Abstract: Electromagnetic method of geoelectrical frequency domain has a wide range of applications in exploring Earth's deep structure, petroleum exploration, environmental and engineering surveying, and its accuracy and efficiency of numerical simulation directly affect the interpretation results of data. However, there are currently issues with low accuracy and long computation time in three-dimensional numerical simulation of frequency domain electromagnetic fields, as well as limitations in computational scale. This paper proposes to use integral equation method and direct solution method to improve the solution accuracy, and adopt technologies such as hybrid parallel processing at multiple levels and multiple grain sizes, distributed storage, etc., to greatly reduce the computation time and expand the computational scale. This paper implements a fast, high-precision, and highly scalable three-dimensional numerical simulation method of frequency domain electromagnetic fields, which includes parallel processing between frequency points, parallel filling of impedance matrix, and parallel direct solution of equations. Firstly, the theoretical framework of integral equation method and its parallel implementation solution are introduced in detail. Then, typical cases are selected to verify the correctness of the program by comparing with previous calculation results. Finally, the scalability is tested for a large-scale example with 16 frequencies, 16×12 495 unknowns, and 861 observation points. Compared to a single node with 32 processes, when the computational scale reaches 256 nodes and 8 192 processes, the speedup ratio is 69.69 and the parallel efficiency is 27.22%. This large-scale parallel algorithm is applicable to both geomagnetic and controlled source audio geomagnetic integral equation methods.

Key words: electromagnetic method, frequency domain, integral equation method, parallel algorithm, high performance computing