Finite Element Resistivity Forward Modeling Using Algebraic Multigrid Preconditioned Conjugate Gradient Method

An algebraic multigrid by smoothed aggregation preconditioned conjugate gradient method is developed to solve the liner system arising from 3-D direct current finite element resistivity forward modeling. The algorithm combines the efficiency of algebraic multigrid method and the stability of conjugate gradient method. Algebraic multigrid by smoothed aggregation keep in high-efficiency while simulation using local quasi-uniform mesh and its convergence effect will reduce while numerical modeling using anisotropic stretched grids. However tensor product non-equidistant mesh, a kind of anisotropic stretched grids, is often used in 3-D direct current resistivity forward modeling. In order to improve this situation, a factor is added to guide correct aggregation. Consequently, a typical example is used to prove that the improvement is the right. Finally, it is natural to conclude that the algorithm suggested in this paper is efficient and robust whether simulation using local quasi-uniform mesh or tensor product non-equidistant mesh