Application Of Algebraic Multigrid Method In Finite Element Simulation Of Direct Current Method

The finite element numerical simulation has become one of the effective ways to solve complex geophysical problems. The finite element method consists of three main processes: mesh generation and optimization,formation of the finite element discrete system, as well as solving algebraic equations. Among them, solving algebraic equations is an important step, which directly influences the accuracy of final results. Therefore, it's significant to seek an efficient method for solving the equations of geophysical finite element simulation.This paper analysis the normal methods for solving algebraic equations of finite element simulation detailedly, such as CG,ICCG etc. After researching normal iterative methods, we introduce a robustly convergent method, which is called algebraic multigrid method(AMG), we describe the basic principles,astringency and algorithms of algebraic multigrid method (AMG) detailedly, and we also applied AMG to numerical examples to analyze the convergence. Usually, the algebraic equations of Direct Current finite element simulation is large-scale and sparse, according to this feature, we propose an AMG preconditioned CG method that is suitable for finite element linear equation. Finally, we write corresponding codes for several algorithms with Matlab. And we calculate some real modals of 2.5D direct current finite element analysis using these algorithms to compare these methods.The results show that AMG method and AMG-PCG method have very fast convergence speed and very high accuracy in solving the algebraic equations of finite element analysis, these two methods are more effective compared to other iterative methods.