基于谱元法的低频平面波电磁场数值模拟

Numerical simulation of low frequency plane wave electromagnetic field based on spectral element method

谱元法是近年来发展成熟的一种数值方法,具有高精度和指数收敛特性。基于谱元法实现了大地电磁的正演模拟,从麦克斯韦方程出发得到电场矢量Helmholtz方程,使用Gauss-Lobatto-Legendre多项式作为基函数离散Helmholtz方程,采用稳定的双共轭梯度算法求解大型稀疏线性方程组得到电磁场分布。通过与国际标准模型COMMEMI2D-0、COMMEMI2D-1的计算对比,验证了算法的有效性和准确性,对几个典型的地电模型进行模拟计算,表明了算法具有有限元的灵活性和谱方法高精度的特性,是一种高效实用的电磁正演计算方法。

The forward modeling of the geophysical magnetotelluric method is a solution to the electromagnetic field of low-frequency plane wave source.The accuracy and efficiency of the numerical solution are important factors in the practicality of the forward modeling.Spectral element method is a numerical method developed in recent years with high precision and exponential convergence.The forward modeling of magnetotellurics is realized based on the spectral element method.The electric field vector Helmholtz equation is obtained from the Maxwell equation.The Gauss-Lobatto-Legendre polynomial is used to discretize the Helmholtz equation.The stable and double conjugate gradient algorithm is used to solve large sparse linear equations,for the electromagnetic field distribution.The calculation and comparison of the international standard models COMMEMI2D-0 and COMMEMI2D-1 verify the effectiveness and accuracy of the algorithm.The simulation calculations of several typical geoelectric models show that the algorithm has the flexibility of finite element.The high precision of the spectral method is an efficient and practical electromagnetic forward calculation method.