Perfectly matched layers for Maxwell's equations in second order formulation Page: 3 of 38
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
Perfectly matched layers for Maxwell's equations in
second order formulation*
Bj6rn Sj6greent N. Anders Peterssont
July 26, 2004
Abstract
We consider the two-dimensional Maxwell's equations in domains external to
perfectly conducting objects of complex shape. The equations are discretized us-
ing a node-centered finite-difference scheme on a Cartesian grid and the boundary
condition are discretized to second order accuracy employing an embedded tech-
nique which does not suffer from a "small-cell" time-step restriction in the explicit
time-integration method. The computational domain is truncated by a perfectly
matched layer (PML). We derive estimates for both the error due to reflections
at the outer boundary of the PML, and due to discretizing the continuous PML
equations. Using these estimates, we show how the parameters of the PML can be
chosen to make the discrete solution of the PML equations converge to the solution
of Maxwell's equations on the unbounded domain, as the grid size goes to zero.
Several numerical examples are given.
1 Introduction
In this paper, we study grid convergence properties of numerical solutions of the two-
dimensional Maxwell's equations, when a perfectly matched layer (PML) is used to trun-
cate an unbounded domain. While there are many types of non-reflecting and absorbing
boundary conditions, we here choose to use PML because it is a simple and straightfor-
ward method, easily implemented for both two and three space dimensions using either
*This work was performed under the auspices of the U.S. Department of Energy by University of
California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
tRoyal Institute of Technology, 100 44 Stockholm, Sweden, bjornsnada.kth. se
$Center for Applied Scientific Computing, Lawrence Livermore National Lab, Livermore, CA 94551,
andersp@llnl.gov.1
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Sjogreen, B & Petersson, A. Perfectly matched layers for Maxwell's equations in second order formulation, article, July 26, 2004; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc1407608/m1/3/: accessed May 29, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.