A real-time multigrid finite hexahedra method for elasticity simulation using CUDA
A real-time multigrid finite hexahedra method for elasticity simulation using CUDA
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DOI：
10.1016/j.simpat.2010.11.005
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发表时间：
2011-02-01
影响因子：
4.2
通讯作者：
Westermann, Ruediger
中科院分区：
文献类型：
--
作者：
Dick, Christian;Georgii, Joachim;Westermann, Ruediger
我们提出了一种多重网格的方法来模拟弹性变形物体在真实的时间在最近的NVIDIA GPU架构。为了准确地模拟大变形，我们考虑了共同旋转的应变公式。我们的方法是基于有限元离散化的可变形物体使用六面体。它借鉴了最近的工作多重网格计划的有效数值解偏微分方程的离散。由于六面体制度引起的数值模板的规则形状，并且由于我们使用所有多重网格步骤的无矩阵配方，计算和数据布局可以被重构以避免并行运行线程的执行发散，并使内存访问合并为单个内存事务。这使得能够通过CUDA并行编程API有效地利用GPU的并行处理单元和高内存带宽。我们展示了高达27和4倍的性能增益相比，一个高度优化的CPU实现一个CPU内核和8个CPU内核，分别。对于由多达269，000个元素组成的六面体模型，我们的方法以每秒11个时间步长实现了基于物理的模拟。(C)2010 Elsevier B.V.保留所有权利。
We present a multigrid approach for simulating elastic deformable objects in real time on recent NVIDIA GPU architectures. To accurately simulate large deformations we consider the co-rotated strain formulation. Our method is based on a finite element discretization of the deformable object using hexahedra. It draws upon recent work on multigrid schemes for the efficient numerical solution of partial differential equations on such discretizations. Due to the regular shape of the numerical stencil induced by the hexahedral regime, and since we use matrix-free formulations of all multigrid steps, computations and data layout can be restructured to avoid execution divergence of parallel running threads and to enable coalescing of memory accesses into single memory transactions. This enables to effectively exploit the GPU's parallel processing units and high memory bandwidth via the CUDA parallel programming API. We demonstrate performance gains of up to a factor of 27 and 4 compared to a highly optimized CPU implementation on a single CPU core and 8 CPU cores, respectively. For hexahedral models consisting of as many as 269,000 elements our approach achieves physics-based simulation at 11 time steps per second. (C) 2010 Elsevier B.V. All rights reserved.