High precision simulation in frequency domain based on improved acoustic equation and MCPML boundary

Numerical dispersion and boundary reflection are two important problems affecting the simulation results in frequency domain. However, restricted by the computational efficiency and memory consumption of impedance matrix decomposition, increasing the length of finite-difference operators or the number of finite-difference grids are not the optimal solution to improve the simulation accuracy. Firstly, the theoretical mechanism of numerical dispersion is analyzed. On this basis, an improved acoustic equation expression with "wave number compensation" is derived and its physical significance is elaborated, which could effectively suppress numerical dispersion and improve simulation accuracy; On the boundary reflection problem, instead of perfectly matched layer (PML) boundary, the multi-axial convolution perfectly matched layer (MCPML) boundary is used to rapidly absorb the residual energy and eliminate the boundary reflection. Combined with the improved acoustic equation and MCPML boundary, a high-precision expression of acoustic equation in frequency domain is studied. The numerical simulations demonstrate that the proposed method in this paper is a high-precision simulation method in frequency domain, with high simulated accuracy and efficiency, clear simulated wave fields and without increasing the calculation amount and memory consumption.