We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number (Formula presented.), approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a (Formula presented.) preconditioning when the variable coefficient wave number (Formula presented.) 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.
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
Adriani A.;Serra Capizzano S.
;
2024-01-01
Abstract
We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number (Formula presented.), approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a (Formula presented.) preconditioning when the variable coefficient wave number (Formula presented.) 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.File | Dimensione | Formato | |
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ClusteringDistribution-Analysis-and-Preconditioned-Krylov-Solvers-for-the-Approximated-Helmholtz-Equation-and-Fractional-Laplacian-in-the-Case-of-ComplexValued-Unbounded-Variable-Coefficient-Wave-Number.pdf
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