---
_id: '4167'
abstract:
- lang: eng
  text: "The electromagnetic field in the vicinity of sharp edges needs a special
    treatment in numeric calculation whenever accurate, fast converging results are
    necessary. One of the fundamental works concerning field singularities has been
    proposed in 1972 [1] and states that the electromagnetic energy density must be
    integrable over any finite\r\ndomain, even if this domain contains singularities.
    It is shown, that the magnetic field \x02H(\x03, ϕ) and electric field \x02E(\x03,
    ϕ) are proportional to ∝ \x03(t−1) for \x03 → 0. The variable \x03 is the distance
    to the edge and t has to fulfill the integrability condition and thus is restricted
    to 0 < t < 1. This result is often used to reduce the error corresponding to the
    singularity without increasing the numerical effort [2 - 5]. For this purpose,
    a correction factor K is estimated by inserting the proportionality into the wave
    equation. It is shown, that this method improves the accuracy of the result significantly,
    however the order of convergence is often not studied. In [4] a method to modify
    the material parameters in order to use analytic results to improve the numeric
    calculation is presented. In this contribution we will - inspired by the scheme
    given in [4] - develop a new method to estimate a correction factor for perfect
    conducting materials (PEC) and demonstrate the improvement of the results compared
    to the standard edge correction. Therefore analytic results (comparable to [1])
    are consequently merged with the scheme in [4]. The main goal of this work is
    the calculation of the second harmonic generation (SHG) in the wave response of
    so-called metamaterials [6]. Frequently these structures\r\ncontain sharp metallic
    edges with field singularities at the interfaces which have a strong impact on
    the SHG signals. Thus, an accurate simulation of singularities is highly important.
    However, the following approach can also be applied to many other setups, and
    one of them is shown in the example below."
article_number: '11515155 '
author:
- first_name: C
  full_name: Classen, C
  last_name: Classen
- first_name: Jens
  full_name: Förstner, Jens
  id: '158'
  last_name: Förstner
  orcid: 0000-0001-7059-9862
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: R
  full_name: Schuhmann, R
  last_name: Schuhmann
citation:
  ama: 'Classen C, Förstner J, Meier T, Schuhmann R. Enhanced FDTD edge correction
    for nonlinear effects calculation. In: <i>2010 IEEE Antennas and Propagation Society
    International Symposium</i>. IEEE; 2010. doi:<a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>'
  apa: Classen, C., Förstner, J., Meier, T., &#38; Schuhmann, R. (2010). Enhanced
    FDTD edge correction for nonlinear effects calculation. <i>2010 IEEE Antennas
    and Propagation Society International Symposium</i>, Article 11515155. 2010 IEEE
    international Symposium Antennas, Toronto, ON, Canada. <a href="https://doi.org/10.1109/aps.2010.5562017">https://doi.org/10.1109/aps.2010.5562017</a>
  bibtex: '@inproceedings{Classen_Förstner_Meier_Schuhmann_2010, title={Enhanced FDTD
    edge correction for nonlinear effects calculation}, DOI={<a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>},
    number={11515155}, booktitle={2010 IEEE Antennas and Propagation Society International
    Symposium}, publisher={IEEE}, author={Classen, C and Förstner, Jens and Meier,
    Torsten and Schuhmann, R}, year={2010} }'
  chicago: Classen, C, Jens Förstner, Torsten Meier, and R Schuhmann. “Enhanced FDTD
    Edge Correction for Nonlinear Effects Calculation.” In <i>2010 IEEE Antennas and
    Propagation Society International Symposium</i>. IEEE, 2010. <a href="https://doi.org/10.1109/aps.2010.5562017">https://doi.org/10.1109/aps.2010.5562017</a>.
  ieee: 'C. Classen, J. Förstner, T. Meier, and R. Schuhmann, “Enhanced FDTD edge
    correction for nonlinear effects calculation,” presented at the 2010 IEEE international
    Symposium Antennas, Toronto, ON, Canada, 2010, doi: <a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>.'
  mla: Classen, C., et al. “Enhanced FDTD Edge Correction for Nonlinear Effects Calculation.”
    <i>2010 IEEE Antennas and Propagation Society International Symposium</i>, 11515155,
    IEEE, 2010, doi:<a href="https://doi.org/10.1109/aps.2010.5562017">10.1109/aps.2010.5562017</a>.
  short: 'C. Classen, J. Förstner, T. Meier, R. Schuhmann, in: 2010 IEEE Antennas
    and Propagation Society International Symposium, IEEE, 2010.'
conference:
  end_date: 2010-07-17
  location: Toronto, ON, Canada
  name: 2010 IEEE international Symposium Antennas
  start_date: 2010-07-11
date_created: 2018-08-28T08:34:52Z
date_updated: 2025-12-16T12:35:39Z
ddc:
- '530'
department:
- _id: '61'
- _id: '15'
- _id: '293'
- _id: '170'
- _id: '230'
- _id: '35'
- _id: '34'
doi: 10.1109/aps.2010.5562017
file:
- access_level: open_access
  content_type: application/pdf
  creator: hclaudia
  date_created: 2018-08-28T08:36:44Z
  date_updated: 2018-09-04T19:31:42Z
  file_id: '4168'
  file_name: 2010 Classen,Förstner, Meier T,Schuhmann_Enhanced FDTD edge correction
    for nonlinear effects calculation.pdf
  file_size: 209412
  relation: main_file
file_date_updated: 2018-09-04T19:31:42Z
has_accepted_license: '1'
keyword:
- tet_topic_numerics
language:
- iso: eng
oa: '1'
publication: 2010 IEEE Antennas and Propagation Society International Symposium
publication_identifier:
  isbn:
  - '9781424449675'
  - '9781424449682'
publication_status: published
publisher: IEEE
status: public
title: Enhanced FDTD edge correction for nonlinear effects calculation
type: conference
urn: '41677'
user_id: '16199'
year: '2010'
...