主講人：郝朝鵬 東南大學研究員

時間：2025年4月23日16：00

地點：徐匯校區三號樓332報告廳

舉辦單位：數理學院

主講人介紹：郝朝鵬于2017年東南大學計算數學博士畢業，后于2020年獲得伍斯特理工學院數學科學博士學位。2020年8月-2023年5月曾任普渡大學Golumb訪問助理教授，2023年7月至今擔任東南大學研究員，研究領域為科學計算和數值分析。現研究興趣包括非局部偏微分方程和隨機微分方程數值解。目前共發表論文三十篇左右。其中多篇文章發表在計算數學國際知名期刊MCOM，SINUM， SISC，SIAM UQ，JCP等。

內容介紹：The constant order fractional Laplacian has been extensively studied in the literature in the past decades. However, it may be insufficient for the heterogeneous effect due to the spatial variability of a complex medium. To account for heterogeneity, the variable-order operators depending on the spatial location variable have been alternatively proposed. Changing directly the constant-order into the variable-order may increase not only the model’s capability but also the complexity of computation. For the fractional Laplacian, an efficient and accurate numerical evaluation in multi-dimension is challenging due to the nature of a singular integral. To overcome this challenge, in our previous work (Hao et al. JCP 2021), we propose a simple and easy-to-implement finite difference scheme for the multi-dimensional fractional Laplacian defined by a hypersingular integral. In this talk, we extend this method to the variable-order case and propose an efficient method for the variable-order fractional Laplacian. We prove that the scheme is of second-order convergence and apply the developed finite difference scheme to solve various equations with the variable-order fractional Laplacian. We present a fast algorithm for computing the variable-order fractional Laplacian. Several numerical examples demonstrate the accuracy and efficiency of our algorithm and verify our theory.