题目一：A symbol-based preconditioner for a sixth-order scheme from multi-dimensional steady-state Riesz space fractional diffusion equations
内容简介： In this work, we employ a sixth-order numerical scheme to approximate the multi-dimensional steady-state Riesz space-fractional diffusion equations (RSFDEs) and subsequently propose a preconditioned conjugate gradient (PCG) method with a symbol-based preconditioner for solving the resulting linear systems. Theoretically, we prove that the PCG solver achieves an optimal convergence rate—i.e., a convergence rate independent of discretization step sizes—by showing that the spectra of the preconditioned matrices are uniformly bounded within the open interval (45/136,34/15). Numerical experiments validate the effectiveness of the proposed preconditioner for three-dimensional steady-state RSFDEs and confirm the rapid convergence of the PCG method.
This is a joint work with Yuan-Yuan Huang, Wei Qu, and Sean Y. Hon
时间：2026年1月10日（周六）上午8:00
地点：腾讯会议194-364-169
题目二：An optimal preconditioner for a high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients
内容简介：In this work, we propose a method for solving multi-dimensional Riesz space fractional diffusion equations with variable coefficients. The Crank–Nicolson (CN) method is used for temporal discretization, while the fourth-order fractional centered difference (4FCD) method is employed for spatial discretization. Using a novel technique, we show that the CN-4FCD scheme for the multi-dimensional case is unconditionally stable and convergent, achieving second-order accuracy in time and fourth-order accuracy in space with respect to the discrete 
-norm. Moreover, leveraging the symmetric multilevel Toeplitz-like structure of the coefficient matrix in the discrete linear systems, we enhance the computational efficiency of the proposed scheme with a sine transform-based preconditioner, ensuring a mesh-size-independent convergence rate for the conjugate gradient method. Finally, numerical examples validate the theoretical analysis and demonstrate the superior performance of the proposed preconditioner compared to existing methods.
This is a joint work with Yuan-Yuan Huang, Wei Qu, and Sean Y. Hon
时间：2026年1月10日（周六）上午9:20
地点：腾讯会议986-419-649
报告人：Siu Long LEI（李兆隆）
报告人简介：Siu Long LEI（李兆隆）教授是澳门大学科技学院数学系副教授。他于香港科技大学（HKUST）获得数学博士学位，现任东亚工业与应用数学学会（EASIAM）执行委员。
他的研究方向包括数值线性代数和微分方程的数值方法，尤其专注于分数阶与非局部偏微分方程所导出的大规模结构化线性系统的快速求解器与预处理技术，以及相关应用，例如计算金融中的期权定价问题。
他在《Journal of Scientific Computing》《Journal of Computational Physics》《Numerical Linear Algebra with Applications》等国际权威期刊上发表多篇论文，其中多篇为高被引论文。
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信息科学技术学院
2026年1月8日