论文标题
加速散射问题解决方案的“插值构成的绿色函数”方法
"Interpolated Factored Green Function" Method for accelerated solution of Scattering Problems
论文作者
论文摘要
本文介绍了一种新颖的{\ em插值的绿色函数}方法（IFGF），以加速对散射理论和其他领域的整体操作员的加速评估。与这些字段中的现有加速方法一样，IFGF算法以$ \ Mathcal {O}（n \ log n）$ n $ - 点表面网格的成本来评估基于绿色功能的积分运算符的动作。导致极其简单算法的IFGF策略利用了特定绿色函数固有的缓慢变化{\ em Analytic因子}，该策略的分析性直至无穷大，因此允许根据经典插入方法的递归应用程序来加速对田间产生的领域的评估。与其他方法不同，IFGF方法不利用快速傅立叶变换（FFT），因此比在分布式内存计算机系统中有效并行化的其他方法更适合。 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$λ$.
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$λ$.
