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Article
Analysis of Feast Spectral Approximations Using the DPG Discretization
Mathematics and Statistics Faculty Publications and Presentations
  • Jay Gopalakrishnan, Portland State University
  • Luka Grubišić, University of Zagreb
  • Jeffrey S. Ovall, Portland State University
  • Benjamin Q. Parker, Portland State University
Document Type
Pre-Print
Publication Date
2-1-2019
Subjects
  • Eigenvalues -- Data processing,
  • Galerkin methods,
  • Discretization (Mathematics),
  • Finite element method
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 operator. 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.

Description

Originally published in arViv.org. May be accessed at https://arxiv.org/abs/1901.07724.

Persistent Identifier
https://archives.pdx.edu/ds/psu/28637
Citation Information
Gopalakrishnan, J., Grubišić, L., Ovall, J., & Parker, B. Q. (2019). Analysis of FEAST spectral approximations using the DPG discretization. arXiv preprint arXiv:1901.07724.