基于八叉树网格的弹性动力学问题的大规模并行显式求解器
A massively parallel explicit solver for elasto-dynamic problems exploiting octree meshes
摘要：
显式动力学的典型应用领域是冲击、碰撞试验，最重要的是波传播模拟。由于这些问题的数值高要求的性质，高效的自动网格生成器和瞬态求解器是必需的。为此，一个并行显式求解器利用平衡八叉树网格的优点。为了避免标准有限元分析中的悬点问题，采用比例边界有限元法作为空间离散格式。因此，任意形状的星凸多面体元素直接生成。考虑到八叉树单元的缩放和变换，预先计算有限数量的唯一单元模式的刚度和质量矩阵。最近提出的质量集总技术扩展到3D产生一个良好的条件对角质量矩阵。这使我们能够利用显式时间积分器的优点，即，可以有效地计算节点位移而不需要求解线性方程组。我们在分布式计算环境中实现了所提出的方案与中心差分法（CDM）。我们的并行显式求解器的性能进行了评估，通过几个数值基准的例子，包括复杂的几何形状和各种实际应用。对于这些具有高达十亿个自由度并且在高达16，384个计算核心上运行的示例，观察到显著的加速。
英文摘要：
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and transient solvers are required. To this end, a parallel explicit solver exploiting the advantages of balanced octree meshes is introduced. To avoid the hanging nodes problem encountered in standard finite element analysis (FEA), the scaled boundary finite element method (SBFEM) is deployed as a spatial discretization scheme. Consequently, arbitrarily shaped star-convex polyhedral elements are straightforwardly generated. Considering the scaling and transformation of octree cells, the stiffness and mass matrices of a limited number of unique cell patterns are pre-computed. A recently proposed mass lumping technique is extended to 3D yielding a well-conditioned diagonal mass matrix. This enables us to leverage the advantages of explicit time integrator, i.e., it is possible to efficiently compute the nodal displacements without the need for solving a system of linear equations. We implement the proposed scheme together with a central difference method (CDM) in a distributed computing environment. The performance of our parallel explicit solver is evaluated by means of several numerical benchmark examples, including complex geometries and various practical applications. A significant speedup is observed for these examples with up to one billion of degrees of freedom and running on up to 16,384 computing cores.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
