Modified space-time radial basis function collocation method for solving three-dimensional transient elastodynamic problems

In this paper, we improve the traditional space-time radial basis function (RBF) collocation method for solving three-dimensional elastodynamic problems. The proposed approach arranges source points outside the entire space-time domain by introducing space and time amplification factors, rather than locating them within the computational domain. Additionally, a multiple-scale technique is developed to address the ill-conditioning issue in the resulting matrix system. The coefficient matrix produced by the modified RBF collocation method depends solely on the space-time distances between the collocation points and the source points, making it simple in structure and easy to compute. Numerical examples involving complex geometries and mixed boundary conditions are simulated to verify the performance of the presented approach. In cases where exact solutions are unavailable, the results achieved by the proposed method closely match those obtained by the finite element method (FEM), validating the effectiveness of the developed approach. In addition, the proposed approach has faster convergence rate than the FEM. Comparison results among the modified method, the FEM, and the traditional space-time RBF collocation method demonstrate the superior accuracy of the proposed approach, positioning it as a promising tool for handling transient elastodynamic problems.