報告題目：Computation of moments for Maxwell’s equations with random nterfaces via pivoted low-rank approximation
報 告 人：郝永樂博士 周口師範學院
報告時間：2020年6月18日下午 3:30-4:30
報告地點：騰訊會議 ID：368 452 008
會議密碼：061820
點擊鍊接入會，或添加至會議列表：https://meeting.tencent.com/s/sN0cwS0DQvj6
校内聯系人：張凱 zhangkaimath@jlu.edu.cn
報告摘要：
In this talk, the aim to compute the mean field and variance of solutions to three-dimensional Maxwell’s equations with random interfaces via shape calculus and pivoted low-rank approximation. Based on the perturbation theory and shape calculus, we characterize the statistical moments of solutions to Maxwell’s equations with random interfaces in terms of the perturbation magnitude via the first order shape-Taylor expansion. In order to capture oscillations with high resolution close to the interface, an adaptive finite element method using Nédélec’s third order edge elements of the first kind is employed to solve the deterministic Maxwell’s equations with the mean interface to approximate the expectation of solutions. For the second moment computation, an efficient low-rank approximation of the pivoted Cholesky decomposition is proposed to compute the two-point correlation function to approximate the variance of solutions. Numerical experiments are presented to demonstrate our theoretical results.
報告人簡介：
Yongle Hao is a Lecturer at the School of Mathematics and Statistics,Zhoukou Normal University. Before taking up the current position, he obtained his PhD in Mathematics from Jilin University (2018). His research interest is numerical methods for stochastic partial differential equations.
