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.

翻译：我们为虚拟几何提供了分布式平行网格曲线缩略法。 主要的应用程序是生成大型弯曲网格, 用于使用非结构化的高阶方法进行分析。 因此, 我们设计了一种技术, 以产生由高质量元素组成的几何精确的网格。 为此, 我们主张在基于惩罚的第二阶优化器上保持一定度, 使用全球近距离宽度将扭曲残留物汇合在一起。 为了减少方法的记忆足迹、 等待时间和能量消耗, 我们合并了三个主要元素。 首先, 我们提出一个没有矩阵的GMRES解析器, 预先设定了以区块相接连的过度松缩为条件, 以降低记忆足迹的三次。 我们还提出了一种适应性惩罚技术, 以减少非线性迭代数。 第三, 我们提出一个需要的线性求解容忍度指标, 以减少线性迭代数以万计的核心, 方法曲线由成数以百万计的夸度元素构成高度伸展的微元素组成。