B-spline convected particle domain interpolation method

The B-spline material point method (BSMPM) has been shown to be a promising approach to effectively mitigate the cell-crossing instability by using high-order B-spline basis functions. However, the BSMPM still suffers from the quadrature error, another well-known source of inaccuracy in the material point methods. On the other hand, the convected particle domain interpolation (CPDI) method effectively reduces the quadrature error by using alternative basis functions. The B-spline basis functions can be naturally used within the CPDI formulation, here called the BSCPDI method. The BSCPDI may be prone to the cell-crossing instability since the alternative basis functions in the BSCPDI are always C0-continuous despite the high-continuity of the B-spline basis functions used as the original grid basis functions. In this paper, the reproducibility of the BSCPDI effective basis function gradients and the susceptibility of the method to the cell-crossing instability are investigated analytically and numerically. The effectiveness of the BSCPDI in mitigating the quadrature error is also investigated through numerical simulations.