UM E-Theses Collection (澳門大學電子學位論文庫)
Title
BCCB preconditioners for 2D space-fractional diffusion equations
English Abstract
In this thesis, two dimensional two-sided 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 first-order 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
Mathematics -- Department of Mathematics


Supervisor
Lei Siu Long
Files In This Item:
Full-text (Intranet only)
Location
1/F Zone C
Supervisor
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