Mathematical Sciences Department
Numerical Methods Seminar
Speaker: Prof. Yanzhi Zhang (Missouri University of Science and Technology)
Thursday, March 30, 2023
11:00 am - 12:00 pm
Zoom Meeting ID: 989 0924 4378
Title: Numerical methods for heterogeneous problems with variable-order fractional Laplacian
Abstract: In this talk, I will introduce the recently developed meshfree methods based on the radial basis functions to solve problems with the variable-order fractional Laplacian. The proposed methods take advantage of the analytical Laplacian of the radial basis functions so as to accommodate the discretization of the classical and variable-order fractional Laplacian in a single framework and avoid the large computational cost for numerical evaluation of the fractional derivatives. Moreover, our methods are simple and easy to handle complex geometry and local refinements, and their computer program implementation remains the same for any dimension. The effects of variable-order fractional Laplacian will also be discussed.