报告题目：近似影响域对非局部模型局部收敛性的影响（convergence to local limit of nonlocal models with approximated interaction neighborhoods）
报告人 (Speaker)：阴小波 教授（华中师范大学）
报告时间 (Time)：2023年12月8日(周五) 14：00
报告地点 (Place)：校本部F309
邀请人(Inviter)：刘东杰
主办部门：永利数学系
报告摘要： Many nonlocal models have adopted a finite and radially symmetric nonlocal interaction domains. When solving them numerically, it is sometimes convenient to adopt polygonal approximations of such interaction domains. A crucial question is, to what extent such approximations affect the nonlocal operators and the corresponding nonlocal solutions. While recent works have analyzed this issue for nonlocal operators in the case of a fixed horizon parameter, the question remains open in the case of a small or vanishing horizon parameter, which happens often in many practical applications and has significant impact on the reliability and robustness of nonlocal modeling and simulations. In this report, we are interested in addressing this issue and establishing the convergence of new nonlocal solutions by polygonal approximations to the local limit of the original nonlocal solutions. Our finding reveals that the new nonlocal solution does not converge to the correct local limit when the number of sides of polygons is uniformly bounded. On the other hand, if the number of sides tends to infinity, the desired convergence can be shown. These results may be used to guide future computational studies of nonlocal problems.
