A localized MQRBF-FD method with adaptive shape parameter optimization for acoustic wave simulation

Accurately simulating acoustic wave propagation is crucial for seismic exploration and acoustic imaging. Traditional numerical methods often struggle to balance accuracy and computational efficiency, particularly when applied to heterogeneous media. The multiquadric radial basis function (MQRBF)-FD method offers flexibility in handling irregular geometries but encounters difficulties in selecting optimal shape parameters and maintaining computational efficiency for large-scale problems. In this paper, we introduce a localized MQRBF-FD method with adaptive shape parameter optimization to address these challenges. This approach combines the spatial approximation flexibility of MQRBF with the computational efficiency of the finite difference (FD) method for time derivatives. The method employs an enhanced random walk algorithm and Adam-BP model to adaptively determine the shape parameters based on Fourier expansions of the wave function. This strategy improves both accuracy and stability in complex media. By performing localized computations, the method minimizes unnecessary global interactions, thus ensuring computational efficiency. Extensive validation, including comparisons with traditional methods in both 2D and 3D scenarios, across various media and grid types, demonstrates significant improvements in accuracy, stability, and acceptable computational cost.