科学研究
报告题目:

Computation of moments for Maxwell's equations with random interfaces via pivoted low-rank approximation

报告人:

张凯 教授(吉林大学)

报告时间:

报告地点:

理学院东北楼四楼报告厅(404)

报告摘要:

An efficient numerical method is developed for the computation of 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 Nedelec'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 consolidate our theoretical results. This is the jointed work with Prof. YL Hao(ZKNU), Prof. FD Kang(CityU), and Prof. JZ Li(SUSTC).