Three-Dimensional Direct Current Resistivity Finite Element Method Forward Modelling Based on Jacobi Preconditioned Conjugate Gradient Algorithm

Abstract

The calculation speed and accuracy of resistivity forward model are important for direct current exploration. This study proposes a calculation method for the forward model. First, we structured the unstructured grid to enable dissection of the three-dimensional finite element space. We then solved the large sparse linear equations, using the preconditioned conjugate gradient method. The diagonal matrix in the Jacobi iteration was used as the pre-processed matrix, which had the characteristics of a convenient inversion solution and consumed less memory; therefore, it substantially increased the speed to solve large linear equations. The forward modelling performed using synthetic data shows that the preconditioned conjugate gradient algorithm exhibits fast calculation speed and high accuracy. These results are in accordance with the potential distribution rule of the underground electric field. The results have value for three-dimensional direct current exploration in the field of engineering. Furthermore, it provides a reference for solving large linear equations of the finite element method in other fields.