gprMax/docs/source/comparisons_numerical.rst

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Numerical comparisons
*********************

This section presents some comparisons of models using different numerical modelling techniques.

FDTD/MoM
========

The Finite-Difference Time-Domain (FDTD) method from gprMax is compared with the Method of Moments (MoM) from the MATLAB antenna toolbox (http://uk.mathworks.com/products/antenna/).

Bowtie antenna in free space
----------------------------

This example considers the input impedance of a planar bowtie antenna in free space. The length and height of the bowtie are 100mm, giving a flare angle of :math:`90^\circ`.

FDTD model
^^^^^^^^^^

:download:`antenna_bowtie_fs.in <../../tests/numerical/vs_MoM_MATLAB/antenna_bowtie_fs/antenna_bowtie_fs.in>`

.. literalinclude:: ../../tests/numerical/vs_MoM_MATLAB/antenna_bowtie_fs/antenna_bowtie_fs.in
    :language: none
    :linenos:

A Gaussian waveform with a centre frequency of 1.5GHz was used to excite the antenna, which was fed by a transmission line with a characteristic impedance of 50 Ohms.

The module ``plot_antenna_params`` from the ``tools`` subpackage was used to calculate and plot the input impedance from the FDTD model.

MoM model
^^^^^^^^^

The bowtie antenna was created using the antenna toolbox in MATLAB, and the ``bowtieTriangular`` class.

.. code-block:: matlab

    bowtie = bowtieTriangular('Length', 0.1)
    zin = impedance(bowtie, 33.33e6:33.33e6:6e9)

Results
-------

:numref:`antenna_bowtie_fs_ant_params` shows the input impedance (resistive and reactive) for the FDTD (gprMax) and MoM (MATLAB) models. The frequency resolution for the FFT used in both models was :math:`\Delta f = 33.33~MHz`.

.. _antenna_bowtie_fs_ant_params:

.. figure:: ../../tests/numerical/vs_MoM_MATLAB/antenna_bowtie_fs/antenna_bowtie_fs_ant_params.png
    :width: 600 px

    Input impedance (resistive and reactive) of a bowtie antenna in free space using FDTD (gprMax) and MoM (MATLAB) models.

The match...