Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper introduces a scalable, robust, and efficient algorithm to deal with 2D and 3D elastostatics contact problems between deformable bodies in a finite element framework. The proposed solution combines a treatment of the contact problem by a node-to-node pairing algorithm with a penalization technique and a non-conforming h-adaptive refinement of quadrilateral/hexahedral meshes based on an estimate-mark-refine approach in a parallel framework. One of the special features of our parallel strategy is that contact paired nodes are hosted by the same MPI tasks, which reduces the number of exchanges between processes for building the contact operator. The mesh partitioning introduced in this paper respects this rule and is based on an equidistribution of elements over processes, without any other constraints. In order to preserve the domain curvature while hierarchical mesh refinement, super-parametric elements are used. This functionality enables the contact zone to be well detected during the AMR process, even for an initial coarse mesh and low-order discretization schemes. The efficiency of our contact-AMR-HPC strategy is assessed on 2D and 3D Hertzian contact problems. Different AMR detection criteria are considered. Various convergence analyses are conducted. Parallel performances up to 1024 cores are illustrated. Furthermore, memory footprint and preconditionners performance are analyzed.

翻译：针对三维弹性静力学接触力学问题，并行实现数值自适应网格细化（AMR）策略是迈向超越当前性能水平的复杂仿真的关键步骤。本文提出了一种可扩展、鲁棒且高效的算法，用于在有限元框架下处理可变形体之间的二维和三维弹性静力学接触问题。所提出的解决方案结合了通过节点对节点配对算法与惩罚技术处理接触问题的方法，以及在并行框架中基于估计-标记-细化方法对四边形/六面体网格进行非协调h自适应细化。我们并行策略的一个特殊之处在于，接触配对的节点由相同的MPI任务托管，这减少了构建接触算子时进程间的交换次数。本文引入的网格划分遵循此规则，并基于进程间元素的均衡分布，无需任何其他约束。为了在分层网格细化过程中保持域曲率，采用了超参数单元。此功能使得在AMR过程中即使对于初始粗网格和低阶离散化方案，也能很好地检测接触区域。我们通过二维和三维赫兹接触问题评估了接触-AMR-HPC策略的效率。考虑了不同的AMR检测标准。进行了多种收敛性分析。展示了高达1024核的并行性能。此外，还分析了内存占用和预处理器性能。