Speaker: Dr. Yanzhi Zhang from Missouri University of Science and Technology
Date and Time: Friday, April 2, 2021, 11am – 12pm via Zoom. Please contact Qingning Zhou to obtain the Zoom link.
Title: Numerical Methods for Nonlocal Problems with the Fractional Laplacian
Abstract: Recently, the fractional Laplacian has received great attention in modeling complex phenomena that involve long-range interactions. However, its nonlocality introduces considerable challenges in both mathematical analysis and numerical simulations. So far, numerical methods for the fractional Laplacian still remain limited. It is well known that the fractional Laplacian can be defined either in a pseudo-differential form via the Fourier transforms or in a hypersingular integral form. In this talk, I will discuss three different groups of numerical methods to discretize the fractional Laplacian. In the first group, we introduce the Fourier pseudospcetral methods based on the pseudo-differential form of the fractional Laplacian. The second group is operator factorization methods based on the hypersingular integral definition. In the third group, we combine both pseudo-differential and hypersingular integral forms of the fractional Laplacian and introduce meshfree methods with radial basis functions. The properties of these methods will be discussed, and some applications of nonlocal problems with the fractional Laplacian will also be demonstrated.