Distributed solution of large-scale Dirichlet Laplacian eigenproblems

Antti Hannukainen (Aalto University), 21.03.2022, Exactum B120 (hybrid via zoom), 2pm-4pm

For zoom access, please contact Bjørn Jensen

In this talk, I present a method for solving eigenvalue problems (EVPs) in distributed computing environments. I consider the Dirichlet Laplacian as a representative example of EVP arising from many relevant engineering problems. It is well known that the Laplacian is smoothing, e.g., rapid variations in boundary data decay exponentially fast when moving from the boundary towards the interior. First, I explain how this phenomenon is used to obtain information on the eigenfunctions of the Dirichlet Laplacian in some subset using only local computations. Second, I discuss how such local eigenfunction information is used to devise a subspace-type eigensolver. I conclude with numerical examples computed on a cluster of workstations.