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Efficient preconditioner of one-sided space fractional diffusion equation
Lin,Xue Lei1; Ng,Michael K.1; Sun,Hai Wei2
Source PublicationBIT Numerical Mathematics

In this paper, we propose an efficient preconditioner for the linear systems arising from the one-sided space fractional diffusion equation with variable coefficients. The shifted Gru ¨ nwald formula is employed to discretize the one-sided Riemann–Liouville fractional derivative. The matrix structure of resulting linear systems is Toeplitz-like, which is a summation of an identity matrix and a diagonal-times-nonsymmetric-Toeplitz matrix. A diagonal-times-nonsymmetric-Toeplitz preconditioner is proposed to reduce the condition number of the Toeplitz-like matrix, where the diagonal part comes from the variable coefficients and the nonsymmetric Toeplitz part comes from the Riemann–Liouville derivative. Theoretically, we show that the condition number of the preconditioned matrix is uniformly bounded by a constant independent of discretization step-sizes under certain assumptions on the coefficient function. Due to the uniformly bounded condition number, the Krylov subspace method for the preconditioned linear systems converges linearly and independently on discretization step-sizes. Numerical results are reported to show the efficiency of the proposed preconditioner and to demonstrate its superiority over other tested preconditioners.

KeywordOne-sided Space-fractional Derivative Preconditioning Toeplitz-like Matrix Variable Diffusion Coefficients
URLView the original
Indexed BySCIE
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000444946100009
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Cited Times [WOS]:15   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorLin,Xue Lei; Ng,Michael K.; Sun,Hai Wei
Affiliation1.Department of MathematicsHong Kong Baptist University,Kowloon Tong,Hong Kong
2.Department of MathematicsUniversity of Macau,Macao
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lin,Xue Lei,Ng,Michael K.,Sun,Hai Wei. Efficient preconditioner of one-sided space fractional diffusion equation[J]. BIT Numerical Mathematics,2018,58(3):729-748.
APA Lin,Xue Lei,Ng,Michael K.,&Sun,Hai Wei.(2018).Efficient preconditioner of one-sided space fractional diffusion equation.BIT Numerical Mathematics,58(3),729-748.
MLA Lin,Xue Lei,et al."Efficient preconditioner of one-sided space fractional diffusion equation".BIT Numerical Mathematics 58.3(2018):729-748.
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