An Unconditionally Stable Locally 1-D Node-Based Radial Point Interpolation Method

In this letter, an unconditionally stable node-based radial point interpolation method (RPIM) is developed and proposed. With the application of the locally 1-D scheme, an implicit time-marching formulation for the proposed method is derived. The Courant-Friedrich-Levy stability condition is removed, and the time step is limited only by modeling accuracy. Numerical results not only verify the unconditionally stability of the proposed method, but also show that compared with the conventional RPIM method, the CPU time can be reduced by more than 80% with no more than 3% sacrifice of accuracy. In addition, the proposed method is approximately 30% faster than the leapfrog alternating-direction-implicit-RPIM method.