Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 曾闵丽 副教授，莆田学院
| | Inviter: | 白中治 研究员 | Title:
| On tau Matrix-based Approximate Inverse Preconditioning Technique for Diagonal-plus-Toeplitz Linear Systems from Spatial Fractional Diffusion Equations | Time & Venue:
| 2019.8.12 19:00-20:00 N702 | Abstract:
| Due to the special structure of the discretized linear systems from the spatial fractional diffusion equations, the resulting coefficient matrices of discretized systems have a diagonal-plus-Toeplitz structure. Standard circulant preconditioners may not work for such Toeplitz-like linear systems. However, because the resulting Toeplitz matrix is symmetric positive definite (SPD), we can employ the tau matrix to approximate it. By making use of the piecewise interpolation polynomials, we propose a new approximate inverse preconditioner to handle the diagonal-plus-Toeplitz coefficient matrices. The tau matrix-based approximate inverse (TAI) preconditioning technique can be implemented very efficiently by using discrete sine transforms (DST). Theoretically, we have proved that the spectrum of the resulting preconditioned matrices are clustered around one. Thus, Krylov subspace methods with the proposed preconditioners converge very fast. To demonstrate the efficiency of the new preconditioners, numerical experiments are implemented. The numerical results show that with the proper interpolation node numbers, the performance of the tau matrix-based splitting preconditioning technique is better than the other testing preconditioners. | |
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