TY - JOUR
T1 - A Fast Two-Level Strang Splitting Method for Multi-Dimensional Spatial Fractional Allen-Cahn Equations with Discrete Maximum Principle
AU - Cai , Yao-Yuan
AU - Fang , Zhi-Wei
AU - Chen , Hao
AU - Sun , Hai-Wei
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 340
EP - 360
PY - 2023
DA - 2023/04
SN - 13
DO - http://doi.org/10.4208/eajam.2022-248.161022
UR - https://global-sci.org/intro/article_detail/eajam/21652.html
KW - Two-level Strang splitting method, circulant and skew-circulant matrix splitting, discrete maximum principle, fast Fourier transform.
AB - <p style="text-align: justify;">Numerical solutions of the multi-dimensional spatial fractional Allen-Cahn
equations are studied. After the semi-discretization of the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations with the Toeplitz structure is
obtained. In order to reduce the computational complexity, a two-level Strang splitting method is proposed, where the Toeplitz matrix in the system is represented as the
sum of circulant and skew-circulant matrices. Therefore, the method can be quickly
implemented by the fast Fourier transform, avoiding expensive Toeplitz matrix exponential calculations. It is shown that the discrete maximum principle of the method is
unconditionally preserved. Moreover, the analysis of errors in the infinite norm with
second-order accuracy is carried out in both time and space. Numerical tests support
the theoretical findings and show the efficiency of the method.</p>