Naslov
Analysis of FEAST Spectral Approximations Using the DPG Discretization

Autori
Gopalakrishnan, Jay ; Grubišić, Luka ; Ovall, Jeffrey ; Parker, Benjamin

Izvornik
Computational methods in applied mathematics (1609-4840) 19 (2019), 2; 251-266

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Discontinuous Petrov-Galerkin Finite Element Methods ; FEAST Method ; Eigenvalue Problems ; Optical Fiber ; Subspace Iteration

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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