بيانات النشر: Uppsala universitet, Avdelningen för beräkningsvetenskap
Uppsala universitet, Numerisk analys
Univ Insubria, Dept Sci & High Technol, Via Valleggio 11, I-22100 Como, Italy.
Univ Milano Bicocca, Dept Math & Applicat, Via Cozzi 53, I-20125 Milan, Italy.
نبذة مختصرة : We consider the Helmholtz equation and the fractional Laplacian in the case of the complex-valued unbounded variable coefficient wave number ðœ‡, approximated by finite differences. In a recent analysis, singular value clustering and eigenvalue clustering have been proposed for a ðœ 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.
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