Numerical simulation of two-dimensional strong magnetic field and its gradient tensor in space-wavenumber domain
DAI Shikun1,2, RAN Yingqiang1,2, ZHANG Ying1,2, CHEN Qingrui1,2, LING Jiaxuan1,2, JIA Jinrong1,2
1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha, Hunan 410083, China; 2. School of Geosciences and Info-physics, Central South University, Changsha, Hunan 410083, China
Abstract:On the basis of the Poisson equation of magnetic potential, a two-dimensional numerical simulation method of the mixed space-wavenumber domain is proposed. The method uses the one-dimensional Fourier transform and transforms the partial differential equation suitable for the magnetic potential of a two-dimensional strong magnetic body into an ordinary differential equation with independent different wavenumbers. In other words, it changes the two-dimensional numerical simulation question into a one-dimensional one for solutions and employs the one-dimensional finite element method to solve the one-dimensional numerical simulation question, so as to greatly reduce storage demands and computational loads. Furthermore, a high-precision approximate solution of the solved strong magnetic field is obtained by using a compact operator for iteration. In the algorithm, the vertical direction is reserved as the spatial domain, and the mesh can be flexibly divided according to the demand, which is conducive to simulating complex conditions. In addition, the ordinary differential equation among different wavenumbers is independent and has excellent parallelism. The algorithm makes full use of the rapidness of the Fourier transform and the stability of the iterative algorithm and realizes the two-dimensional numerical simulation of the strong magnetic field and its gradient tensor. Three models (cylinder and prism models under horizontal terrain and model under undulating terrain) are calculated, and the numerical solution is compared with the analytical solution and the numerical solution by COMSOL software. The results show that the algorithm is fast and highly accurate and thus is suitable for undulating terrain.
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