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Updates to info on dispersive materials (Debye, Lorentz, Drude). Added a separate References section.

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27
docs/source/app_references.rst 普通文件
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@@ -0,0 +1,27 @@
**********
References
**********
.. [BER1998] Bergmann, T., Robertsson, J. O., & Holliger, K. (1998). Finite-difference modeling of electromagnetic wave propagation in dispersive and attenuating media. Geophysics, 63(3), 856-867. (http://dx.doi.org/10.1190/1.1444396)
.. [BOU1996] Bourgeois, J. M., & Smith, G. S. (1996). A fully three-dimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment. Geoscience and Remote Sensing, IEEE Transactions on, 34(1), 36-44. (http://dx.doi.org/10.1109/36.481890)
.. [BUR1981] Burrough, P. A. (1981). Fractal dimensions of landscapes and other environmental data. Nature, 294(5838), 240-242. (http://dx.doi.org/10.1038/294240a0)
.. [DOB1985] Dobson, M. C., Ulaby, F. T., Hallikainen, M. T., & El-Rayes, M. (1985). Microwave dielectric behavior of wet soil-Part II: Dielectric mixing models. Geoscience and Remote Sensing, IEEE Transactions on, (1), 35-46. (http://dx.doi.org/10.1109/tgrs.1985.289498)
.. [HILL1998] Hillel, D. (1998). Environmental soil physics: Fundamentals, applications, and environmental considerations. Academic press. (http://dx.doi.org/10.1016/b978-012348525-0/50030-6)
.. [GED1998] Gedney, S. D. (1998). The perfectly matched layer absorbing medium. Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method, 263-344.
.. [GIAK2012] Giannakis, I., Giannopoulos, A., & Davidson, N. (2012). Incorporating dispersive electrical properties in FDTD GPR models using a general Cole-Cole dispersion function. In 2012 14th International Conference on Ground Penetrating Radar (GPR). (http://dx.doi.org/10.1109/icgpr.2012.6254866)
.. [GIA2014] Giannakis, I., & Giannopoulos, A. (2014). A Novel Piecewise Linear Recursive Convolution Approach for Dispersive Media Using the Finite-Difference Time-Domain Method. Antennas and Propagation, IEEE Transactions on, 62(5), 2669-2678. (http://dx.doi.org/10.1109/tap.2014.2308549)
.. [GIA1997] Giannopoulos, A. (1997). The investigation of Transmission-Line Matrix and Finite-Difference Time-Domain Methods for the Forward Problem of Ground Probing Radar, D.Phil thesis, Department of Electronics, University of York, UK. (http://etheses.whiterose.ac.uk/id/eprint/2443)
.. [GIA2012] Giannopoulos, A. (2012). Unsplit implementation of higher order PMLs. Antennas and Propagation, IEEE Transactions on, 60(3), 1479-1485. (http://dx.doi.org/10.1109/tap.2011.2180344)
.. [IRE2013] Ireland, D., & Abbosh, A. (2013). Modeling human head at microwave frequencies using optimized Debye models and FDTD method. Antennas and Propagation, IEEE Transactions on, 61(4), 2352-2355. (http://dx.doi.org/10.1109/tap.2013.2242037)
.. [KUN1993] Kunz, K. S., & Luebbers, R. J. (1993). The finite difference time domain method for electromagnetics. CRC press.
.. [LI2013] Li, J., Guo, L. X., Jiao, Y. C., & Wang, R. (2013). Composite scattering of a plasma-coated target above dispersive sea surface by the ADE-FDTD method. Geoscience and Remote Sensing Letters, IEEE, 10(1), 4-8. (http://dx.doi.org/10.1109/lgrs.2012.2189751)
.. [LUE1994] Luebbers, R., Steich, D., & Kunz, K. (1993). FDTD calculation of scattering from frequency-dependent materials. Antennas and Propagation, IEEE Transactions on, 41(9), 1249-1257. (http://dx.doi.org/10.1109/8.247751)
.. [PIE2009] Pieraccini, M., Bicci, A., Mecatti, D., Macaluso, G., & Atzeni, C. (2009). Propagation of large bandwidth microwave signals in water. Antennas and Propagation, IEEE Transactions on, 57(11), 3612-3618. (http://dx.doi.org/10.1109/tap.2009.2025674)
.. [TAF2005] Taflove, A., & Hagness, S. C. (2005). Computational electrodynamics. Artech house.
.. [TEI1998] Teixeira, F. L., Chew, W. C., Straka, M., Oristaglio, M. L., & Wang, T. (1998). Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils. Geoscience and Remote Sensing, IEEE Transactions on, 36(6), 1928-1937. (http://dx.doi.org/10.1109/36.729364)
.. [TUR1987] Turcotte, D. L. (1987). A fractal interpretation of topography and geoid spectra on the Earth, Moon, Venus, and Mars. Journal of Geophysical Research: Solid Earth (1978–2012), 92(B4), E597-E601. (http://dx.doi.org/10.1029/jb092ib04p0e597)
.. [TUR1997] Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics. Cambridge university press. (http://dx.doi.org/10.1017/cbo9781139174695)
.. [VIA2005] Vial, A., Grimault, A. S., Macías, D., Barchiesi, D., & de La Chapelle, M. L. (2005). Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method. Physical Review B, 71(8), 085416. (http://dx.doi.org/10.1103/physrevb.71.085416)
.. [WAR2011] Warren, C., & Giannopoulos, A. (2011). Creating finite-difference time-domain models of commercial ground-penetrating radar antennas using Taguchi’s optimization method. Geophysics, 76(2), G37-G47. (http://dx.doi.org/10.1190/1.3548506)
.. [YEE1966] Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag, 14(3), 302-307. (http://dx.doi.org/10.1109/TAP.1966.1138693)

1
docs/source/examples_2D.rst
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@@ -170,6 +170,7 @@ You can now view an image of the B-scan using the command:
.. _cylinder_Bscan_results:
.. figure:: images/cylinder_Bscan_results.png
:width: 800px
B-scan of model of a metal cylinder buried in a dielectric half-space.

1
docs/source/examples_3D.rst
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@@ -65,6 +65,7 @@ Results
.. _GSSI_1500_cylinder_Bscan_results:
.. figure:: images/GSSI_1500_cylinder_Bscan_results.png
:width: 800px
B-scan of model of a metal cylinder buried in a dielectric half-space with a model of an antenna similar to a GSSI 1.5GHz antenna.

21
docs/source/features.rst
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@@ -140,26 +140,5 @@ Alongside improvements to the input file there is a new output file format – H
In addition, the Visualization Toolkit (VTK) (http://www.vtk.org) is being used for improved handling and viewing of the detailed 3D FDTD geometry meshes. The VTK is an open-source system for 3D computer graphics, image processing and visualisation. It also has a number of free readers available including Paraview (http://www.paraview.org). For further details see the :ref:`geometry view command <geometryview>`.
**References**
.. [PIE2009] Pieraccini, M., Bicci, A., Mecatti, D., Macaluso, G., & Atzeni, C. (2009). Propagation of large bandwidth microwave signals in water. Antennas and Propagation, IEEE Transactions on, 57(11), 3612-3618. (http://dx.doi.org/10.1109/tap.2009.2025674)
.. [IRE2013] Ireland, D., & Abbosh, A. (2013). Modeling human head at microwave frequencies using optimized Debye models and FDTD method. Antennas and Propagation, IEEE Transactions on, 61(4), 2352-2355. (http://dx.doi.org/10.1109/tap.2013.2242037)
.. [LI2013] Li, J., Guo, L. X., Jiao, Y. C., & Wang, R. (2013). Composite scattering of a plasma-coated target above dispersive sea surface by the ADE-FDTD method. Geoscience and Remote Sensing Letters, IEEE, 10(1), 4-8. (http://dx.doi.org/10.1109/lgrs.2012.2189751)
.. [VIA2005] Vial, A., Grimault, A. S., Macías, D., Barchiesi, D., & de La Chapelle, M. L. (2005). Improved analytical fit of gold dispersion: Application to the modeling of extinction spectra with a finite-difference time-domain method. Physical Review B, 71(8), 085416. (http://dx.doi.org/10.1103/physrevb.71.085416)
.. [BER1998] Bergmann, T., Robertsson, J. O., & Holliger, K. (1998). Finite-difference modeling of electromagnetic wave propagation in dispersive and attenuating media. Geophysics, 63(3), 856-867. (http://dx.doi.org/10.1190/1.1444396)
.. [GIAK2012] Giannakis, I., Giannopoulos, A., & Davidson, N. (2012). Incorporating dispersive electrical properties in FDTD GPR models using a general Cole-Cole dispersion function. In 2012 14th International Conference on Ground Penetrating Radar (GPR). (http://dx.doi.org/10.1109/icgpr.2012.6254866)
.. [TEI1998] Teixeira, F. L., Chew, W. C., Straka, M., Oristaglio, M. L., & Wang, T. (1998). Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils. Geoscience and Remote Sensing, IEEE Transactions on, 36(6), 1928-1937. (http://dx.doi.org/10.1109/36.729364)
.. [GIA2014] Giannakis, I., & Giannopoulos, A. (2014). A Novel Piecewise Linear Recursive Convolution Approach for Dispersive Media Using the Finite-Difference Time-Domain Method. Antennas and Propagation, IEEE Transactions on, 62(5), 2669-2678. (http://dx.doi.org/10.1109/tap.2014.2308549)
.. [DOB1985] Dobson, M. C., Ulaby, F. T., Hallikainen, M. T., & El-Rayes, M. (1985). Microwave dielectric behavior of wet soil-Part II: Dielectric mixing models. Geoscience and Remote Sensing, IEEE Transactions on, (1), 35-46. (http://dx.doi.org/10.1109/tgrs.1985.289498)
.. [TUR1987] Turcotte, D. L. (1987). A fractal interpretation of topography and geoid spectra on the Earth, Moon, Venus, and Mars. Journal of Geophysical Research: Solid Earth (1978–2012), 92(B4), E597-E601. (http://dx.doi.org/10.1029/jb092ib04p0e597)
.. [TUR1997] Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics. Cambridge university press. (http://dx.doi.org/10.1017/cbo9781139174695)
.. [BUR1981] Burrough, P. A. (1981). Fractal dimensions of landscapes and other environmental data. Nature, 294(5838), 240-242. (http://dx.doi.org/10.1038/294240a0)
.. [HILL1998] Hillel, D. (1998). Environmental soil physics: Fundamentals, applications, and environmental considerations. Academic press. (http://dx.doi.org/10.1016/b978-012348525-0/50030-6)
.. [WAR2011] Warren, C., & Giannopoulos, A. (2011). Creating finite-difference time-domain models of commercial ground-penetrating radar antennas using Taguchi’s optimization method. Geophysics, 76(2), G37-G47. (http://dx.doi.org/10.1190/1.3548506)
.. [LUE1994] Luebbers, R., Steich, D., & Kunz, K. (1993). FDTD calculation of scattering from frequency-dependent materials. Antennas and Propagation, IEEE Transactions on, 41(9), 1249-1257. (http://dx.doi.org/10.1109/8.247751)
.. [BOU1996] Bourgeois, J. M., & Smith, G. S. (1996). A fully three-dimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment. Geoscience and Remote Sensing, IEEE Transactions on, 34(1), 36-44. (http://dx.doi.org/10.1109/36.481890)
.. [GED1998] Gedney, S. D. (1998). The perfectly matched layer absorbing medium. Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method, 263-344.
.. [GIA2012] Giannopoulos, A. (2012). Unsplit implementation of higher order PMLs. Antennas and Propagation, IEEE Transactions on, 60(3), 1479-1485. (http://dx.doi.org/10.1109/tap.2011.2180344)

10
docs/source/gprmodelling.rst
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@@ -28,6 +28,7 @@ temporal :math:`\Delta t` steps play a very significant role -- since the smalle
.. _yeecell:
.. figure:: images/yeecell.png
:width: 550px
3D FDTD Yee cell
@@ -46,6 +47,7 @@ One of the most challenging issues in modelling *open boundary* problems, such a
.. _abcs:
.. figure:: images/abcs.png
:width: 600px
GPR forward problem showing computational domain bounded by Absorbing Boundary Conditions (ABCs)
@@ -64,6 +66,7 @@ A right-handed Cartesian coordinate system is used with the origin of space coor
.. _coord3d:
.. figure:: images/coord3d.png
:width: 500px
gprMax coordinate system and conventions.
@@ -105,10 +108,3 @@ The cells of the RIPML, which have a user adjustable thickness, very efficiently
gprMax now offers the ability (for advanced users) to customise the parameters of the PML which allows its performance to be better optimised for specific applications. For further details see the :ref:`PML commands section <pml>`.
This user guide, can not serve as an in depth tutorial and a review of the FDTD method. However, some useful hints and tips are given here in order to cover the most fundamental aspects of using an FDTD based program and avoid the most common errors.
**References**
.. [GIA1997] Giannopoulos, A. (1997). The investigation of Transmission-Line Matrix and Finite-Difference Time-Domain Methods for the Forward Problem of Ground Probing Radar, D.Phil thesis, Department of Electronics, University of York, UK
.. [KUN1993] Kunz, K. S., & Luebbers, R. J. (1993). The finite difference time domain method for electromagnetics. CRC press.
.. [TAF2005] Taflove, A., & Hagness, S. C. (2005). Computational electrodynamics. Artech house.
.. [YEE1966] Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag, 14(3), 302-307.

3
docs/source/index.rst
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@@ -34,4 +34,5 @@ gprMax User Guide
:maxdepth: 2
:caption: Appendices
app_waveforms
app_waveforms
app_references

59
docs/source/input.rst
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@@ -287,9 +287,9 @@ Allows you to add dispersive properties to an already defined ``#material`` base
.. math::
\chi_p (t) = \frac{\epsilon_{rs} - \epsilon_{r \infty}}{\tau_p} e^{-t/\tau_p} \equiv \frac{\Delta \epsilon_r}{\tau_p} e^{-t/\tau_p},
\chi_p (t) = \frac{\Delta \epsilon_{rp}}{\tau_p} e^{-t/\tau_p},
where :math:`\epsilon_{rs}` is the zero-frequency relative permittivity, :math:`\epsilon_{r \infty}` is the relative permittivity at infinite frequency, and :math:`\tau_p` is the pole relaxation time.
where :math:`\Delta \epsilon_{rp} = \epsilon_{rsp} - \epsilon_{r \infty p}`, :math:`\epsilon_{rsp}` is the zero-frequency relative permittivity, :math:`\epsilon_{r \infty p}` is the relative permittivity at infinite frequency, and :math:`\tau_p` is the pole relaxation time.
The syntax of the command is:
@@ -298,19 +298,20 @@ The syntax of the command is:
#add_dispersion_debye: i1 f1 f2 f3 f4 ... str1
* ``i1`` is the number of Debye poles.
* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_r = \epsilon_{rs} - \epsilon_{r \infty}` , for the first Debye pole.
* ``f2`` is the relaxation time (seconds), :math:`\tau`, for the first Debye pole.
* ``f3`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_r = \epsilon_{rs} - \epsilon_{r \infty}` , for the second Debye pole.
* ``f4`` is the relaxation time (seconds), :math:`\tau`, for the second Debye pole.
* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp1} = \epsilon_{rsp1} - \epsilon_{r \infty p1}` , for the first Debye pole.
* ``f2`` is the relaxation time (seconds), :math:`\tau_{p1}`, for the first Debye pole.
* ``f3`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp2} = \epsilon_{rsp2} - \epsilon_{r \infty p2}` , for the second Debye pole.
* ``f4`` is the relaxation time (seconds), :math:`\tau_{p2}`, for the second Debye pole.
* ...
* ``str1`` identifies the material to add the dispersive properties to.
For example to create a model of water with a single Debye pole, :math:`\epsilon_{rs} = 80.1`, :math:`\epsilon_{r \inf} = 4.9` and :math:`\tau = 9.231\times 10^{-12}` seconds use: ``#material: 4.9 0.0 1.0 0.0 my_water`` and ``#add_dispersion_debye: 1 75.2 9.231e-12 my_water``.
For example to create a model of water with a single Debye pole, :math:`\epsilon_{rsp1} = 80.1`, :math:`\epsilon_{r \infty p1} = 4.9` and :math:`\tau_{p1} = 9.231\times 10^{-12}` seconds use: ``#material: 4.9 0 1 0 my_water`` and ``#add_dispersion_debye: 1 75.2 9.231e-12 my_water``.
.. note::
* You can continue to add pairs of values for :math:`\Delta \epsilon_r` and :math:`\tau` for as many Debye poles as you have specified with ``i1``.
* You can continue to add pairs of values for :math:`\Delta \epsilon_{rp}` and :math:`\tau_p` for as many Debye poles as you have specified with ``i1``.
* The relative permittivity in the ``#material`` command should be given as the relative permittivity at infinite frequency, i.e. :math:`\epsilon_{r \infty}`.
* Values for the relaxation times should always be greater than the time step :math:`\Delta t` used in the model.
* Temporal values associated with pole frequencies and relaxation times should always be greater than the time step :math:`\Delta t` used in the model.
#add_dispersion_lorenz:
@@ -328,7 +329,7 @@ where
\beta_p = \sqrt{\omega_p^2 - \delta_p^2} \quad \textrm{and} \quad \gamma_p = \frac{\omega_p^2 \Delta \epsilon_r}{\beta_p},
where :math:`\omega_p` is the frequency of the pole pair, :math:`\delta_p` is the damping coefficient, and :math:`j=\sqrt{-1}`.
where :math:`\Delta \epsilon_{rp} = \epsilon_{rsp} - \epsilon_{r \infty p}`, :math:`\epsilon_{rsp}` is the zero-frequency relative permittivity, :math:`\epsilon_{r \infty p}` is the relative permittivity at infinite frequency, :math:`\omega_p` is the frequency (Hertz) of the pole pair, :math:`\delta_p` is the damping coefficient (Hertz) , and :math:`j=\sqrt{-1}`.
The syntax of the command is:
@@ -337,19 +338,20 @@ The syntax of the command is:
#add_dispersion_lorenz: i1 f1 f2 f3 f4 f5 f6 ... str1
* ``i1`` is the number of Lorenz poles.
* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_r = \epsilon_{rs} - \epsilon_{r \infty}` , for the first Lorenz pole.
* ``f2`` is the relaxation time (seconds), :math:`\tau`, for the first Lorenz pole.
* ``f3`` is the damping factor for the first Lorenz pole.
* ``f4`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_r = \epsilon_{rs} - \epsilon_{r \infty}` , for the second Lorenz pole.
* ``f5`` is the relaxation time (seconds), :math:`\tau`, for the second Lorenz pole.
* ``f6`` is the damping factor for the second Lorenz pole.
* ``f1`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp1} = \epsilon_{rsp1} - \epsilon_{r \infty p1}` , for the first Lorenz pole.
* ``f2`` is the frequency (Hertz), :math:`\omega_{p1}`, for the first Lorenz pole.
* ``f3`` is the damping coefficient (Hertz), :math:`\delta_{p1}`, for the first Lorenz pole.
* ``f4`` is the difference between the zero-frequency relative permittivity and the relative permittivity at infinite frequency, i.e. :math:`\Delta \epsilon_{rp2} = \epsilon_{rsp2} - \epsilon_{r \infty p2}` , for the second Lorenz pole.
* ``f5`` is the frequency (Hertz), :math:`\omega_{p2}`, for the second Lorenz pole.
* ``f6`` is the damping coefficient (Hertz), :math:`\delta_{p2}`, for the second Lorenz pole.
* ...
* ``str1`` identifies the material to add the dispersive properties to.
.. note::
* You can continue to add triplets of values for :math:`\Delta \epsilon_r`, :math:`\tau` and :math:`\delta` for as many Lorenz poles as you have specified with ``i1``.
* You can continue to add triplets of values for :math:`\Delta \epsilon_{rp}`, :math:`\omega_p` and :math:`\delta_p` for as many Lorenz poles as you have specified with ``i1``.
* The relative permittivity in the ``#material`` command should be given as the relative permittivity at infinite frequency, i.e. :math:`\epsilon_{r \infty}`.
* Values for the relaxation times should always be greater than the time step :math:`\Delta t` used in the model.
* Temporal values associated with pole frequencies and relaxation times should always be greater than the time step :math:`\Delta t` used in the model.
#add_dispersion_drude:
@@ -361,7 +363,7 @@ Allows you to add dispersive properties to an already defined ``#material`` base
\chi_p (t) = \frac{\omega_p^2}{\gamma_p} (1-e^{-\gamma_p t}),
where :math:`\omega_p` is the frequency of the pole, :math:`\gamma_p` is the inverse of the pole relaxation time.
where :math:`\omega_p` is the frequency (Hertz) of the pole, and :math:`\gamma_p` is the inverse of the pole relaxation time (Hertz).
The syntax of the command is:
@@ -370,17 +372,17 @@ The syntax of the command is:
#add_dispersion_drude: i1 f1 f2 f3 f4 ... str1
* ``i1`` is the number of Drude poles.
* ``f1`` is the relaxation time (seconds), :math:`\tau`, for the first Drude pole.
* ``f2`` is the **x** for the first Drude pole.
* ``f3`` is the relaxation time (seconds), :math:`\tau`, for the second Drude pole.
* ``f4`` is the **x** for the second Drude pole.
* ``f1`` is the frequency (Hertz), :math:`\omega_{p1}`, for the first Drude pole.
* ``f2`` is the inverse of the relaxation time (Hertz), :math:`\gamma_{p1}`, for the first Drude pole.
* ``f3`` is the frequency (Hertz), :math:`\omega_{p2}`, for the second Drude pole.
* ``f4`` is the inverse of the relaxation time (Hertz), :math:`\gamma_{p2}` for the second Drude pole.
* ...
* ``str1`` identifies the material to add the dispersive properties to.
.. note::
* You can continue to add pairs of values for :math:`\tau` and **x** for as many Drude poles as you have specified with ``i1``.
* The relative permittivity in the ``#material`` command should be given as the relative permittivity at infinite frequency, i.e. :math:`\epsilon_{r \infty}`.
* Values for the relaxation times should always be greater than the time step :math:`\Delta t` used in the model.
* You can continue to add pairs of values for :math:`\omega_p` and :math:`\gamma_p` for as many Drude poles as you have specified with ``i1``.
* Temporal values associated with pole frequencies and relaxation times should always be greater than the time step :math:`\Delta t` used in the model.
#soil_peplinski:
@@ -452,11 +454,6 @@ At the boundaries between different materials in the model there is the question
* If an object is anistropic then dielectric smoothing is automatically turned off for that object.
* Non-volumetric object building commands, ``#edge`` and ``#plate`` cannot have dielectric smoothing.
**References**
.. [LUE1994] Luebbers, R., Steich, D., & Kunz, K. (1993). FDTD calculation of scattering from frequency-dependent materials. Antennas and Propagation, IEEE Transactions on, 41(9), 1249-1257. (http://dx.doi.org/10.1109/8.247751)
.. [BOU1996] Bourgeois, J. M., & Smith, G. S. (1996). A fully three-dimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment. Geoscience and Remote Sensing, IEEE Transactions on, 34(1), 36-44. (http://dx.doi.org/10.1109/36.481890)
#edge:
------