李天怡 博士 (河南师范大学数学与统计学院)

白中治 研究员

All-at-Once Implementation for Subdiffusion Equation With Time Nonuniform Mesh

10月15日（周四）10:00-11:00，南楼733

Geometrically increased time step sizes (GITSS) are introduced for the temporal discretization of the Caputo fractional derivative in subdiffusion equations. The resulting all-at-once linear system has a block lower triangular Toeplitz-like coefficient matrix, whose structured form enables efficient computation. By combining a divide-and-conquer strategy with block forward substitution, a fast solver is developed with a computational complexity of O(MN), where M and N are the degrees of freedom in space and time, respectively. Numerical experiments demonstrate that the proposed method requires substantially less CPU time than the widely used exponential-sum-approximation (ESA) method. Although under the GITSS the convergence order of the L1 scheme is slightly less than that of the graded mesh, the Toeplitz-like structure brought by the GITSS has more potential to develop the fast algorithm.