IMA Numerics - May-07-2021

An approach for investigating eigenvector localization

Jeffrey Ovall

Portland State University, Or, USA.

Domain geometry and properties of the coefficients of selfadjoint elliptic operators can cause certain eigenvectors to be highly localized in relatively small subdomains. Such localization phenomena have generated a lot of interest in the physics and mathematics communities since the late 1950s, but the underlying mechanisms driving localization are still not fully understood, despite advances on the mathematical side during the last decade. Computational approaches for identifying likely regions of localization and approximating localized eigenvectors and/or their corresponding eigenvalues have emerged in the past two years. We present a new approach in which filtered subspace iteration (FEAST) is applied to a perturbed version of the selfadjoint operator, where the complex perturbation is chosen to highlight eigenvectors that are sufficiently localized (within a user-specified tolerance) in a given region. Theoretical and computational results will be presented.

We will meet in google meet, use the link below to connect with us

May 7, 2021, 15:00 Chile, via https://meet.google.com/viw-rqds-ikc

If you are interested in giving a talk, please contact: paulina.sepulveda @pucv.cl

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