FEAST for differential eigenvalue problems

Abstract

An operator analogue of the FEAST matrix eigensolver is developed to compute the discrete part of the spectrum of a differential operator in a region of interest in the complex plane. Unbounded search regions are handled with a novel rational filter for the right half-plane. If the differential operator is normal or self-adjoint, then the operator analogue preserves that structure and robustly computes eigenvalues to near machine precision accuracy. The algorithm is particularly adept at computing high-frequency modes of differential operators that possess self-adjoint structure with respect to weighted Hilbert spaces.

arXiv commentExpanded discussion for clarity in several places, revised statement of theorem 5.2 for clarity

References in corpus (5)

• A Density Matrix-based Algorithm for Solving Eigenvalue Problems
• The automatic solution of partial differential equations using a global spectral method
• On the infinite-dimensional QR algorithm
• The Riesz basis property of an indefinite Sturm-Liouville problem with non-separated boundary conditions
• Continuous analogues of Krylov methods for differential operators

Cited by in corpus (6)

• A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations
• On symmetrizing the ultraspherical spectral method for self-adjoint problems
• Complex moment-based methods for differential eigenvalue problems
• Twice is enough for dangerous eigenvalues
• Projection method for eigenvalue problems of linear nonsquare matrix pencils
• Analysis of FEAST spectral approximations using the DPG discretization