论文标题
在虚拟几何形状上平行预先条件的网格弯曲的自动惩罚和学位延续
Automatic penalty and degree continuation for parallel pre-conditioned mesh curving on virtual geometry
论文作者
论文摘要
我们提出了一种用于虚拟几何形状的分布式并行网格弯曲方法。主要应用程序是在适用于非结构化高阶方法分析的复杂几何形状上生成大规模的曲线。因此，我们设计了该技术来生成由高质量元素组成的几何准确的网格。为此，我们主张在基于罚款的二阶优化器上延续学位，该优化器使用全球紧密的公差来融合失真残差。为了减少方法记忆足迹，等待时间和能耗，我们结合了三种主要成分。首先，我们提出了一个无基质的GMRES求解器，该求解器已通过块连续过度删除，以减少记忆足迹3次。我们还提出了一种自适应惩罚技术，以减少非线性迭代的数量。第三，我们提出了所需的线性求解器公差的指标，以减少线性迭代的数量。在数千个核心上，该方法曲线网眼由数百万个四分之一的元素组成，这些元素具有高度伸展的元素，同时匹配虚拟拓扑。
We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable for analysis with unstructured high-order methods. Accordingly, we devise the technique to generate geometrically accurate meshes composed of high-quality elements. To this end, we advocate for degree continuation on a penalty-based second-order optimizer that uses global tight tolerances to converge the distortion residuals. To reduce the method memory footprint, waiting time, and energy consumption, we combine three main ingredients. First, we propose a matrix-free GMRES solver pre-conditioned with successive over-relaxation by blocks to reduce the memory footprint three times. We also propose an adaptive penalty technique, to reduce the number of non-linear iterations. Third, we propose an indicator of the required linear solver tolerance to reduce the number of linear iterations. On thousands of cores, the method curves meshes composed of millions of quartic elements featuring highly stretched elements while matching a virtual topology.
