The CK-MPM approach introduces a compact-kernel solution to address instability issues in Material Point Method simulations while maintaining computational efficiency.

• Eliminates cell-crossing instabilities that plague traditional MPM implementations
• Preserves the computational efficiency of original MPM through compact support
• Reduces numerical diffusion without the drawbacks of previous approaches
• Enables more robust simulation of complex physical phenomena like granular flows and fracture mechanics

This advancement matters for engineering because it provides more reliable and accurate simulations for critical applications in geomechanics, materials science, and structural analysis with minimal computational overhead.

CK-MPM: A Compact-Kernel Material Point Method