PU-CPI solution of Laplacian eigenvalue problems

06/18/2020

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by   Antti Hannukainen, et al.

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The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval (0,Λ). A domain decomposition Ritz method, PU-CPI, 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 of PU-CPI is obtained from local subspaces consistent with a decomposition of the domain into subdomains. These local subspaces are constructed independently of each other using only data 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.