GPU-acceleration of stiffness matrix calculation and efficient initialization of EFG meshless methods
GPU-acceleration of stiffness matrix calculation and efficient initialization of EFG meshless methods
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DOI：
10.1016/j.cma.2013.02.011
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发表时间：
2013-05
影响因子：
7.2
通讯作者：
Alexander Karatarakis;P. Metsis;M. Papadrakakis
中科院分区：
文献类型：
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作者：
Alexander Karatarakis;P. Metsis;M. Papadrakakis
无网格方法在裂纹扩展和扩展、大位移、应变局部化和复杂几何等问题上具有许多优点。尽管它们不依赖于网格，但在构建刚度矩阵之前，无网格方法需要一个初步步骤来识别节点和高斯点之间的相关性。这是在有限元法中隐式地执行网格生成，但必须在EFG方法中显式地完成，并且可能很耗时。此外，所得到的矩阵更密集，问题的表述和求解的计算成本远高于传统的有限元法。这主要是由于节点和集成点之间的相互作用大大增加，因为它们的影响范围扩大了。由于这些原因，在无网格EFG方法中计算刚度矩阵是一项非常需要计算的任务，需要特别注意，以便在实际应用中负担得起。在本文中，我们解决了预处理阶段，处理定义节点和高斯点之间以及相互作用节点之间必要的相关性的问题，以及刚度矩阵的计算。提出了一种计算刚度矩阵的新方法，该方法具有几个计算优点，其中一个优点是易于并行化，可以利用图形处理单元（gpu）加速计算。
Meshless methods have a number of virtues in problems concerning crack growth and propagation, large displacements, strain localization and complex geometries, among other. Despite the fact that they do not rely on a mesh, meshless methods require a preliminary step for the identification of the correlation between nodes and Gauss points before building the stiffness matrix. This is implicitly performed with the mesh generation in FEM but must be explicitly done in EFG methods and can be time-consuming. Furthermore, the resulting matrices are more densely populated and the computational cost for the formulation and solution of the problem is much higher than the conventional FEM. This is mainly attributed to the vast increase in interactions between nodes and integration points due to their extended domains of influence. For these reasons, computing the stiffness matrix in EFG meshless methods is a very computationally demanding task which needs special attention in order to be affordable in real-world applications. In this paper, we address the pre-processing phase, dealing with the problem of defining the necessary correlations between nodes and Gauss points and between interacting nodes, as well as the computation of the stiffness matrix. A novel approach is proposed for the formulation of the stiffness matrix which exhibits several computational merits, one of which is its amenability to parallelization which allows the utilization of graphics processing units (GPUs) to accelerate computations.