论文标题
Schwarz结构域分解方法的分析，用于导体样筛选连续模型
Analysis of the Schwarz domain decomposition method for the conductor-like screening continuum model
论文作者
论文摘要
我们研究了Schwarz重叠的域分解方法应用于特殊领域的泊松问题，该域由构造组成，包括大量固定尺寸的子域的结合。这些域是由子域由范德华球组成的计算化学中的应用。与域分解方法理论一样，施瓦茨方法的收敛速率与稳定的子空间分解有关。我们为这个域家族得出了这种稳定的分解，并分析了稳定性“常数”如何取决于域的相关几何特性。为此，我们介绍了用于为领域家庭形式化几何形状的新描述符。我们显示，对于越来越多的子域，Schwarz方法的收敛速率如何取决于特定的局部几何描述符和一个全局几何描述符。该分析还自然地提供了该域家族的拉普拉斯特征值问题的最小特征值的描述符。
We study the Schwarz overlapping domain decomposition method applied to the Poisson problem on a special family of domains, which by construction consist of a union of a large number of fixed-size subdomains. These domains are motivated by applications in computational chemistry where the subdomains consist of van der Waals balls. As is usual in the theory of domain decomposition methods, the rate of convergence of the Schwarz method is related to a stable subspace decomposition. We derive such a stable decomposition for this family of domains and analyze how the stability "constant" depends on relevant geometric properties of the domain. For this, we introduce new descriptors that are used to formalize the geometry for the family of domains. We show how, for an increasing number of subdomains, the rate of convergence of the Schwarz method depends on specific local geometry descriptors and on one global geometry descriptor. The analysis also naturally provides lower bounds in terms of the descriptors for the smallest eigenvalue of the Laplace eigenvalue problem for this family of domains.
