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Feko模型中SEP和FEM的优势

更新时间：2019-12-18 21:13:01 大小：384K 上传用户：18139413306查看TA发布的资源 标签：Feko模型SEPFEM 下载积分：2分 评价赚积分 （如何评价?） 打赏 收藏 评论(0) 举报

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Combining the Advantages of the SEP and FEM to Model Complex Dielectric Geometries in Feko

This paper describes automotive windscreen antenna analysis in Feko, requiring the hybridization of the multilevel fast multiple method based on the surface equivalence principle,  the finite element method and windscreen antenna analysis for the most efficient solution. 


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Combining_the_Advantages_of_the_SEP_and_FEM_to_Model_Complex_Dielectric_Geometries_in_Feko.pdf 384K

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Combining the Advantages of the SEP and FEM to  
Model Complex Dielectric Geometries in Feko  
Johann van Tonder1, Marianne Bingle1, Marlize Schoeman1, Ulrich Jakobus2, and Johan Huysamen1  
1Altair Development S.A. (Pty) Ltd, Stellenbosch, South Africa  
2Altair Engineering GmbH, Böblingen, Germany  
Abstract—This paper describes automotive windscreen antenna  
analysis in Feko, requiring the hybridization of the multilevel  
fast multiple method based on the surface equivalence principle,  
the finite element method and windscreen antenna analysis for  
the most efficient solution.  
I. INTRODUCTION  
Altair Feko [1] has a wide range of techniques to model  
complex dielectrics, including the method of moments (MoM)  
based on either the surface equivalence principle (SEP) or the  
volume equivalence principle (VEP), the finite element method  
(FEM), the finite difference time domain method (FDTD), and  
Fig. 1. Multiple dielectric regions with junctions.  
special formulations for planar multilayer structures,  
windscreen antennas, skin effect, thin sheets, coatings, etc. For  
large structures the MoM is accelerated by using the multilevel  
fast multiple method (MLFMM). Since each formulation has  
its own advantages and limitations, it is often required to use a  
combination of these techniques for optimal performance.  
Over the years Feko has become synonymous with hybridizing  
different solver techniques. This paper will focus on  
automotive windscreen antenna analysis, requiring the  
Fig. 2. Equivalent electric and magnetic currents on the boundaries.  
hybridization of the MLFMM based on SEP and FEM and  
windscreen antenna analysis. The outline of the paper is as  
III. FINITE ELEMENT METHOD  
follows: the strengths and weaknesses of the SEP and FEM are  
The FEM represents dielectric regions as tetrahedral  
volume elements, where each element could have its own  
dielectric properties. The FEM tetrahedral volume elements of  
the head of a human phantom is shown in Fig. 3. In the hybrid  
FEM/MLFMM method, the MLFMM is only applied to the  
boundary surface elements of the FEM, significantly  
improving the efficiency of the MLFMM for cases with high  
levels of geometrical detail and for highly lossy dielectrics.  
outlined in Sections II and III, respectively; these techniques  
are then combined with windscreen antenna analysis to reduce  
both runtime and memory in Section IV.  
II. SURFACE EQUIVALENCE PRINCIPLE  
The SEP represents homogeneous dielectric regions as  
shown in Fig. 1 by modeling their surfaces as mesh triangles  
and placing equivalent electric currents J and magnetic  
currents M at these boundaries. These equivalent currents on  
dielectric and metallic triangles between medium A and  
medium B are shown in Fig. 2. Using the SEP, the MLFMM  
requires a matrix-vector-product for every region during the  
iterative solution. It is efficient for a small number of low  
contrast homogeneous dielectric regions. Unfortunately, there  
are drawbacks for high contrast and highly lossy dielectrics:  
fine mesh leads to a larger MLFMM near-field matrix;  
inhomogeneous mesh will degrade parallel runtime  
and memory efficiency due to “load imbalance”;  
the MLFMM addition theorem will require too many  
multipoles and might become unstable.  
Fig. 3. FEM tetrahedral volume elements.  
978-1-5386-7845-9/18/$31.00 ©2018 IEEE  
7
requiring only the metallic elements on the windscreen to be  
meshed.  
IV. WINDSCREEN ANTENNA ANALYSIS  
Consider a typical automotive windscreen antenna analysis  
in Fig. 4. The complex detail of the antenna module can be  
seen in the close-up, including multiple different dielectric  
regions, e.g., air, enclosing radome, ceramic substrate, etc.  
Either the SEP or FEM can be used to model the antenna  
module, but computational resources below will show that the  
FEM is more efficient to treat the fine detail and multiple  
dielectric regions, including the high dielectric ceramic  
substrate (relative permittivity 19.7).  
TABLE I  
MULTILAYER WINDSCREEN PROPERTIES  
The runtime and memory requirements for the model in  
Fig. 4 are given in Table II, where we compare resources  
when the SEP versus the FEM are used to model the complex  
antenna module. The FEM model reduces both the total  
runtime and memory footprint by a factor of 2. Calculation of  
the matrix elements is 4.4 times faster, and the iterative  
solution of the linear equations is 5.6 times faster. For this  
relative small problem, the time to initialise the Green’s  
function for the windscreen antenna is significant. For larger  
problems this time will be less dominant in the total runtime,  
resulting in final speed-ups greater than the factor of 2  
reported here.  
TABLE II  
COMPUTATIONAL RESOURCES  
(160K UNKNOWNS; 4 PARALLEL PROCESSES ON  
INTEL(R) XEON(R) CPU E7-4820 V3 @ 1.90 GHZ)  
Fig. 4. Windscreen antenna analysis with close-up of antenna module.  
V. CONCLUSION  
Automotive windscreen antenna analysis with complex  
antenna modules requires the hybridization of the MLFMM-  
SEP, the FEM and windscreen antenna analysis. It is shown  
that the FEM is more efficient to model the fine details and  
multiple dielectrics as compared to the SEP, which is more  
suited to low-contrast homogeneous dielectrics.  
Fig. 5. Windscreen consisting of multilayer dielectrics.  
The windscreen itself consists of multilayer dielectrics as  
shown in Fig. 5, with the dielectric properties and layer  
thicknesses given in Table I. Meshing the windscreen layers  
with these extreme thickness values (especially the Siglasol  
layer) in a full three-dimensional simulation will be too  
complex. Windscreen analysis in Feko automatically takes  
these layers and the windscreen curvature into account,  
REFERENCES  
[1] Altair Feko, Altair Engineering, Inc.,
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