预处理共轭梯度法在电磁正演中的应用

Preconditioning Conjugate Gradient Method in the Application of the Electromagnetic Forward Modeling

对于电磁场中的正演数值模拟,不论采取何种方法,最后都演变成求解一个规模庞大的线性方程组;而方程组的解法对数值计算的求解效率及精度起很大的决定作用。利用Pascal矩阵预处理共轭梯度法,克服了复线性方程组中系数矩阵病态特性和加快收敛速度,不但提高了正演计算速度和精度,而且保证了求解的数值稳定性及高效性。经粗细网格不同剖分方式验证,该算法可行有效。

For forward numerical simulation of electromagnetic field,no matter what method,finally has evolved into a large scale of solving a system of linear equations,and the solutions of equations for the solution efficiency and precision of numerical calculation plays a decision role.Pascal matrix preconditioning conjugate gradient method is used to overcome the double line equations in matrix pathological characteristics and speed up the convergence rate,not only improve forward modeling calculation speed and accuracy,and ensure the numerical stability and efficiency of solving,verified by different thickness of grid subdivision method.The algorithm is feasible and effective.