Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations

Journal Article · Sat Sep 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0570-6· OSTI ID:22769243

Lu, Kang-Ya ^[1]

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1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing (China)

We propose three new preconditioners: diagonal and optimal-circulant splitting preconditioner, diagonal and skew-circulant splitting preconditioner, and diagonal and optimal-skew-circulant splitting preconditioner for solving the diagonal-plus-Toeplitz linear system discretized from the spatial fractional diffusion equations. Theoretical analysis shows that these three preconditioners can make the eigenvalues of the preconditioned matrices be clustered around 1, especially when the grids of the discretizations are refined. These results coincide with the one about the diagonal and circulant splitting preconditioner constructed recently by Bai et al. (Numer Linear Algebra Appl 24:e2093, 2017). Numerical experiments exhibit that the proposed preconditioners can significantly improve the convergence of the Krylov subspace iteration methods like GMRES and BiCGSTAB, and they outperform the diagonal and circulant splitting preconditioner as well.

• OSTI ID: 22769243
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 4 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGEBRA
CONVERGENCE
DIFFUSION EQUATIONS
EIGENVALUES
GRIDS
MATRICES