论文标题
通过与亚对象相关的约束平衡域分解
Balancing domain decomposition by constraints associated with subobjects
论文作者
论文摘要
BDDC预处理的一个简单变体，其中介绍了在选定的子对象集（子域子方，子方面和子两个对之间的顶点）上施加约束。我们能够证明，预处理的条件号由$ c \ big（1+ \ log（l/h）\ big）^2 $界定，其中$ c $是一个常数，$ h $和$ l $是网格和子对象的特征大小。由于几乎可以自由地选择$ L $，因此从理论上讲，条件号可以小至$ O（1）$。我们将讨论预定器的利弊及其在异质问题中的应用。提供了超级计算机的数值结果。
A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by $C \big(1+\log (L/h)\big)^2$, where $C$ is a constant, and $h$ and $L$ are the characteristic sizes of the mesh and the subobjects, respectively. As $L$ can be chosen almost freely, the condition number can theoretically be as small as $O(1)$. We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.
