Iterative algorithm for computing magnetic field considering remanent magnetization and demagnetization

SUMMARY Efficient and high-precision methods for performing large-scale numerical calculations under high magnetic susceptibility conditions are essential for magnetic exploration applications. This paper proposes an algorithm for magnetic field modelling considering both demagnetization and remanent magnetization. The 3-D partial differential equation of magnetic potential is reduced to a 1-D ordinary differential equation in the space-wavenumber domain through a 2-D Fourier transform in the horizontal direction. Using the quadratic interpolation finite element method to obtain the pentagonal equation, the chasing method is used to solve the equation efficiently, and a contraction operator based on electromagnetic integral equation method is introduced to ensure stable iteration convergence. The validity of the algorithm was confirmed by comparing it with analytical solutions. Numerical examples demonstrate the importance of considering demagnetization under high magnetization conditions. Test results reveal that magnetic susceptibility is the sole factor affecting convergence among the factors examined. Further analysis showed that, for the same magnetic susceptibility, the algorithm converges with the same number of iterations and higher precision is achieved with an increasing number of nodes. Under the same grid configuration, higher magnetic susceptibility requires more iterations to converge and results in lower algorithm precision. The algorithm presented in this paper shows higher efficiency compared to those based on integral equations. Moreover, we demonstrate the algorithm's high accuracy when applied to models with anomalies near boundaries. Finally, the adaptability of the algorithm to complex geological models and undulating topography is verified by combining model tests with DEM data. This algorithm presents an efficient and high-precision method for magnetic field calculations under conditions of high susceptibility and strong remanent magnetization, offering promising prospects for geoscience applications.