摘要
针对电磁感应测井问题,基于区域分解的原理对体积分方程提出了一种快速有效的数值计算方法。把求解区域分解成两个区域,离源近的区域和离源远的区域,在离源远的区域采用玻恩近似;离源近的区域采用体积分方程法求解。然后,通过源近区和源远区的相互迭代来考虑两区之间相互的耦合。在整个求解中涉及到格林函数与体电流的卷积都采用了快速傅立叶变换来加速。通过上述的处理能使体积分的计算区域只限于离源近的区域,从而使得用于精确计算的未知量大为减少,在确保精度的条件下总的计算时间也降为原问题(整个区域采用体积分方程结合快速傅立叶变换求解)的1/4～1/2左右。
In modeling the electromagnetic induction, based on the principle of domain decomposition, a fast and effective numerical computational method is developed to deal with the volume integral equation. Firstly, the solution area is divided into two parts, namely, the area near the source and the area far from it, in which the born approximation and the volume integral equation are employed in those areas respectively. Secondly, Mutual iteration of both the two areas is used to relate the coupling of them. In addition, throughout the solution process, the involved convolution of Green＇s Function and the volume current is accelerated by Fast Fourier Transform （FFT）. In so doing, the computational area of volume integral could be confined to the area near the source, and thus the unknown quantity used for precise computation could be reduced dramatically. Given required precision, the time for computation would be only 1/4 to 1/2 of the original when the volume integral equation and Fast Fourier Transform are used for solution in the total area.
出处
《电波科学学报》
EI
CSCD
北大核心
2008年第5期932-936,986,共6页
Chinese Journal of Radio Science
基金
中海油田服务股份有限公司资助项目(JSB07YF)
自然科学基金重点资助项目(60431010)
关键词
区域分解
体积分方程
玻恩近似
快速傅立叶变换
domain decomposition
volume integral equation
born approximation
fast fourier transform
