GPU Material Point Method Simulation Speedup

The simulation domain is divided into a background grid structure that segments the computational space. Particles are mapped to specific grid blocks, allowing localized computation and memory access. This segmentation enables the GPU to process particles in parallel while minimizing global memory access by confining operations to local grid blocks.

A background grid is pre-built before particle simulation begins. The grid structure, including block mappings and neighbor relationships, is constructed in advance to avoid repeated setup overhead during time-stepping. This preliminary action eliminates redundant computation in each simulation step.

The background grid mapping is rebuilt periodically rather than at every time step. The grid structure is reconstructed when particles have sufficiently moved or when simulation conditions warrant it, reducing the frequency of expensive rebuild operations while maintaining adequate accuracy.

Instead of fully rebuilding the entire grid mapping structure every step, the implementation performs partial updates only where necessary. Grid blocks that contain particles are updated, while empty or stable regions retain their existing mappings, reducing overall computational overhead.

Particles are sorted not only by spatial position but also by grid block membership, introducing an additional organizational dimension. This multi-dimensional sorting allows particles to be efficiently grouped for memory access patterns that optimize GPU coalesced reads and writes without requiring exhaustive fine-grained sorting.

Sorting is performed locally within each grid block rather than globally across all particles. This local sorting approach optimizes memory access for each block's particles independently, achieving efficient coalesced access patterns while avoiding the computational cost of global sorting.