Numerical method for random Maxwell's equations

发布时间：2024-10-10 作者：77779193永利官网浏览次数：

Speaker:	张凯	DateTime:	2024/10/11（周五）上午10：30-11：30
Brief Introduction to Speaker: 张凯，吉林大学数学学院计算数学系教授, 博士生导师。张凯老师1999年本科毕业于吉林大学数学系，2006年获吉林大学博士学位，博士论文被评为吉林省优秀博士论文。2008年获得香港中文大学联合培养博士学位。2008-2010年，赴密歇根州立大学开展博士后工作。现为吉林大学唐敖庆特聘教授。张凯老师先后赴伊利诺伊州立大学，奥本大学，香港浸会大学，南方科技大学等开展合作研究，研究兴趣为随机偏微分方程的数值解法。主要从事随机麦克斯韦方程和随机声波方程数值方法，机器学习求解反散射问题的研究。先后主持国家自然科学基金等项目11项，发表论文50余篇。		Place:	六号楼二楼报告厅
Abstract:A numerical method is developed for efficiently computing the mean field and variance of solutions to three-dimensional Maxwell's equations with random interfaces, utilizing shape calculus and pivoted low-rank approximation. By applying perturbation theory and shape calculus, we describe the statistical moments of these solutions in relation to the perturbation magnitude through a first-order shape-Taylor expansion. To achieve high-resolution oscillation capture near the interface, an adaptive finite element method using Nedelec's third-order edge elements of the first kind is employed, solving the deterministic Maxwell's equations with the mean interface to approximate the expected solutions. For computing the second moment, a low-rank approximation based on the pivoted Cholesky decomposition is introduced to efficiently estimate the two-point correlation function and approximate the variance. Numerical experiments are provided to support our theoretical findings.

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