论文标题
基于带边矩阵的辅助拓扑的代数多机方法
An algebraic multigrid method based on an auxiliary topology with edge matrices
论文作者
论文摘要
本文介绍了一种新型方法，用于代数多机方法，用于来自某些椭圆二阶偏差方程的有限元离散的大型线性方程系统。基于由边缘和顶点贡献组成的离散能量，我们能够制定粗化标准，即使方程式系统也可以保证两级收敛。这种能量还使我们能够用规定的稀疏模式构建延长，这些稀疏模式仍然可以准确地保留核向量。这些允许简单的优化，简化并行化并减少粗糙级别的通信。数值实验证明了实现方法的效率和鲁棒性。
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete energy made up of edge and vertex contributions, we are able to develop coarsening criteria that guarantee two-level convergence even for systems of equations. This energy also allows us to construct prolongations with prescribed sparsity pattern that still preserve kernel vectors exactly. These allow for a straightforward optimization that simplifies parallelization and reduces communication on coarse levels. Numerical experiments demonstrate efficiency and robustness of the method and scalability of the implementation.
