Sparse direct linear solvers are at the computational core of domain decomposition preconditioners and therefore have a strong impact on their performance. In this paper, we consider the Fast and Robust Overlapping Schwarz (FROSch) solver framework of the Trilinos software library, which contains a parallel implementations of the GDSW domain decomposition preconditioner. We compare three different sparse direct solvers used to solve the subdomain problems in FROSch. The preconditioner is applied to different model problems; linear elasticity and more complex fully-coupled deformation diffusion-boundary value problems from chemo-mechanics. We employ FROSch in fully algebraic mode, and therefore, we do not expect numerical scalability. Strong scalability is studied from 64 to 4096 cores, where good scaling results are obtained up to 1728 cores. The increasing size of the coarse problem increases the solution time for all sparse direct solvers.

翻译：稀疏直接线性求解器是区域分解预条件子的计算核心，因此对其性能具有重要影响。本文研究了Trilinos软件库中的快速鲁棒重叠Schwarz（FROSch）求解器框架，该框架包含GDSW区域分解预条件子的并行实现。我们比较了三种用于求解FROSch子域问题的不同稀疏直接求解器。该预条件子被应用于不同的模型问题：线性弹性问题以及化学-力学中更复杂的完全耦合变形-扩散边值问题。我们采用全代数模式下的FROSch，因此未预期其数值可扩展性。在64至4096核范围内开展了强可扩展性研究，在1728核以内获得了良好的可扩展结果。粗问题规模的增加使得所有稀疏直接求解器的求解时间均有所增长。