Clustering/Distribution Analysis and Preconditioned Krylov Solvers for the Approximated Helmholtz Equation and Fractional Laplacian in the Case of Complex-Valued, Unbounded Variable Coefficient Wave Number μ

• We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number ?, approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a ? preconditioning when the variable coefficient wave number ? is uniformly bounded. Here, we extend the analysis to the unbounded case by focusing on the case of a power singularity. Several numerical experiments concerning the spectral behavior and convergence of the related preconditioned GMRES are presented.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Caputo fractional derivatives

Helmholtz equations

eigenvalue asymptotic distribution

spectral symbol

clustering

Generalized Locally Toeplitz sequences

preconditioning

Publication and Content Type

ref (subject category)

art (subject category)