Large-scale,fine,and efficient numerical simulation of a geothermal field plays an important role in geothermal energy development.Confronted with the problem of large computation and high storage requirements for complex underground models in a three-dimensional(3-D)numerical simulation of a geothermal field,a mixed space-wavenumber domain 3-D numerical simulation algorithm is proposed in this paper.According to the superposition principle of temperature field,the geothermal field is decomposed into background and abnormal temperature fields for calculation.The uniform layered model is used to solve the background field.When the abnormal field is solved,the horizontal two-dimensional(2-D)Fourier transform is used to transform the 3-D differential equation satisfied by an abnormal field into a series of one-dimensional ordinary differential equations with different wavenumbers,which greatly reduces the calculation and storage.The unit division of an ordinary differential equation is flexible,and the calculation amount is small.The algorithm fully takes advantage of the efficiency of the Fourier transform and the quickness of the catch-up method to solve linear equations with a fixed bandwidth,which effectively improves the computational efficiency.Compared with the COMSOL Multiphysics professional simulation finite element software,the time consumption and memory requirements of the algorithm proposed in this paper are reduced by multiple orders of magnitude in terms of ensuring accuracy and the same mesh division.The more the number of calculated nodes is,the more obvious is the advantage.We design models to study the thermal conductivity,heat flux boundary,regional tectonic morphology,and topographic relief of the geothermal field distribution.A 3-D geophysical model is developed based on topographic elevation data,geothermal geology,and geophysical exploration data in the Qiabuqia area of Gonghe Basin,Qinghai Province,China.Numerical simulation of the geothermal field in this area is realized,which shows that the algorithm is suitable for precise and efficient simulation of an arbitrary complex terrain and geological conditions..