The Resistivity FEM Numerical Modeling on 3‐D Undulating Topography

Abstract

Abstract Based on the basic equation in stable current field equation, three‐dimension boundary value problem and the corresponding variation problem, this paper studied the algorithm of finite element numerical modeling of resistivity on 3‐D undulate topography. In the discretization of the area of integration, we used triangular prism as the minimum element of study and derived the type‐function of trilinear interpolation and element stiffness matrix. We store only the nonzero elements in sparse stiffness matrix by the way of variable bandwidth and 1‐D array, which can save the internal memory. We decomposed the large sparse matrix only once by Cholesky decomposing algorithm, and can obtain all the solutions of the system of equations by back substitution, which can save computing time when solving the sounding problem with multiple points of electricity‐supply. The results of model calculation showed that the 3‐D numerical solutions are in accordance with analytical solutions or 2‐D numerical solutions, and the calculation precision meets the error requirement. On the section with pole‐pole array on 2‐D ridge or the section with middle gradient array on 3‐D valley, the 3‐D numerical solutions are also very close to the results of physical experiment or boundary element method.