研究生学术论坛：杨红博士生 - 走向现代数学学术报告（No. 710）

报告题目：Two new banded preconditioners for Riesz space fractional diffusion equations with variable coefficients

报告人：杨红 博士生（汕头大学）

报告时间：2024年5月14日 15:00

报告地点：东海岸校区-D实209

摘要：In this report, we consider the preconditioned iteration methods for one-dimensional and two-dimensional Riesz space fractional diffusion equations with separable variable diffusion coefficients. The shift Grunwald (SG) operator and the implicit finite difference (IFD) method are applied to discretize the problem and obtain the IFD-SG scheme. For one-dimensional problems, we transform the asymmetric discretized linear system into a symmetric one and solve the resulted linear system by PCG method. Due to the off-diagonal decay properties of the coefficient matrix, we propose two new banded preconditioners: the banded preconditioner with parameter compensation and the banded preconditioner with new compensation. Theoretical analysis indicates that when the time step and spatial grid size satisfy certain relationships, the spectra of the preconditioned matrices are uniformly bounded. For two-dimensional problems with separable variable diffusion coefficients, we propose two corresponding new banded preconditioners for the symmetric linear system and analyze the spectra of the preconditioned matrices. Numerical results are reported to illustrate the efficiency of the proposed preconditioners.

个人简介：杨红，汕头大学在读博士研究生，研究方向为数值代数，在Appl. Math. Comput.上发表学术论文。