An exponential Runge-Kutta method with dimensional splitting technique for multidimensional fractional Allen-Cahn equations

讲座时间 Datetime: 2021年12月17日，星期五，10:00-11:00

地点 Venue: 海琴2号楼 A457

报告人 Speaker:  孙海卫 教授

单位 Affiliation: 澳门大学

报告摘要 Abstract:

In this talk, we study numerical methods for solving the multidimensional Allen-Cahn equations with spatial fractional Riesz derivatives. A fully discrete numerical scheme is proposed using an exponential Runge-Kutta method with the dimensional splitting strategy for the time integration with finite difference discretization in space. Theoretically, we prove that the proposed numerical scheme can unconditionally preserve the discrete maximum principle. The error estimate is also established in the fully discrete sense. In practical computation, the proposed algorithm can be carried out by computing linear systems and the matrix exponential associated with only 1D discretized matrices that possess the Toeplitz structure.  Meanwhile, fast methods for inverting the Toeplitz matrix and computing the Toeplitz exponential multiplying a vector are exploited to reduce the complexity. Numerical examples are given to illustrate the effectiveness and efficiency of the proposed scheme.

 It is a joint work with Prof. Hao CHEN.