3D Magnetic Field Forward Modeling using Quadratic Finite Element Continuous Fourier Transform and parallel CPU/GPU acceleration

Efficient and high-precision methods for magnetic field modeling are crucial for the accurate inversion and interpretation of magnetic survey data. In response, an efficient magnetic field forward modeling algorithm using Quadratic Finite Element Continuous Fourier Transform (QFE-CFT), leveraging CPU/GPU parallel computing, has been proposed to meet these demands. By applying a two-dimensional Fourier transform in the horizontal directions, the three-dimensional partial differential equation is reduced to a set of independent one-dimensional ordinary differential equations in the vertical direction, significantly improving computational efficiency and enabling parallel acceleration. The finite element method is then employed to form a five-diagonal linear system, which is efficiently solved using the chasing method. Finally, the magnetic field in the spatial domain is obtained using the Quadratic Finite Element Continuous Inverse Fourier Transform (QFE-CIFT). A model with anomalous spheres near the boundary of the considered computation area was designed to validate the accuracy and effectiveness of the algorithm. Comparisons with the standard-FFT, Gauss-FFT, and NUFFT algorithms demonstrated that the proposed method is unaffected by boundary effects. By utilizing OpenMP for equation solving and GPU acceleration for the QFE-CFT, the computational efficiency of the CPU/GPU parallel algorithm is significantly enhanced compared to the CPU serial algorithm, achieving an acceleration ratio of up to 86 times under the given hardware conditions. This approach provides a powerful tool for high-precision magnetic data inversion and geological interpretation.