Article
Analysis of FEAST Spectral Approximations Using the DPG Discretization
Computational Methods in Applied Mathematics
(2019)
Abstract
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential opera- tor. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov–Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of the algorithm beyond the confines of the theoretical assumptions. The utility of the algorithm is illustrated by applying it to compute guided transverse core modes of a realistic optical fiber.
Disciplines
Publication Date
2019
DOI
10.1515/cmam-2019-0030
Citation Information
Jeffrey S. Ovall. "Analysis of FEAST Spectral Approximations Using the DPG Discretization" Computational Methods in Applied Mathematics (2019) Available at: http://works.bepress.com/jeffrey_ovall/38/