Analysis of FEAST Spectral Approximations Using the DPG Discretization

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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Mar 27, 2019
Source ID
10.1515/cmam-2019-0030

Entities

People

  • Benjamin Quanah Parker
  • Jayadeep Gopalakrishnan
  • Jeffrey S. Ovall
  • Luka Grubišić

Organizations

  • Air Force Office of Scientific Research
  • Croatian Science Foundation
  • National Science Foundation
  • Portland State University
  • University of Zagreb

Tags

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra
  • Theoretical Analysis.