Preconditioning the coarse problem of BDDC methods ‐ three-level, algebraic multigrid, and vertex-based preconditioners
Preconditioning the coarse problem of BDDC methods ‐ three-level, algebraic multigrid, and vertex-based preconditioners
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预处理 BDDC 方法的粗略问题 - 三级、代数多重网格和基于顶点的预处理器
DOI：
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发表时间：
2019
影响因子：
1.3
通讯作者：
J. Weber
中科院分区：
文献类型：
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作者：
A. Klawonn;M. Lanser;O. Rheinbach;J. Weber
公平的比较三个平衡区域分解的约束（BDDC）方法与近似的粗空间求解器是第一次尝试。比较了BDDC方法与代数多重网格预条件的粗糙问题，一个三层次的BDDC方法，和BDDC方法与基于顶点的粗糙预条件最近推出的克拉克Dohrmann，肯德尔皮尔逊，和奥洛夫Widlund。第一次，所有的方法都在一个共同的框架中提出和讨论。条件数界限提供了所有的方法。所有的方法都是在一个共同的高度并行可扩展的BDDC软件包的基础上PETSc的，以允许一个公平的比较。数值结果显示并行可扩展性的线弹性方程。这首次包括对基于顶点的近似BDDC方法的并行可扩展性测试。
A fair comparison of three Balancing Domain Decomposition by Constraints (BDDC) methods with an approximate coarse space solver is attempted for the first time. The comparison is made for a BDDC method with an algebraic multigrid preconditioner for the coarse problem, a three-level BDDC method, and a BDDC method with a vertex-based coarse preconditioner which was recently introduced by Clark Dohrmann, Kendall Pierson, and Olof Widlund. For the first time, all methods are presented and discussed in a common framework. Condition number bounds are provided for all approaches. All methods are implemented in a common highly parallel scalable BDDC software package based on PETSc, to allow for a fair comparison. Numerical results showing the parallel scalability are presented for the equations of linear elasticity. For the first time, this includes parallel scalability tests for the vertex-based approximate BDDC method.