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On the initial estimate of interface forces in FETI methods

机译：关于FETI方法中界面力的初始估计

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摘要

The balanced domain decomposition (BDD) method and the finite element tearing and interconnecting (FETI) method are two commonly used non-overlapping domain decomposition methods. Due to strong theoretical and numerical similarities, these two methods are generally considered as being equivalently efficient. However, for some particular cases, such as for structures with strong heterogeneities, FETI requires a large number of iterations to compute the solution compared to BDD. In this paper, the origin of the poor efficiency of FETI in these particular cases is traced back to bad initial estimates of the interface stresses. To improve the estimation of interface forces, a novel strategy for splitting interface forces between neighboring substructures is proposed. The additional computational cost incurred is not significant. This yields a new initialization for the FETI method and restores numerical efficiency which makes FETI comparable to BDD even for problems where FETI was performing poorly. Various simple test problems are presented to discuss the efficiency of the proposed strategy and to illustrate the so-obtained numerical equivalence between the BDD and FETI solvers.
机译：平衡域分解（BDD）方法和有限元撕裂和互连（FETI）方法是两种常用的非重叠域分解方法。由于强烈的理论和数值相似性，通常认为这两种方法等效。但是，对于某些特殊情况，例如对于具有强异质性的结构，与BDD相比，FETI需要大量迭代才能计算解。在本文中，在这些特殊情况下，FETI效率低下的根源可追溯到对界面应力的不良初始估计。为了改善界面力的估计，提出了一种在相邻子结构之间分配界面力的新策略。所产生的额外计算成本并不大。这为FETI方法产生了新的初始化，并恢复了数值效率，即使在FETI性能不佳的问题上，FETI仍可与BDD相提并论。提出了各种简单的测试问题，以讨论所提出策略的效率并说明BDD和FETI求解器之间的数值等效性。

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