近似与原始多级FETI-DP方法：多级扩展及与BDDC的交互
Inexact and primal multilevel FETI-DP methods: a multilevel extension and interplay with BDDC
AI总结：
本文提出了一种多级FETI-DP方法，结合多级BDDC方法，通过近似求解粗问题提升求解效率，并验证了其与BDDC预条件算子的谱一致性。
摘要：
我们研究了一种框架，该框架允许在FETI-DP方法中近似求解粗问题。该框架基于FETI-DP系统的鞍点公式，并采用块三角预条件子。其中一个块近似求解粗问题，我们使用多级BDDC方法作为主要工具。这种策略自然导致多级FETI-DP方法的一种变体，我们证明了多级FETI-DP和BDDC预条件算子的谱本质上是相同的。理论通过一组数值实验加以说明，我们还展示了当粗问题被代数多网格近似时的一些实验结果。
英文摘要：
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.
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