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学术报告-孙海卫

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2020-11-18 14:51:00

学术报告


题      目:Tau preconditioner for multi-dimensional Riesz space fractional diffusion equations with applications



报  告  人:孙海卫   教授  (邀请人:陈小山 )

                                   澳门大学




时      间:2020-11-18 14:30--15:30


地      点:学院401


报告人简介:

        1983年本科毕业于中山大学数学系,1989年获中山大学应用数学专业硕士学位,1996年获香港中文大学应用数学专业博士学位。于2001至2004年期间分别在美国肯塔基州大学高性能计算实验室和亚拉巴马州大学化学工程系做博士后。2004年到澳门大学数学系工作,2017年被聘为教授。孙海卫教授的研究领域是科学计算,数值偏微分方程,数值线性代数和金融计算。他在SIAM Journal on Scientific Computing等期刊发表学术论文三十余篇。主持或曾经主持澳门科学技术发展基金四项。

摘      要:

       In this talk, we study the spectra of the tau-preconditioner for the multi-level Toeplitz matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion quations via the finite difference method. The preconditioned conjugate gradient method with a tau preconditioner, which can be diagonalized by the sine transform, is employed to solve the resulting linear system. Theoretically, we prove that the spectra of the preconditioned matrices are uniformly bounded in the open interval (1/2,3/2) and thus the preconditioned conjugate gradient method converges linearly. The proposed method can be extended to multi-level Toeplitz matrices generated by functions with zeros of fractional order. Our theoretical results fill in the gap in the literature. Numerical examples are presented to demonstrate our new theoretical results in the literature and show the convergence performance of the proposed preconditioner that is better than other existing preconditioners.