We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reaction-convection-diffusion equation. We focus on two kinds of partitions of unity, and study the dependence on the overlap and on the number of subdomains. In particular, the second kind of partition of unity, which is non-zero in the interior of the whole overlapping region, gives more favorable convergence properties, especially when increasing the overlap width, in comparison with the first kind of partition of unity, whose gradient is zero on the subdomain interfaces and which would be the natural choice for ORAS solver instead.

翻译：我们研究单位分割的选择对反应-对流-扩散方程对称优化限制性加法Schwarz（SORAS）预条件子收敛性的影响。重点考察两类单位分割，并分析其与重叠区域宽度及子域数量的依赖关系。特别地，第二类单位分割在整个重叠区域内部非零，相较于第一类（其梯度在子域交界面处为零，本为ORAS求解器的自然选择）而言，在增加重叠宽度时展现出更优的收敛特性。