A new radial basis function collocation method based on the quasi-uniform nodes for 2D fractional wave equation

TL;DR

This paper introduces a novel mesh-free radial basis function collocation method with quasi-uniform nodes for solving 2D fractional wave equations, significantly improving computational efficiency and accuracy, especially in complex models.

Contribution

The paper presents a new RBF collocation method using quasi-uniform nodes and directional fractional Laplacian, enhancing efficiency and accuracy over traditional methods for 2D fractional wave equations.

Findings

The new method reduces CPU time compared to pseudo-spectral methods.

It maintains high accuracy with fewer points in complex models.

Performance improves as the computational domain size increases.

Abstract

We mainly concerned with a decoupled fractional Laplacian wave equation in this paper. A new time-space domain radial basis function (RBF) collocation method is introduced to solve the fractional wave equation, which describes seismic wave propagation in attenuation media. The directional fractional Laplacian is adopted to cope with the fractional Laplacian of RBFs. In order to increase the computational efficiency, we introduced the quasi-uniform nodes configuration scheme, which is suitable for mesh-free discretization of wave equations. The comparison between the new method and the commonly-used pseudo-spectral method are implemented on square homogeneous models with different model size. The CPU time and relative errors of different methods show that the quasi-uniform configuration scheme provides better performance and the calculation efficiency advantage is significantly prominent as the computation domain increases. The relative errors indicate that the RBF collocation method with quasi-uniform configuration could improve the computational efficiency effectively and provide satisfactory accuracy. This advantage was especially highlighted in complex models, where the new approach achieved the same accuracy with only a half number of points. The implementation on the 2D complex model further demonstrated the accuracy, efficiency, and flexibility of the proposed new method.