Strang's splitting method for
spatial fractional Allen-Cahn equations

主讲人：孙海卫

摘要：In this talk, we study the numerical solutions of the spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations with Toeplitz structure is obtained.  For the sake of reducing the computational complexity, Strang splitting methods are proposed where the Toeplitz matrix in the system is split into the sum of a circulant matrix and a skew circulant matrix. Therefore, the proposed method can be quickly implemented by the fast Fourier transform, substituting to calculate the expensive Toeplitz matrix exponential. Theoretically, the discrete maximum principle of our method is unconditionally preserved. Moreover, the analysis of error in norms in Banach space with second-order accuracy is conducted in both time and space. Finally, numerical tests are given to corroborate our theoretical conclusions and the efficiency of the proposed method.

主讲人简介：孙海卫，澳门大学数学系主任、教授，1996年于香港中文大学获博士学位。主要研究领域为数值线性代数、分数阶偏微分方程快速算法、数值偏微分方程以及计算金融等。在SIAM J. Numer. Anal, SIAM J. Sci. Comput等众多计算数学权威期刊上发表高水平研究论文80余篇，担任国际期刊“International Joural Computer Mathematics"的编委。共主持澳门科学技术发展基金5项，于2018年获得澳门自然科学二等奖。

邀请人：李东方

时间：2022年3月2日（星期三）9:00-11:00

地点：腾讯会议室   ID:668480527  密码：0302