Sine transform based preconditioning techniques for space fractional diffusion equations. (English) Zbl 07729591
Summary: We study the preconditioned iterative methods for the linear systems arising from the numerical solution of the multi-dimensional space fractional diffusion equations. A sine transform based preconditioning technique is developed according to the symmetric and skew-symmetric splitting of the Toeplitz factor in the resulting coefficient matrix. Theoretical analyses show that the upper bound of relative residual norm of the GMRES method when applied to the preconditioned linear system is mesh-independent which implies the linear convergence. Numerical experiments are carried out to illustrate the correctness of the theoretical results and the effectiveness of the proposed preconditioning technique.
MSC:
| 65F08 | Preconditioners for iterative methods |
| 65F10 | Iterative numerical methods for linear systems |
| 35R11 | Fractional partial differential equations |
Keywords:
finite difference method; GMRES method; numerical range; space fractional derivative; \(\tau\) preconditioner; Toeplitz matrixReferences:
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