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We mainly concerned with a decoupled fractional Laplacian wave equation inthis paper. A new time-space domain radial basis function (RBF) collocationmethod is introduced to solve the fractional wave equation, which describesseismic wave propagation in attenuation media. The directional fractionalLaplacian is adopted to cope with the fractional Laplacian of RBFs. In order toincrease the computational efficiency, we introduced the quasi-uniform nodesconfiguration scheme, which is suitable for mesh-free discretization of waveequations. The comparison between the new method and the commonly-usedpseudo-spectral method are implemented on square homogeneous models withdifferent model size. The CPU time and relative errors of different methodsshow that the quasi-uniform configuration scheme provides better performanceand the calculation efficiency advantage is significantly prominent as thecomputation domain increases. The relative errors indicate that the RBFcollocation method with quasi-uniform configuration could improve thecomputational efficiency effectively and provide satisfactory accuracy. Thisadvantage was especially highlighted in complex models, where the new approachachieved the same accuracy with only a half number of points. Theimplementation on the 2D complex model further demonstrated the accuracy,efficiency, and flexibility of the proposed new method.

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