A convected particle Gauss-quadrature interpolation for the cell crossing error reduction

Convected particle domain interpolation (CPDI) is a developed extension technique of the material point method (MPM), which can effectively reduce cell crossing error. However, it is still possible that CPDI does not ensure the convergence rate expected in the case of large deformation. Thus, this paper presents a new method, named convected particle Gauss-quadrature interpolation (CPGI), enhancing CPDI formulation by gauss quadrature. The CPGI considers the particle domain as four independent corner points and derives the particle-to-node mapping equations using gauss quadrature. Through numerical examples of axial vibration, generalized vortex, and collision, this work demonstrates the CPGI algorithm’s effectiveness in reducing the cell crossing error over the time of traversing the grid. Furthermore, the CPGI is evaluated using other different algorithms and initial configurations. As a result of the results, the algorithm has significant advantages in terms of accuracy and can provide reasonable efficiency.