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Numerical subgrid scale models for the Yee scheme
Department of Mathematics and Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0002-6321-8619
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The Yee scheme is a very common and practical algorithm for the simulation of wave propagation on uniform grids.  We develop numerical subgrid scale models in order to incorporate effects of obstacles and holes that are smaller than the grid spacing. The models are based on pre-computing at the microscale, and are thus including the effect of the detailed small scale shape.  Numerical examples in 1D, 2D and 3D are given.

Keyword [en]
Yee, FDTD, Subcell
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-95505OAI: diva2:528692
QS 2012Available from: 2012-07-30 Created: 2012-05-28 Last updated: 2012-07-30Bibliographically approved
In thesis
1. Modified Stencils for Boundaries and Subgrid Scales in the Finite-Difference Time-Domain Method
Open this publication in new window or tab >>Modified Stencils for Boundaries and Subgrid Scales in the Finite-Difference Time-Domain Method
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis centers on modified stencils for the Finite-Difference Time-Domain method (FDTD), or Yee scheme, when modelling curved boundaries, obstacles and holes smaller than the discretization length.  The goal is to increase the accuracy while keeping the structure of the standard method, enabling improvements to existing implementations with minimal effort.

We present an extension of a previously developed technique for consistent boundary approximation in the Yee scheme.  We consider both Maxwell's equations and the acoustic equations in three dimensions, which require separate treatment, unlike in two dimensions.

The stability properties of coefficient modifications are essential for practical usability.  We present an analysis of the requirements for time-stable modifications, which we use to construct a simple and effective method for boundary approximations. The method starts from a predetermined staircase discretization of the boundary, requiring no further data on the underlying geometry that is being approximated.

Not only is the standard staircasing of curved boundaries a poor approximation, it is inconsistent, giving rise to errors that do not disappear in the limit of small grid lengths. We analyze the standard staircase approximation by deriving exact solutions of the difference equations, including the staircase boundary. This facilitates a detailed error analysis, showing how staircasing affects amplitude, phase, frequency and attenuation of waves.

To model obstacles and holes of smaller size than the grid length, we develop a numerical subgrid method based on locally modified stencils, where a highly resolved micro problem is used to generate effective coefficients for the Yee scheme at the macro scale.

The implementations and analysis of the developed methods are validated through systematic numerical tests.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. xi, 34 p.
Trita-CSC-A, ISSN 1653-5723 ; 2012:07
FDTD, Yee, Staircasing
National Category
Computational Mathematics
urn:nbn:se:kth:diva-95510 (URN)978-91-7501-417-3 (ISBN)
Public defence
2012-06-15, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Swedish e‐Science Research Center

QC 20120530

Available from: 2012-05-30 Created: 2012-05-28 Last updated: 2013-04-09Bibliographically approved

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