This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF algorithm evaluates the action of Green function-based integral operators at a cost of $\mathcal{O}(N\log N)$ operations for an $N$-point surface mesh. The IFGF strategy, which leads to an extremely simple algorithm, capitalizes on slow variations inherent in a certain Green function {\em analytic factor}, which is analytic up to and including infinity, and which therefore allows for accelerated evaluation of fields produced by groups of sources on the basis of a recursive application of classical interpolation methods. Unlike other approaches, the IFGF method does not utilize the Fast Fourier Transform (FFT), and is thus better suited than other methods for efficient parallelization in distributed-memory computer systems. Only a serial implementation of the algorithm is considered in this paper, however, whose efficiency in terms of memory and speed is illustrated by means of a variety of numerical experiments -- including a 43 min., single-core operator evaluation (on 10 GB of peak memory), with a relative error of $1.5\times 10^{-2}$, for a problem of acoustic size of 512$\lambda$.
翻译:本文介绍了一种新颖的“内插因素绿色功能”方法(IFGF),用于加速评估分散理论和其他领域的一体化操作者。与这些领域现有的加速方法一样,IFGF算法以基于绿色功能的综合操作者以美元=mathcal{O}(N\log N)美元计算,对基于绿色功能的综合操作者以美元+美元+点表面网格的成本评估其行动。IFGF战略导致一种极为简单的算法,利用某种绿色函数 ~分析系数} 所固有的缓慢变化,该算法具有分析性,包括不精确性,因此可以加速评估各种来源群体根据传统内插法的反复应用而生成的字段。与其他方法不同,IFGF方法没有使用快速四重变法(FFT),因此比其他方法更适合在分布式和模模样计算机系统中高效平行。然而,本文只考虑对算法的连续实施,但从记忆和速度方面的效率看,要用一系列数字存储力的峰值手段来说明,包括一个具有15度的10度的10级级级的高级操作者-25级的10级的高度的数学问题。