---
res:
bibo_abstract:
- "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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: C
foaf_name: Classen, C
foaf_surname: Classen
- foaf_Person:
foaf_givenName: Jens
foaf_name: Förstner, Jens
foaf_surname: Förstner
foaf_workInfoHomepage: http://www.librecat.org/personId=158
orcid: 0000-0001-7059-9862
- foaf_Person:
foaf_givenName: Torsten
foaf_name: Meier, Torsten
foaf_surname: Meier
foaf_workInfoHomepage: http://www.librecat.org/personId=344
orcid: 0000-0001-8864-2072
- foaf_Person:
foaf_givenName: R
foaf_name: Schuhmann, R
foaf_surname: Schuhmann
bibo_doi: 10.1109/aps.2010.5562017
dct_date: 2010^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/9781424449675
- http://id.crossref.org/issn/9781424449682
dct_language: eng
dct_publisher: IEEE@
dct_subject:
- tet_topic_numerics
dct_title: Enhanced FDTD edge correction for nonlinear effects calculation@
...