Computation of moments for Maxwell's equations with random interfaces via pivoted low-rank approximation
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
Original language | English |
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Pages (from-to) | 1-19 |
Journal / Publication | Journal of Computational Physics |
Volume | 371 |
Online published | 15 May 2018 |
Publication status | Published - 15 Oct 2018 |
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Abstract
The aim of this paper is 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.
Research Area(s)
- Edge element, Low-rank approximation, Maxwell's equations, Random interfaces, Shape calculus
Citation Format(s)
Computation of moments for Maxwell's equations with random interfaces via pivoted low-rank approximation. / Hao, Yongle; Kang, Fengdai; Li, Jingzhi et al.
In: Journal of Computational Physics, Vol. 371, 15.10.2018, p. 1-19.
In: Journal of Computational Physics, Vol. 371, 15.10.2018, p. 1-19.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review