走向现代数学学术报告 - 孙海卫教授（No. 738)

题目：A splitting ADI scheme for wave equations with integral-type fractional Laplacian

报告人：孙海卫 教授（澳门大学）

时间：2024年10月11号 15:00

地点：东海岸校区 - D实209

摘要： In this talk, we investigate the numerical solution of the 2D wave equations with integral-type fractional Laplacian. After splitting out the Riesz fractional derivatives from the fractional Laplacian, we treat the Riesz fractional derivatives with an implicit scheme while solving the rest part explicitly. Thanks to the tensor structure of the Riesz fractional derivatives, a splitting alternative direction implicit (S-ADI) scheme is proposed by incorporating an ADI remainder. Then the Gohberg-Semencul formula, combined with fast Fourier transform, is proposed to solve the derived Toeplitz linear systems at each time integration. Theoretically, we demonstrate that the S-ADI scheme is unconditionally stable and possesses second-order accuracy. Finally, numerical experiments are performed to demonstrate the accuracy and efficiency of the S- ADI scheme. It is a joint work with Tao Sun and Michel K. Ng.

报告人介绍：孙海卫，澳门大学数学系教授、博士生导师，1996 年毕业于香港中文大學数学系获得博士学位。主要研究领域包括数值线性代数、偏微分方程数值解、和计算金融学等。在 SISC，SINUM，SIMAX，JCP 等计算数学杂志发表超过 120 篇高水平研究论文，担任过国际学术期刊 EAJAM 和 IJCM 编委，于 2018 年获得澳门特区政府颁发的自然科学二等奖，在 2019 年第 8 届华人数学家大会（ICCM）作 45分钟大会报告，共主持澳门科技发展基金 6 项。