摘要
常规的三维时间域航空电磁模拟通常采用隐式步长方法进行时间离散,需要几次矩阵分解和上百次右端源项回带,计算效率较低.为了提高正演计算效率,本文提出使用有理Krylov方法求解时间域电场扩散方程.首先使用非结构四面体网格进行空间离散,采用Nédélec矢量基函数近似四面体单元内的电场;然后基于有限元离散给出矩阵指数和矢量乘积表示的电场显式解;最后采用有理Arnoldi算法构造Krylov子空间内的正交基函数并进一步求解矩阵指数与矢量的乘积,直接得到任意时刻的电场解向量,避免步长离散过程.此外,本文还提出一种指数加权偏移参数优化方法,使得有理Arnoldi近似在瞬变衰减晚期具备更高的精度,从而降低Krylov子空间阶数并提高计算效率.通过和层状模型解析解的对比验证了有理Krylov方法的精度.针对三维异常体模型使用全局网格和局部网格剖分并和其他数值方法比较,进一步说明了有理Krylov方法的有效性.
Traditional Three-Dimensional(3 D)time-domain airborne Electromagnetic(EM)modeling utilizes an implicit time discretization technique to calculate the EM responses in the time domain,which requires several matrix decompositions and hundreds of forward and backward substitutions.This reduces largely the modeling efficiency.To speed up the 3 Dforward modeling for time-domain Airborne Electromagnetic(AEM),we propose to solve the diffusion equation for the electric field using the rational Krylov method.The spatial discretization is completed by the unstructured tetrahedral grids,where lowest order Nédélec first kind vector basis functions are adopted to approximate the electric field inside each element.Then we derive the electric field solutions directly in terms of the product of a matrix exponential function with a vector.The rational Krylov method is used to solve the matrix function,where the orthogonal basis vectors in the rational Krylov subspace are constructed using the rational Arnoldi algorithm.Finally,the electric field is calculated for any desired time by the rational Arnoldi approximation,which avoids explicit or implicit time stepping.In addition,an exponential weight is incorporated into the rational Arnoldi approximation errors when optimizing the shift parameters,resulting in small approximation errors at late times.This further reduces the size of the rational Krylov subspace and improves the computational efficiency.We verify the correctness and accuracy of the proposed rational Krylov method by comparing the forward modeling results for a homogeneous half-space model with the semi-analytic solution.Furthermore,we prove the effectiveness of the presented rational Krylov method by comparing our solutions with time-domain finite-element and finite-volume solutions for a 3 Dabnormal model using global and local grids.The simulations of AEM responses for two typical 3 Dabnormal models demonstrate that the rational Krylov method can speed up the time-domain AEM forward modeling for as up to 7 times while keeping high modeling accuracy.
作者
邱长凯
殷长春
刘云鹤
张博
任秀艳
齐彦福
蔡晶
QIU ChangKai;YIN ChangChun;LIU YunHe;ZHANG Bo;REN XiuYan;QI YanFu;CAI Jing(Development and Research Center,China Geological Survey,Beijing 100037,China;College of Geo-Exploration Science and Technology,Jilin University,Changchun 130026,China;School of Geological Engineering and Geomatics,Chang′an University,Xi′an 710054,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2020年第2期715-725,共11页
Chinese Journal of Geophysics
基金
国家自然科学基金项目(41530320,41774125,41804098)
国家重点研发计划重点专项(2018YFC0603800,2016YFC0303100,2017YFC0601900)
中科院先导专项(XDA14020102)
中央级公益性科研院所基本科研业务费专项经费(JYYWF20180103)联合资助
关键词
航空电磁
时间域
三维正演
有限元法
有理Krylov方法
Airborne electromagnetic
Time-domain
3Dforward modeling
Finite-element method
Rational Krylov method
