The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval $(0,\Lambda)$. A novel domain decomposition Ritz method, partition of unity condensed pole interpolation method, is proposed. This method can be used in distributed computing environments where communication is expensive, e.g., in clusters running on cloud computing services or networked workstations. The Ritz space is obtained from local subspaces consistent with a decomposition of the domain into subdomains. These local subspaces are constructed independently of each other, using data only related to the corresponding subdomain. Relative eigenvalue error is analysed. Numerical examples on a cluster of workstations validate the error analysis and the performance of the method.

翻译：本条的目的是在(0,\Lambda)美元之间的间隔内大致计算对称 Dirichlet Laplacian 的对称天平值。 提出了一种新的域分解 Ritz 法, 统一压缩极间插法的分割。 这种方法可用于通信费用昂贵的分布式计算环境, 例如在云计算服务或网络化工作站运行的集群中。 Ritz 空间来自与将域分解成子数据一致的地方子空间。 这些本地子空间是独立建造的, 使用的数据只与相应的子数据相关。 分析相对的偏差值错误。 一组工作站的数值实例验证了错误分析和方法的性能 。