Abstract

A hybrid operator splitting method is developed for computations of two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting the solutions into the random space using the polynomial chaos (PC) projection method, the deterministic and random parts of the solutions are solved separately. There are two independent stages in the algorithm: the Yee scheme with domain decomposition implemented on a staggered grid for the deterministic part and the Monte Carlo sampling in the post-processing stage. These two stages of the algorithm are subject of computational studies. A parallel implementation is proposed for which the computational cost grows linearly with the number of random interfaces. Output statistics of Maxwell solutions are obtained including means, variance and time evolution of cumulative distribution functions (CDF). The computational results are presented for several configurations of domains with random interfaces. The novelty of this article lies in using level set functions to characterize the random interfaces and, under reasonable assumptions on the random interfaces (see Figure 1), the dimensionality issue from the PC expansions is resolved (see Sections 1.1.2 and 1.2).

Original languageEnglish (US)
Pages (from-to)194-213
Number of pages20
JournalInternational Journal of Numerical Analysis and Modeling
Volume11
Issue number1
StatePublished - 2014

Fingerprint

Chaos theory
Polynomials
Polynomial Chaos
Maxwell equations
Distribution functions
Mathematical operators
Statistics
Sampling
Decomposition
Operator Splitting Method
Chaos Expansion
Staggered Grid
Processing
Monte Carlo Sampling
Cumulative distribution function
Domain Decomposition
Parallel Implementation
Projection Method
Costs
Post-processing

Keywords

  • Evolution of probability distribution
  • Maxwell equations
  • Monte Carlo simulation
  • Polynomial chaos
  • Random interface
  • Random media
  • Stochastic partial differential equation

ASJC Scopus subject areas

  • Numerical Analysis

Cite this

Maxwell solutions in media with multiple random interfaces. / Jung, Chang Yeol; Kwon, Bongsuk; Mahalov, Alex; Binh Nguyen, Thien.

In: International Journal of Numerical Analysis and Modeling, Vol. 11, No. 1, 2014, p. 194-213.

Research output: Contribution to journalArticle

Jung, Chang Yeol ; Kwon, Bongsuk ; Mahalov, Alex ; Binh Nguyen, Thien. / Maxwell solutions in media with multiple random interfaces. In: International Journal of Numerical Analysis and Modeling. 2014 ; Vol. 11, No. 1. pp. 194-213.
@article{3461c324252548068146a54f9f03004d,
title = "Maxwell solutions in media with multiple random interfaces",
abstract = "A hybrid operator splitting method is developed for computations of two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting the solutions into the random space using the polynomial chaos (PC) projection method, the deterministic and random parts of the solutions are solved separately. There are two independent stages in the algorithm: the Yee scheme with domain decomposition implemented on a staggered grid for the deterministic part and the Monte Carlo sampling in the post-processing stage. These two stages of the algorithm are subject of computational studies. A parallel implementation is proposed for which the computational cost grows linearly with the number of random interfaces. Output statistics of Maxwell solutions are obtained including means, variance and time evolution of cumulative distribution functions (CDF). The computational results are presented for several configurations of domains with random interfaces. The novelty of this article lies in using level set functions to characterize the random interfaces and, under reasonable assumptions on the random interfaces (see Figure 1), the dimensionality issue from the PC expansions is resolved (see Sections 1.1.2 and 1.2).",
keywords = "Evolution of probability distribution, Maxwell equations, Monte Carlo simulation, Polynomial chaos, Random interface, Random media, Stochastic partial differential equation",
author = "Jung, {Chang Yeol} and Bongsuk Kwon and Alex Mahalov and {Binh Nguyen}, Thien",
year = "2014",
language = "English (US)",
volume = "11",
pages = "194--213",
journal = "International Journal of Numerical Analysis and Modeling",
issn = "1705-5105",
publisher = "University of Alberta",
number = "1",

}

TY - JOUR

T1 - Maxwell solutions in media with multiple random interfaces

AU - Jung, Chang Yeol

AU - Kwon, Bongsuk

AU - Mahalov, Alex

AU - Binh Nguyen, Thien

PY - 2014

Y1 - 2014

N2 - A hybrid operator splitting method is developed for computations of two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting the solutions into the random space using the polynomial chaos (PC) projection method, the deterministic and random parts of the solutions are solved separately. There are two independent stages in the algorithm: the Yee scheme with domain decomposition implemented on a staggered grid for the deterministic part and the Monte Carlo sampling in the post-processing stage. These two stages of the algorithm are subject of computational studies. A parallel implementation is proposed for which the computational cost grows linearly with the number of random interfaces. Output statistics of Maxwell solutions are obtained including means, variance and time evolution of cumulative distribution functions (CDF). The computational results are presented for several configurations of domains with random interfaces. The novelty of this article lies in using level set functions to characterize the random interfaces and, under reasonable assumptions on the random interfaces (see Figure 1), the dimensionality issue from the PC expansions is resolved (see Sections 1.1.2 and 1.2).

AB - A hybrid operator splitting method is developed for computations of two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting the solutions into the random space using the polynomial chaos (PC) projection method, the deterministic and random parts of the solutions are solved separately. There are two independent stages in the algorithm: the Yee scheme with domain decomposition implemented on a staggered grid for the deterministic part and the Monte Carlo sampling in the post-processing stage. These two stages of the algorithm are subject of computational studies. A parallel implementation is proposed for which the computational cost grows linearly with the number of random interfaces. Output statistics of Maxwell solutions are obtained including means, variance and time evolution of cumulative distribution functions (CDF). The computational results are presented for several configurations of domains with random interfaces. The novelty of this article lies in using level set functions to characterize the random interfaces and, under reasonable assumptions on the random interfaces (see Figure 1), the dimensionality issue from the PC expansions is resolved (see Sections 1.1.2 and 1.2).

KW - Evolution of probability distribution

KW - Maxwell equations

KW - Monte Carlo simulation

KW - Polynomial chaos

KW - Random interface

KW - Random media

KW - Stochastic partial differential equation

UR - http://www.scopus.com/inward/record.url?scp=84887080405&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887080405&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84887080405

VL - 11

SP - 194

EP - 213

JO - International Journal of Numerical Analysis and Modeling

JF - International Journal of Numerical Analysis and Modeling

SN - 1705-5105

IS - 1

ER -