大地电磁三维正演聚集多重网格算法

为了加快大地电磁三维正演的求解速度，本文将一种新型的代数多重网格算法——聚集多重网格（aggregation-based algebraic multigrid， AGMG）算法引入大地电磁三维正演模拟中。首先从准静态条件下的麦克斯韦方程出发，利用交错网格有限体积法进行离散，并采用第一类Dirichlet边界条件形成大型稀疏复线性方程组；然后阐述AGMG算法的粗化策略和套迭代技术，并实施3种不同的AGMG求解算法：1）传统的V循环AGMG算法；2）AGMG预处理共轭梯度（AGMG-CG）；3）AGMG预处理广义共轭残差法（AGMG-GCR）。最终实现大地电磁法三维正演模拟。对典型地电模型进行正演模拟，并与已有的大地电磁三维正反演程序（ModEM）进行结果对比，以验证本文算法的准确性。另外，不同剖分网格和极化方式正演模拟结果与准残量最小化（QMR）迭代算法的对比表明，AGMG预处理求解算法（AGMG-CG、AGMG-GCR）不仅能够改善算法的稳定性，而且能够快速有效地求解正演问题；其中AGMG-GCR迭代次数更少，求解速度更快，误差衰减曲线更光滑，在144×152×104网格剖分情况下，相对于现有ModEM程序能够提高十几倍的计算速度，尤其适合大规模大地电磁三维正演问题。

Three-Dimensional Magnetotelluric Modelling Using Aggregation-Based Algebraic Multigrid Method

To speed up 3D magnetotelluric (MT) modelling,we introduce a novel algebraic multigrid-aggregation-based algebraic multigrid method (AGMG) into three dimensional forward modeling of magnetotelluric.We used the finite-volume algorithm based on the Yee's grids to discretize quasi-static Maxwell's equations with Dirichlet boundary conditions,and used the AGMG method to solve the final large sparse linear equation system in electric field.Through the coarsening of AGMG and the aggregating based on N-passes of a pairwise matching algorithm applied to the matrix graph,we proposed three different AGMG algorithms:1) the classic V-cycle AGMG algorithm;2) the AGMG preconditioned conjugate gradient algorithm (AGMG-CG);3) the AGMG pretreated generalized conjugate residual method (AGMG-GCR).We performed 3D MT modelling for typical geo-electric models with different iteration,and analyzed the features of the AGMG techniques through comparing with ModEM algorithm.The results show that the AGMG methods are accurate and robust,the AGMG preconditioner improves the convergence of the classic V-cycle AGMG and Krylov subspace methods greatly.The AGMG-GCR method is the most effective one presented in this paper,which speeds up the modeling by ten times more than the ModEM codes for large-scale grids (144 × 152 × 104).The AGMGGCR is especially suitable for large-scale 3D MT modeling because of its high precision,fast convergence,and robust iteration.