Canonical test cases for electromagnetic diffusion models
This suite of software and models provides a set of canonical test cases for electromagnetic diffusion models of the average energy density in highly reverberant environments in which the field is diffuse. It was developed in the Department of Electronic Engineering at the University of York for research into the Electromagnetic Diffusion Model for Stochastic Fields, particularly for electromagnetic compatibility (EMC) applications in reverberant environments.
The electromagnetic diffusion model
The power balance (PWB) method of estimating the average diffuse field in a system of coupled cavities, as implemented in AEGPWB, assumes that the energy density in each cavity is uniform (Hill1994,Junqua2005). It therefore cannot account for the inhomogeneity in the diffuse field arising from any loss in the cavity. The electromagnetic diffusion model (EDM), another statistical energy analysis (SEA) method, was proposed as a natural generalization of the PWB method that is able to predict such inhomogeneity (Flintoft2017). The EDM is a straightforward translation of the acoustic diffusion model (ADM) into the electromagnetic domain (Navarro2015,Savioja2015); the differences between the EDM and ADM are essentially confined to the auxiliary calculations of the absorption and transmission efficiencies of surface and apertures respectively. However, the validity and accuracy of the EDM must still be established independently of the ADM since the realms of application are significantly different and the electromagnetic field is polarized. A suite of canonical test cases was therefore created into order to explore the realm of validity of the EDM.
Test case features
The test cases include:
Absorption in cavity walls;
Absorption in volumetric lossy objects.
Transmission through electrically small and large apertures.
Excitation by point, surface and volume sources.
A range of boundary exchange coefficient absorption models.
Time dependent and steady-state solutions.
The test-cases are implemented using a combination of Open Source tools:
There are four implementations of the test cases:
FEM_SDM_2D: An approximate two-dimensional solution using Kantorovich reduction. The partitioned cavity is implemented using a single domain method (SDM). This implicitly enforces continuity of the energy density and its flux through the aperture.
FEM_DDM_2D: An approximate two-dimensional solution using Kantorovich reduction of the partitioned cavity cases implemented using a coupled dual domain method (DDM) with an energy exchange boundary condition. This enforces continuity of the energy density flux through the aperture. An iterative method is used to find the solution.
FEM_SDM_3D: A full three-dimensional solution. The partitioned cavity is implemented using a single domain method (SDM).
FEM_DDM_3D: A full three-dimensional solution of the partitioned cavity cases implemented using a coupled dual domain method (DDM).
There is a list and description of the main variables in doc/Variables.md.
The outline work-flow is as follows. First set the input parameters in
parameters.geo file. The mesh is then created the if required using Gmsh.
This must be done interactively via the GUI. The mesh must be saved in the
INRIA Medit mesh format, choosing the export option "physical entities".
The normal vectors for all surfaces enclosing a cavity must be pointing outwards.
$ gmsh SDM_2D.geo Mesh -> 2D Mesh -> 3D Save As -> INRA Mesh -> physical entities -> model.mesh
The problem is then solved using FreeFEM++:
$ FreeFem++ Model1.edp
This should create ASCII data files
the energy density, reverberant energy density, energy density
flux and reverberant energy density flux fields respectively. These are
post-processed using Octave:
$ octave octave> Model1
Beware the scoping rules in FreeFEM++. Certain entities are implemented as "macros" and cannot be declared and defined separately. This mean that sometimes code has to be repeated in different blocks.
parameters.geois read by the Gmsh, FreeFEM++ and Octave scripts.
Bugs and support
The test case implementation is still under development and no doubt will contain many bugs. Known significant bugs are listed in the file doc/Bugs.md in the source code.
For general guidance on how to write a good bug report see, for example:
Some of the tips in http://www.catb.org/esr/faqs/smart-questions.html are also relevant to reporting bugs.
There is a Wiki on the bitbucket project page.
How to contribute
We welcome any contributions to the development of the code, including:
Improving the user documentation.
Items in the to-do list in the file doc/ToDo.md.
The implementation notes are licensed under the GNU Free Documentation Licence, version 1.3. For details see the file doc/Implementation_Notes/fdl-1.3.txt.
Papers using the test-cases and associated tool chain
(Robinson2017) M. P. Robinson, I. D. Flintoft, J. F. Dawson, A. C. Marvin, F. I. Funn, L. Dawson and X. Zhang, "Effect of loading on field uniformity: Energy diffusion in reverberant environments", Proceedings of the XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science. Montreal, Canada, pp.E13–2, 2017. Postprint
(Flintoft2017) I. D. Flintoft, A. C. Marvin, F. I. Funn, L. Dawson, X. Zhang, M. P. Robinson and J. F. Dawson, "Evaluation of the diffusion equation for modelling reverberant electromagnetic fields", IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 3, pp. 760–769, 2017. Postprint
(Flintoft2017b) I. D. Flintoft and J. F. Dawson, “3D electromagnetic diffusion models for reverberant environments”, 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA2017), Verona, Italy, pp. 11-15 Sep. 2017.
(Geuzaine2009) C. Geuzaine and J.-F. Remacle, "Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities", International Journal for Numerical Methods in Engineering 79(11), pp. 1309-1331, 2009.
(Hecht2012) F. Hecht, “New development in FreeFEM++”, Journal of Numerical Mathematics, vol. 20, no. 3-4, pp. 251–265, 2012.
(Hill1994) D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk, "Aperture excitation of electrically large, lossy cavities", IEEE Transactions on Electromagnetic Compatibility, vol. 36, no. 3, pp. 169-178, Aug 1994.
(Junqua2005) I. Junqua, J.-P. Parmantier and F. Issac, "A Network Formulation of the Power Balance Method for High-Frequency Coupling", Electromagnetics, vol. 25 , no. 7-8, pp. 603-622, 2005.
(Navarro2015) J. M. Navarro and J. Escolano, “Simulation of building indoor acoustics using an acoustic diffusion equation model”, Journal of Building Performance Simulation, vol. 8, no. 1, pp. 3-14, 2015.
(Savioja2015) L. Savioja and U. Peter Svensson, “Overview of geometrical room acoustic modeling techniques”, J. Acoust. Soc. Am., vol. 138, no .2, pp. 708–730, 2015.