The resistivity FEM numerical modeling on 3-D undulating topography
三维地形直流电阻率有限元法模拟

Based on stable electricity flow field equation,three-dimension boundary question and its corresponding variation question,the algorithm of resistivity FEM numerical modeling on a 3-D topography is studied.The integral area is divided into many tri-prism units with anomalous shapes and landform characteristics.The function of tri-linear interpolation and the matrix of tri-prism unit are then deduced.Using varied band matrix and one-dimension array to collect the large sparse matrix,the integral coefficient of all the nodes,we could save memory space.Before solving the system of linear equations,the Cholesky algorithm was adopted to decompose the large sparse matrix only once,and then we obtained the potentials of all nodes of hundreds of different current electrodes by backward substitutions.This is an important step to improve the speed of forward modeling when there are more sounding-points.The results of this modeling show that the 3-D numerical solution is in agreement with the analytic solution on level stratified medium,on 2-D mountain ridge with pole to pole array,or on 3-D mountain valley with central gradient array.The 3-D numerical solution is also in agreement with the results from physical experiment or boundary element method.