Adapting free-space fast multipole method for layered media Green's function: Algorithm and analysis
Adapting free-space fast multipole method for layered media Green's function: Algorithm and analysis
复制标题
采用层状介质格林函数的自由空间快速多极子方法：算法与分析
DOI：
10.1016/j.acha.2019.10.001
复制
发表时间：
2019
影响因子：
2.5
通讯作者：
Huang, Jingfang
中科院分区：
文献类型：
--
作者：
Cho, Min Hyung;Huang, Jingfang
给出了一种精确、高效地计算频域分层介质格林函数与给定密度函数卷积的数值算法。这种新算法不像经典的快速多极子、快速直接求解器和H矩阵算法那样直接压缩卷积矩阵，而是考虑了原始矩阵的转换形式，因此高度优化的自由空间快速多极子方法的现有块可以很容易地适应分层介质的格林函数。对Sommerfeld积分进行了渐近分析，以估计在新的“多极”和“局部”展开中的衰减率。为了避免源和目标接近时原积分表示中被积函数的高度振荡，引入了数学上等价的交替方向积分表示。数值验证了原始方向表示和替代方向表示的新展开式和求积规则的收敛。
We present a numerical algorithm for an accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution matrix directly as in the classical fast multipole, fast direct solver, and H-matrix algorithms, this new algorithm considers a translated form of the original matrix so existing blocks from the highly optimized free-space fast multipole method can be easily adapted to the layered media Green's function. An asymptotic analysis is performed on the Sommerfeld integrals to provide an estimate of the decay rate in the new “multipole” and “local” expansions. To avoid the highly oscillatory integrand in the original integral representations when the source and target are close to each other, mathematically equivalent alternative direction integral representations are introduced. The convergence of the new expansions and quadrature rules for the original and alternative direction representations are numerically validated.
层状介质中电场并进格林函数的高效准确计算
影响因子：
2.5
作者：
M. H. Cho;W. Cai
通讯作者：
W. Cai
影响因子：
4.1
作者：
Cheng, Hongwei;Crutchfield, William Y.;Zhao, Junsheng
通讯作者：
Zhao, Junsheng
DOI：
--
发表时间：
1999
期刊：
影响因子：
--
作者：
Jingfang Huang
通讯作者：
Jingfang Huang