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发布于:2018-04-16 13:47:25   |   作者:[学院] 数学学院   |   浏览次数:2830
时间:2018年4月19日下午16:30
地址:清水河校区 主楼A1 – 512
主办:数学学院
承办:数学学院
范围:全校

报告题目:Spectral analysis and multigrid preconditioners for space-fractional diffusion equations

 

报告人:Marco Donatelli(意大利因苏布里亚大学副教授)

 

报告时间:2018年4月19日下午16:30

 

报告地点:清水河校区 主楼A1 – 512

 

报告摘要:Fractional partial diffusion equations (FDEs) are a generalization of classical partial differential equations, used to model anomalous diffusion phenomena. Several discretization schemes (finite differences, finite volumes, etc.) combined with (semi)-implicit methods leads to a Toeplitz-like matrix-sequence. In the constant diffusion coefficients case such a matrix-sequence reduces to a Toeplitz one, then exploiting well-known results on Toeplitz sequences, we are able to describe its asymptotic eigenvalue distribution. In the case of nonconstant diffusion coefficients, we show that the resulting matrix-sequence is a generalized locally Toeplitz (GLT) and then we use the GLT machinery to study its singular value/eigenvalue distribution as the matrix size diverges. The new spectral information is employed for analyzing preconditioned Krylov and multigrid methods recently appeared in the literature, with both positive and negative results. Moreover, such spectral analysis guides the design of new preconditioning and multigrid strategies. We propose new structure preserving preconditioners with minimal bandwidth (and so with efficient computational cost) and multigrid methods for 1D and 2D problems. Some numerical results confirm the theoretical analysis and the effectiveness of the new proposals

 

报告人简介: Prof. Marco Donatelli是意大利因苏布里亚大学科学与高科技系-数值分析组的副教授。目前担任SIAM J. Sci. Comput., SIAM J. Imaging Sci., SIAM J. Matrix Anal. Appl., IMA J. Numer. Anal., Inverse Problems, Appl. Math. Comput., Linear Algebra Appl., BIT, J. Comput. Appl. Math., Appl. Numer. Math.等著名国际杂志编委。他还是National Group for Scientific Calcolus (GNCS),Italian Society of Applied and Industrial Mathematics (SIMAI),Society for Industrial and Applied Mathematics  (SIAM) 的成员。