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Analysis of FEAST Spectral Approximations Using the DPG Discretization

Jay Gopalakrishnan ORCID logo , Luka Grubišić ORCID logo , Jeffrey Ovall ORCID logo and Benjamin Parker ORCID logo EMAIL logo

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.

Award Identifier / Grant number: FA9451-18-2-0031

Award Identifier / Grant number: HRZZ-9345

Award Identifier / Grant number: DMS-1522471

Award Identifier / Grant number: DMS-1624776

Funding statement: This work was supported by the AFOSR (through AFRL Cooperative Agreement #18RDCOR018, under grant FA9451-18-2-0031), the Croatian Science Foundation grant HRZZ-9345, bilateral Croatian-USA grant (administered jointly by Croatian-MZO and NSF), and NSF grant DMS-1522471. The numerical studies were facilitated by the equipment acquired using NSF’s Major Research Instrumentation grant DMS-1624776.

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Received: 2019-01-24
Revised: 2019-02-08
Accepted: 2019-02-08
Published Online: 2019-03-27
Published in Print: 2019-04-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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