A parallel implementation of a compatible discretization scheme for steady-state Stokes problems is presented in this work. The scheme uses generalized moving least squares to generate differential operators and apply boundary conditions. This meshless scheme allows a high-order convergence for both the velocity and pressure, while also incorporates finite-difference-like sparse discretization. Additionally, the method is inherently scalable: the stencil generation process requires local inversion of matrices amenable to GPU acceleration, and the divergence-free treatment of velocity replaces the traditional saddle point structure of the global system with elliptic diagonal blocks amenable to algebraic multigrid. The implementation in this work uses a variety of Trilinos packages to exploit this local and global parallelism, and benchmarks demonstrating high-order convergence and weak scalability are provided.

翻译：本文介绍了稳定状态斯托克斯问题兼容的离散计划平行实施情况。该计划使用通用移动最小方块生成差异操作员和适用边界条件。这一无网点计划允许速度和压力的高度趋同,同时纳入类似有限差异的分散化。此外,该方法本质上是可以伸缩的:电流生成过程要求当地对可加速使用GPU的基质进行反向处理,对速度的无差异处理取代了全球系统的传统支撑点结构,用可变距多电网的椭圆对角块取代了全球系统的传统支撑点结构。在这项工作中,使用各种Trilinos套件来利用这种本地和全球的平行化,并提供了显示高度级趋同性和可变性的基准。