Inexact and primal multilevel FETI‐DP methods: a multilevel extension and interplay with BDDC
Inexact and primal multilevel FETI‐DP methods: a multilevel extension and interplay with BDDC
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DOI：
10.1002/nme.7057
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发表时间：
2022-06
影响因子：
2.9
通讯作者：
B. Sousedík
中科院分区：
文献类型：
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作者：
B. Sousedík
我们研究了一个框架，可以近似解决 FETI-DP 方法中的粗略问题。它基于带有块三角预处理器的 FETI-DP 系统的鞍点公式。其中一个块近似粗略问题，我们使用多级 BDDC 方法作为主要工具。这种策略自然会导致多级 FETI-DP 方法的一个版本，并且我们表明多级 FETI-DP 和 BDDC 预处理算子的谱本质上是相同的。该理论通过一组数值实验进行了说明，并且我们还提出了一些用代数多重网格近似粗解时的实验。
We study a framework that allows to solve the coarse problem in the FETI‐DP method approximately. It is based on the saddle‐point formulation of the FETI‐DP system with a block‐triangular preconditioner. One of the blocks approximates the coarse problem, for which we use the multilevel BDDC method as the main tool. This strategy then naturally leads to a version of multilevel FETI‐DP method, and we show that the spectra of the multilevel FETI‐DP and BDDC preconditioned operators are essentially the same. The theory is illustrated by a set of numerical experiments, and we also present a few experiments when the coarse solve is approximated by algebraic multigrid.