# A generalized Holland model for wave diffraction by thin wires

february, 2007

Publication type:

International conference with proceedings

Conference:

Conference on Computational Electromagnetism and Acoustics, Oberwolfach Allemagne

External link:

Abstract:

The general context of the problem we are interested in is the
simulation of electromagnetic wave diffraction by thin wires. We make two assumptions
on such obstacles: we suppose the wires to be perfectly conducting,
and suppose their thickness is much smaller than the wavelength of the
field. For example, antennas satisfy these hypothesis.
We propose to study the model problem of acoustic
diffraction by thin obstacles, and we wish to perform such computations
using a volumic method with no mesh refinement.
To our knowledge there exists only one numerical method
matching these previous requirements. It is called the Holland model and was
proposed by Holland and Simpson in the engineer literature
\cite{Holland}. It is suitable for straigth wires aligned with the
axis of a cartesian grid in a FDTD scheme for electromagnetics.
This model assumes that the current is constant across any section
of the wire and that the field has an electrostatic behavior close
to the wire. It is also based on a averaging operator in a region
as large as a cell close to the wire.
This averaging operator involves a parameter called the lineic
inductance that is to be chosen on a empirical basis.
This model is widely used in volumic methods, it provides precise
results (for a well chosen lineic inductance) and can be easily
implemented. Unfortunately it lacks a solid theoretical basis. In
particular, there exist only empirical formulas for the lineic inductance.
For the model problem of bidimensional acoustic diffraction, we
present an augmented finite element method that matches the
requirements stated before. From this alternative method, we are able to recover the
Holland model. This method then generalizes the Holland model for
arbitrary meshes, provides a rigorous setting for it and a
theoretical expression of the lineic inductance.

BibTeX:

@inproceedings{Cla-Col-Dur-2007, author={Xavier Claeys and Francis Collino and Marc Duruflé }, title={A generalized Holland model for wave diffraction by thin wires }, organization={Conference on Computational Electromagnetism and Acoustics, Oberwolfach Allemagne }, year={2007 }, month={2}, }