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

Alternating direction method for high dimensional fractional diffusion equations with preconditioned strategy
 English Abstract

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In this thesis, high dimensional twosided space fractional diffusion equations, derived from the fractional Fick’s law, and with monotonic variable diffusion coef ficients, are solved by alternating direction implicit method. Each linear system corresponding to each spatial direction thus result is solved by Krylov subspace method. The method is accelerated by applying an approximate inverse preconditioner, where under certain conditions we showed that the normalized preconditioned matrix equals to a sum of identity matrix, a matrix with small norm, and a matrix with low rank, such that the preconditioned Krylov subspace method converges superlinearly. We also briefly present some fast algorithms which computational cost for solving the linear systems is O(n log n), where n is the matrix size. The results are illustrated by some numerical examples.
 Issue date

2016.
 Author

Chou, Lot Kei
 Faculty

Faculty of Science and Technology
 Department

Department of Mathematics
 Degree

M.Sc.
 Subject

Fractional calculus
Fractional differential equations
Differential equations  Numerical solutions
 Supervisor

Lei, Siu Long
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991001943699706306