PCPATCH: Software for the Topological Construction of Multigrid Relaxation Methods
PCPATCH: Software for the Topological Construction of Multigrid Relaxation Methods
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PCPATCH：多重网格松弛方法拓扑构建软件
DOI：
10.1145/3445791
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发表时间：
2021
影响因子：
2.7
通讯作者：
Wechsung, Florian
中科院分区：
文献类型：
--
作者：
Farrell, Patrick E.;Knepley, Matthew G.;Mitchell, Lawrence;Wechsung, Florian
有效的松弛方法是良好的多重网格收敛所必需的。对于许多方程，标准的雅可比和高斯-赛德尔是不够的，需要更复杂的空间分解;例子包括半定项或鞍点结构的问题。在这篇文章中，我们提出了一个统一的软件抽象，PCPATCH，多重网格松弛方法的空间分解的拓扑结构。通过收集网格中的拓扑实体（如所有顶点或面）并应用构造规则（如获取每个实体周围单元中的所有自由度）来指定空间分解。该软件在PETSc中实现，仅通过在运行时改变求解器选项即可方便地表达各种方案。反过来，这允许非常快速地开发针对困难问题的快速求解器。
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems.