ARSAdvances in Radio ScienceARSAdv. Radio Sci.1684-9973Copernicus GmbHGöttingen, Germany10.5194/ars-13-49-2015Comparison of electromagnetic solvers for antennas mounted on vehiclesMockerM. S. L.marina.mocker@tum.deHippS.SpinnlerF.TaziH.EibertT. F.Technische Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstrasse 21, 80333 Munich, GermanyCST AG, Bad Nauheimer Str. 19, 64289 Darmstadt, GermanyAudi AG, August-Horch Str., 85055 Ingolstadt, GermanyM. S. L. Mocker (marina.mocker@tum.de)3November2015132495526December201411April201519May2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://ars.copernicus.org/articles/13/49/2015/ars-13-49-2015.htmlThe full text article is available as a PDF file from https://ars.copernicus.org/articles/13/49/2015/ars-13-49-2015.pdf
An electromagnetic solver comparison for various use cases of antennas
mounted on vehicles is presented. For this purpose, several modeling
approaches, called transient, frequency and integral solver, including the
features fast resonant method and autoregressive filter, offered by CST MWS,
are investigated. The solvers and methods are compared for a roof antenna
itself, a simplified vehicle, a roof including a panorama window and a
combination of antenna and vehicle. With these examples, the influence of
different materials, data formats and parameters such as size and complexity
are investigated. Also, the necessary configurations for the mesh and the
solvers are described.
Introduction
For solving electromagnetic problems in complex environments, the choice of
the most appropriate method does not only determine the time efficiency, but
has an influence on the accuracy of the gained results, as well. There is not
a single combination of a numerical method and algebraic solver, in the
following called solver, which can fulfill all requirements. Moreover, many
parameters, such as size in relation to wavelength, complexity and resonating
behavior must be considered. In the following, the transient (T), the
frequency (F) and the integral (I) solver offered in CST MWS
, are investigated.
The T solver is based on the finite integration technique. The geometrical
model is here divided into hexahedra and a time signal is
propagated through the structure .
In general the hexahedral mesh is a very robust way of meshing for
complicated structures, but has some disadvantages, for example in case of
curved geometries. In these cases, the mesh must either be extremely dense or
is meshed by utilizing the perfect boundary approximation technique, where
sub-cellular information is taken into account for curved elements
. An improved mesh can be achieved by subgridding
, where critical areas are meshed with more lines than the
rest.
For highly resonant structures such as antennas, the simulation duration may
be very high or resonances may even not be simulated correctly at all due to
an insufficient decay of energy within the system. This can be solved by an
autoregressive (AR) filter which drastically reduces the
simulation time as the spectral properties can be retrieved from rather few
time steps.
The F solver uses the finite element method. A limit for this method is the
availability of random access memory (RAM) which is used mainly dependent on
the number of mesh cells. The resulting matrix is sparsely populated as
elements are only non-zero if nodes in the discretized geometry are
neighboring. The numerical system size can be reduced by a model order
reduction technique (MOR) .
In a first step, the structure is meshed with surface triangles and only in
case there is a thickness, the volume is meshed with tetrahedra. At critical
points, the mesh is corrected for the highest simulation frequency usually
mainly by further refinements .
The I solver uses the Method of Moments. As only the surface must be meshed,
the method is well suitable for large solution domains. Dielectrics are not
meshed for this solver method in CST MWS.
In the following, the mentioned solvers and methods are investigated in order
to simulate a complex roof antenna mounted on a vehicle accurately and
efficiently. Therefore, several simulations with the roof antenna itself are
conducted. In a second step, the solvers are compared for the purpose of
simulating extended simulation domains as vehicles and roofs. In these
models, monopoles are used as simplified antennas in order to isolate the
problems from each other. Finally, a vehicle including the roof antenna is
simulated. Also, the influence of data formats and materials is taken into
consideration. The values of interest for the feasibility and efficiency of a
simulation are majorly the RAM and time consumption. Especially the time
consumption is only a rough value. The benchmark computer has 2 processors of
the type Intel(R) Xeon(R) CPU with E5640@2.67 GHz and 24 GB RAM. Each of
the processors consists of 4 cores and moreover the Intel(R) Hyper-Threading
Technology is enabled. Some simulations could not be performed on this
computer so the necessary time was estimated. Simulations for the purpose of
time comparability were started in order to estimate the differences in
computation speed. Finally, the given times can be seen as benchmarks.
Roof antenna
The first part of the investigation is a roof antenna itself. The antenna
designed for the north American market consists of a SDARS patch, a GPS patch
and a telephone antenna, which are contained in one antenna assembly as shown
in Fig.. It is built by thin metal sheets and
several dielectrics. All covered services are listed in
Table . The antenna assembly is adapted to a
mounting consisting of metal and plastic for the purpose of sealing and is
covered by a housing of plastic as shown in Fig. .
All solvers explained above, except the I solver, are evaluated for the
antenna model and finally compared to measurement results. All connections
are modeled as coaxial structures. The antenna needs to be slightly modified
for each solver. For the transient solver all ports were implemented as
perfect conducting wires between two points realizing a source, called edge
ports, whereas with the frequency solver a face is used instead of a thin
wire, called discrete face ports, were used. This port modification does not
relevantly change the simulation behavior as the results for the Global
Positioning System (GPS) and Satellite Digital Audio Radio Services (SDARS)
antennas do correspond well to each other.
For the simulations with the T solver, the antenna is meshed using hexahedra
as shown in Fig. . To ensure that all metalizations are
correctly identified in the hexahedral mesh they are thickened in order to
ensure at least 2 mesh lines for each material, even though this was only
mandatory for dielectrics. For the F solver, the antenna is meshed with
tetrahedra as shown in Fig. . The automatic discretization
process is more stable for the hexahedral mesh in comparison to the
tetrahedral mesh, especially if the model contains material jumps in
combination with complicated structures.
Hexahedral mesh.
Tetrahedral mesh.
The simulated and measured reflection parameters of the SDARS antenna are
shown in Fig. and of the telephone antenna in
Fig. . The resonance frequencies are well met for the SDARS and
GPS simulations and roughly for the simulation of the telephone antenna.
In Table the RAM and time consumption are listed for
all simulations.
Efficient and accurate simulations are possible with the F solver. After
simplifications of the model by neglecting details and a manual optimization
of the mesh by assigning discretization densities to different materials in
the model, the number of cells can be reduced to 200 000 cells
. With the adaptive mesh, the results are not completely
correct for resonance frequencies as shown in Fig. . The
adaptive mesh of the F solver does not change the results of the SDARS and
the GPS antenna, but for the telephone antenna. For the frequencies over
1.5 GHz the reflection parameters change by using the adaptive mesh. If the
simulation bandwidth is reduced, the newly arising resonances do not exist. A
reason for this is that adaptive meshing algorithms in time and frequency
domain analyze the simulated structure to increase the mesh density at high
field values in order to decrease the simulation error. While in time domain
the time pulse transports the energy, yielding a broadband adaption of the
mesh, the frequency solver solves the equations at distinct frequency points
and thus adapts at single frequency values. By default the highest possible
frequency is used in order to assure the best resolution. However, maximum
field values might occur at other points in the structure, namely where
resonances take place. In order to account for this effect, it is possible to
set the adaption to the resonances explicitly. If this option is not chosen,
simulation results may differ for varying frequency bands due to different
maximum frequencies. Using the resonant fast S Parameter method based on
MOR does not relevantly improve the scattering parameters or the time
consumption, but drastically increases the maximum RAM consumption. The MOR
in this case is very costly so that the advantages do not carry weight.
In all cases the resonances are more distinct in the simulations with the
F solver, than with the T solver, because the energy only decays very slowly
when propagating through the structure at the appearance of resonances. The
standard configuration is to abort the simulation after a time according to
20 times the length of the input impulse. At this point of time the energy
only decays to ≈-40 dB and ripples still exist in the scattering
parameters. As well the adaptive mesh refinement cannot be used under these
conditions as first results are necessary for the refinement of the mesh. A
way to circumvent this problem is the AR Filter. With the AR Filter, the
resonances can be estimated before the energy is decayed completely, thus,
the simulation duration is reduced to less than one hour. The number of
required adaptive mesh refinements cannot be given in general as it is
dependent on the initial mesh.
S11 of the SDARS patch simulated with different solvers.
S33 of the telephone antenna simulated with different solvers.
Comparison of different solver for the roof antenna.
For useful investigations with the T solver, the AR filter is necessary. Once
some experience with the meshing of the structure could be achieved, the most
efficient simulations still can be undertaken with the F solver. A further
advantage of the F solver is the fact that single frequencies can be
simulated at frequency points of interest after the solver run has finished
without performing adaptive meshing.
Extended simulation domains
Vehicles feature an extended and at the same time complex environment which
strongly influences the far field patterns of roof antennas. A common data
format for vehicles is the Computer Aided Three-Dimensional Interactive
Application (CATIA) format. In this format, every detail is included and the
total amount of data is by far too extensive for the import into
electromagnetic field solver programs. To reduce the amount of data and for
reasons of compatibility the data is simplified to Nasa Structural Analysis
System (NASTRAN) data, in which the surface is represented by triangles as
shown in Fig. . For the investigation of the efficiency and
the accuracy of the solvers, the antenna is simplified to a monopole which is
located in the rear part of the roof.
Nastran mesh of a vehicle.
Far field simulation results at 2 GHz for T, F and I solver with different accuracies.
The simulation with the T solver is carried out in a frequency range from 1
to 2.5 GHz and the impulse is propagated through the structure until the
energy level decreased to -30 dB. The mesh configuration is 10 lines per
wavelength with a mesh line ratio limit of 999, which indicates the ratio of
the largest cell size to the smallest cell size. The adaptive mesh refinement
is an automatic refinement process in order to improve the mesh quality,
especially in areas with high levels of electromagnetic energy the
discretization is refined. It is deactivated in the simulations described in
the following, as each refinement step approximately takes as long as the
simulation duration given in Table . The simulation
with the I solver is carried out for one single frequency point at 2 GHz.
The I solver is configured with first solver order, an accuracy of 0.001 and
10 and 5 mesh cells per wavelength λ are used. The F solver meshing
is configured with the default values allowing curved elements. The far field
patterns simulated with all solvers are approximately similar as shown in
Fig. . The comparability of the RAM and time consumption in
Table is only possible taking into consideration
the varying frequency bandwidth and maximum frequency. The T solver is
simulated in a broad frequency bandwidth with a maximum frequency of 2.5 GHz
whereas the I and F solver are started at one single frequency point at
2 GHz. The decreased maximum frequency means that there are less mesh cells
necessary in total.
Meshing of NASTRAN structure with triangles.
The time efficiency of the solvers is dependent on the number of frequencies
of interest. In case only one frequency point is investigated, the I solver
is faster than the T solver. As soon as scattering parameters should be
simulated at the same time, a larger bandwidth is necessary for reasonable
investigations and the time consumption with the I solver will increase.
Additionally it must be considered that windows are important for the far
field behavior which were not considered in the I solver as they are
dielectrics.
Comparison of different solvers for the monopole on a metallic
vehicle modeled in NASTRAN.
For the I and F solver a reduction of the overall model by deleting parts
which do not influence the far field patterns, brings advantages as there are
less triangles. With the T solver this effect is less distinctive because the
whole box including air is meshed. For this reason, in the following only the
roof is taken into consideration.
Another vehicle model had to be used for the roof comparisons. Usually
vehicle models are prepared in NASTRAN format at AUDI AG. The disadvantage of
the NASTRAN format in CST MWS is that the mesh gets unnecessary fine as the
triangles cannot be loaded as the mesh itself but are meshed a second time as
shown in Fig. . Even if the triangles could be loaded as
the final mesh, the limitation to a specific frequency by the size of the
triangles makes this process inflexible. Originally, the vehicles are saved
in CATIA format which represents the geometry as non-uniform rational basis
splines (NURBS).
Roof with panorama glass window and monopole as simplification of an
antenna.
Far field patterns at 2 GHz simulated with T and with F solver.
In Table , the comparison of a metallic roof imported in
NASTRAN and CATIA format is shown. With the CATIA format, reasonable results
could be gained in the T solver with a mesh configuration of 10 lines per
λ, whereas the NASTRAN format needs 3 times more mesh cells to meet
the resonance frequency and the expected far field. At points, where the
structure is discontinuous or at the end of straight lines describing the
surface, the automatic meshing detects fixpoints, where discretization lines
are applied. It is important to switch off the fixpoints as the hexahedral
mesh would be by far too dense to even start the solver. Still some fixpoints
around the antenna and the port are necessary. The mesh configuration was set
equal to the configuration giving good results for the CATIA model. Within 3
cycles of adaptive mesh refinement the configuration was changed to 34 lines
per λ. The first cycle takes 5 h, the second cycle 8 h and the
third cycle, finally giving the expected resonance frequency of the monopole
takes 10 h. In case the mesh configurations are known, the adaptive mesh can
be skipped and the values as given in Table can be expected.
Another disadvantage of the NASTRAN format is the thickening of the
triangular surface in order to prepare the model for the meshing with
hexahedra. The far field pattern in vertical cut is shown in
Fig. .
Simulated far field results at 2 GHz comparing the simulation using
a roof model in CATIA and NASTRAN format.
The differences between the two plots can be explained by the deviations of
the models which result from the conversion to NASTRAN. The problem changes
when dielectrics as glass are introduced. For that a rectangular glass window
is introduced into the roof as shown in Fig. . The vehicle
roof with and without glass is investigated with the T solver. The
simulations were carried out for a frequency range from 1 to 6.5 GHz. The
metallic roof has a size of approximately 1.35 m × 1.15 m. The
introduced window has a size of 1 m × 0.9 m which means that
approximately 60 % are then consisting of glass. The wavelength λ
in glass, with an ϵr equal to 7, for the highest simulated
frequency of 6.5 GHz is 17.4 mm. In free space the wavelength is 46 mm.
This explains the increased number of mesh cells as shown in
Table which also leads to an increase of RAM and time
consumption. The dramatic increase of time consumption in the simulation with
the panorama glass window can be explained by the fact that data was swapped
from the RAM to the hard disk, as only 12 GB of RAM were available.
Comparison of different solvers for the monopole on a roof and
influence of a panorama glass window.
The results of the simulated far field patterns correspond to typically
observed results. A typical effect with panorama windows is the damping of
the far field in the horizontal direction . This effect is
only observable in the simulation in case the glass has a sufficient
thickness which was in this case set to approximately 4 mm in order to guide
the wave through the glass. The CATIA model with the panorama window was
additionally simulated with the F solver. The frequency in this simulation
ranges from 1 to 6.5 GHz which is the same range as with the simulations
with the T solver. There are some deviations between the simulations with the
T and the F solver. The reflection parameters with the F solver shows a more
broadband resonance and the far field at 2 GHz shown in Fig.
also shows some deviations. Overall the results of the T solver are more
credible. The F solver is faster, but still needs more RAM.
Roof antenna on vehicle
The far field pattern is, in contrast to the scattering parameters, not only
dependent on a small area around the antenna. This is why a simulation of the
model including the vehicle from Fig. and the roof antenna
from Fig. and Fig. is necessary. The
previous investigations and comparisons of the different solvers show that
only the T solver can perform this simulation and high-performance computers
are required. So the simulation is conducted on a workstation with 4 Tesla
K40 graphic processing units (GPU) . For the meshing, 10 lines
per λ, a lower mesh limit of 10 and a mesh line ratio limit of 600 is
used. To ensure that the antenna is meshed in the same way as before
fixpoints were used. Still they must be ignored for the vehicle in NASTRAN
format. These configurations lead to 513 218 568 mesh cells in total. The
accuracy is set to -30 dB.
With these settings the same reflection parameters as with the T solver in
Figs. and are achieved. For the simulation 61 GB
of RAM and an adaptive meshing is necessary with 3 cycles each taking 27 to
43 h. Altogether the simulation duration aggregates to 118 h.
Conclusions
In this paper, the theoretical background of the F, T and I solver and their
accuracy and efficiency for a roof antenna mounted on a vehicle were
discussed. The results show that the choice of the solver is not only
dependent on the structure of the simulation domain, but also on the demanded
results. The scattering parameters are more dependent on the structure
itself, whilst the far field is strongly dependent on the environment. For
the simulation of the roof antenna itself the T solver under usage of the AR
filter and the F solver give good results whereas the vehicle is most
efficiently simulated using the T solver, especially in case it contains
dielectrics as glass. For this reason, the roof antenna including the vehicle
was simulated with the T solver using the AR filter. The meshing of both the
vehicle and the antenna works out the best when importing the data in CATIA
format. The scattering parameters were validated with measurements and the
far field patterns agreed with experiences from similar measurements. By
comparing the different ways of simulations, an efficient way for
investigating further antenna systems concerning scattering parameters as
well as far field patterns could be described.
Acknowledgements
The authors wish to thank AUDI AG for providing CAD Data which are used in
the simulation models and for the measurement data which serve to validate
the simulation results. Also, a special thanks goes to the company CST AG for
parts of the investigations and the simulation
support.Edited by: R. Schuhmann
Reviewed by: S. Lindenmeier and one anonymous referee
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