论文标题
拉普拉斯特征值问题的分布解决方案
Distributed solution of Laplacian eigenvalue problems
论文作者
论文摘要
本文的目的是近似计算在间隔$（0，λ）$内的对称dirichlet laplacian的特征值。提出了一种新型的域分解丽思方法，统一凝聚极插值法的分区。该方法可用于分布式计算环境中，其中通信价格昂贵，例如，在云计算服务或网络工作站上运行的群集中。 RITZ空间是从与域分解为子域一致的局部子空间获得的。这些局部子空间是相互独立构建的，仅使用与相应子域相关的数据。分析相对特征值误差。一组工作站上的数值示例验证了该方法的误差分析和性能。
The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval $(0,Λ)$. 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.
