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

Autor:	Andrea Adriani, Stefano Serra-Capizzano, Cristina Tablino-Possio
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Caputo fractional derivatives Helmholtz equations eigenvalue asymptotic distribution spectral symbol clustering Generalized Locally Toeplitz sequences Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Algorithms, Vol 17, Iss 3, p 100 (2024)
Druh dokumentu:	article
ISSN:	1999-4893
DOI:	10.3390/a17030100
Popis:	We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number μ, approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a τ preconditioning when the variable coefficient wave number μ 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.
Databáze:	Directory of Open Access Journals
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