A Temporally Adaptive Material Point Method with Regional Time Stepping
A Temporally Adaptive Material Point Method with Regional Time Stepping
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DOI：
10.1111/cgf.13524
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发表时间：
2018-09
影响因子：
2.5
通讯作者：
Yu Fang;Yuanming Hu;Shimin Hu;Chenfanfu Jiang
中科院分区：
文献类型：
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作者：
Yu Fang;Yuanming Hu;Shimin Hu;Chenfanfu Jiang
空间和时间自适应算法能够显著提高计算力学和基于物理的动画中许多数值格式的计算效率。最近，由于多材料场景中材料刚度和速度可能存在较大变化，物质点法（MPM）对时间自适应的关键需求日益凸显。在这项工作中，我们针对具有区域时间步长（RTS）的物质点法提出了一种新颖的时间自适应辛欧拉格式，即在不同区域使用不同的时间步长。我们设计了一种以小块为粒度的时间步长调度器，以保持与物质点法的混合粒子/网格特性的自然一致性。我们的方法利用了稀疏分页网格（SPGrid）数据结构，并通过一种实用的多线程粒子 - 网格传输策略同时实现了高效率和显著的易于实现性。我们在包括弹性物体、颗粒介质和流体在内的各种示例上展示了我们的异步物质点法的有效性。
Spatially and temporally adaptive algorithms can substantially improve the computational efficiency of many numerical schemes in computational mechanics and physics‐based animation. Recently, a crucial need for temporal adaptivity in the Material Point Method (MPM) is emerging due to the potentially substantial variation of material stiffness and velocities in multi‐material scenes. In this work, we propose a novel temporally adaptive symplectic Euler scheme for MPM with regional time stepping (RTS), where different time steps are used in different regions. We design a time stepping scheduler operating at the granularity of small blocks to maintain a natural consistency with the hybrid particle/grid nature of MPM. Our method utilizes the Sparse Paged Grid (SPGrid) data structure and simultaneously offers high efficiency and notable ease of implementation with a practical multi‐threaded particle‐grid transfer strategy. We demonstrate the efficacy of our asynchronous MPM method on various examples including elastic objects, granular media, and fluids.