We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.
翻译：我们引入了一种基于适应元素的域分解(DD)方法,用于解决被界定为二、二、二块、二块的支撑点问题。算法并不要求了解受限制的空间。我们假设所有子矩阵都稀少,对角块的光谱相当于正半确定矩阵的总和。后一种假设使DD方法的适应性粗缩空间的设计能够将GenEO理论扩展至支撑点问题。对于通过持续压力的有限元素分离的钢灌木结构,其三维弹性问题的数值结果显示为高达10亿度的自由度。
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