributed-memory parallelization; this paper demonstrates such a capability by means of an OpenMP parallel implementation of the method. A variety of numerical examples presented in this paper demonstrate that the proposed methods enable the efficient solution of large problems over complex geometries on small parallel hardware infrastructures. Numerical examples include acoustic scattering by a sphere of up to $128$ wavelengths, an $80$-wavelength submarine, and a turbofan nacelle that is more than $80$ wavelengths in size, requiring, on a 28-core computer, computing times of the order of a few minutes per iteration and a few tens of iterations of the GMRES iterative solver.
翻译:我们为三维空间的二维表面的声波散落问题提出了一个加速和硬件平行整体平流解解解器。这个方法部分地基于新型的内插加系数绿色功能加速法(IFGF),该方法不采用快速Fleier变换(FFT),而是对绿色基于功能的综合操作者在以美元为单位的以美元为单位的表面分解操作中的行动进行评估,而采用美元为美元(N\log N),而不是与非加速方法有关的美元(Ord(N2/2)美元)的远流成本。IFGF 算法利用了因因素化的绿色功能的缓慢变异性,以便能够根据循环性内插图,快速评估各种来源产生的字段。在拟议方法中,基于绿色分解的分解操作者在绝大多数的计算中,而相对较少的单数个、近似和相邻的美元整体操作者,一种高等级的电流-直流法-直径直径直径法法方法,而整个方法则需要一种快速的直径直径直径法化方法,因此,在纸面法的计算方法上显示,一个快速递化方法,其伸伸缩法的伸缩-直压-直压-直压-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-直达-