In this paper, we introduce MPM Lite, a new hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard MPM practices suffer from a performance bottleneck where expensive implicit solves are proportional to particle-per-cell (PPC) counts due to the the choices of particle-based quadrature and wide-stencil kernels. In contrast, MPM Lite treats particles primarily as carriers of kinematic state and material history. By conceptualizing the background Cartesian grid as a voxel hexahedral mesh, we resample particle states onto fixed-location quadrature points using efficient, compact linear kernels. This architectural shift allows force assembly and the entire time-integration process to proceed without accessing particles, making the solver complexity no longer relate to particles. At the core of our method is a novel stress transfer and stretch reconstruction strategy. To avoid non-physical averaging of deformation gradients, we resample the extensive Kirchhoff stress and derive a rotation-free deformation reference solution, which naturally supports an optimization-based incremental potential formulation. Consequently, MPM Lite can be implemented as modular resampling units coupled with an FEM-style integration module, enabling the direct use of off-the-shelf nonlinear solvers, preconditioners, and unambiguous boundary conditions. We demonstrate through extensive experiments that MPM Lite preserves the robustness and versatility of traditional MPM across diverse materials while delivering significant speedups in implicit settings and improving explicit settings at the same time. Check our project page at https://mpmlite.github.io.

翻译：本文提出MPM Lite，一种新型的拉格朗日/欧拉混合方法，该方法在求解时无需依赖基于粒子的数值积分。标准物质点法（MPM）实践存在性能瓶颈：由于采用基于粒子的积分方案和宽模板核函数，昂贵的隐式求解成本与每单元粒子数（PPC）成正比。相比之下，MPM Lite主要将粒子视为运动状态与材料历史的载体。通过将背景笛卡尔网格概念化为体素六面体网格，我们使用高效紧凑的线性核函数将粒子状态重采样至固定位置的积分点。这一架构转变使得力组装与整个时间积分过程均无需访问粒子，求解器复杂度从此与粒子数量脱钩。我们方法的核心是一种新颖的应力传递与拉伸重构策略。为避免变形梯度的非物理平均，我们对广延性的基尔霍夫应力进行重采样，并推导出无旋转变形参考解，这自然支持基于优化的增量势能表述。因此，MPM Lite可实现为模块化重采样单元与有限元风格积分模块的耦合，从而能直接使用现成的非线性求解器、预处理器以及明确的边界条件。我们通过大量实验证明，MPM Lite在保持传统MPM对各种材料鲁棒性与通用性的同时，在隐式设定中实现显著加速，并同步提升显式设定的性能。项目页面详见 https://mpmlite.github.io。