学术报告

题      目：Sine transform based preconditioners for fractional diffusion inverse source problems

报  告  人：庞宏奎   教授  (邀请人：骆其伦 )

                                    江苏师范大学

时      间：6月26日  11：00-12：00

地     点：数科院西楼111报告厅

报告人简介:

       庞宏奎，江苏师范大学数学与统计学院教授，硕士生导师，2011年毕业于澳门大学数学系，获理学博士学位，主要研究方向为数值代数、科学与工程计算。主持国家自然科学基金面上项目、国家自然科学基金青年项目、江苏省自然科学基金面上项目等省部级以上课题5项；在SIAM J. Sci. Comput.、SIAM J. Matrix Anal. Appl.、J. Sci. Comput.、J. Comput. Phys.、Numer. Linear Algebra Appl.、Numer. Algor.、Linear Algebra Appl.等学术期刊上发表论文多篇；在高等教育出版社出版译著1部。

摘      要：

       We investigate an inverse problem with quasi-boundary value regularization for recovering a source term of space-time fractional diffusion equations from the final observation. A sine transform based preconditioner is established for the discrete linear systems arising from the finite difference discretization of the regularized well-posed problem. According to the multilevel $\tau$-structure and 2-by-2 block form, the proposed preconditioner can be inverted efficiently by the fast sine transform and fast Fourier transform. Theoretically, we show that except for a number of outliners, the eigenvalues of the preconditioned matrix are located within a rectangular domain which is uniformly bounded away from zero. Numerical experiments are performed to demonstrate the effectiveness of the proposed preconditioner.