UM ETheses Collection (澳門大學電子學位論文庫)
 Title

BCCB preconditioners for 2D spacefractional diffusion equations
 English Abstract

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In this thesis, two dimensional twosided space fractional diffusion equations with variable diffusion coefficients are discussed. The problems can be solved by an implicit finite difference scheme, which is proven to be uniquely solvable, unconditionally stable and firstorder convergent in infinity norm. Nonsingular block circulant with circulant block preconditioners are proposed to accelerate the convergence rate of the Krylov subspace linear system solver efficiently. The preconditoned matrix equals to a sum of the identity matrix, a matrix with small norm and a matrix with low rank under certain conditions, so that a fast convergence is obtained. Moreover, the preconditioners are practical with both an operation cost of O(N log N) and an O(N) memory. Numerical examples are also given.
 Issue date

2015.
 Author

Zhang, Xin He
 Faculty

Faculty of Science and Technology
 Department

Department of Mathematics
 Degree

M.Sc.
 Subject

Fractional differential equations
Differential equations  Numerical solutions
 Supervisor

Lei, Siu Long
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991000749199706306