6th European Conference on Antennas and Propagation (EUCAP)
State of the Art of Electromagnetic Modelling in FEKO Ulrich Jakobus and Gronum Smith EM Software & Systems – S.A. (Pty) Ltd Stellenbosch, South Africa
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Abstract—Different computational techniques are required to solve the broad spectrum of electromagnetic problems. This paper illustrates the benefits of a true hybridisation of different techniques with full bi-directional coupling. Fast methods to reduce the total simulation time and/or memory requirement will also be discussed, as well as using these various methods not only for the analysis stage but also for the design synthesis and optimisation. Keywordshybridisation, parallelisation, FEKO
I.
optimisation,
fast
II.
HYBRIDISATION OF CEM TECHNIQUES
A. Dominant Techniques The full wave solutions that have dominated the industry are the integral equation Method of Moments (MoM, frequency domain), the Finite Element Method (FEM, frequency or time domain) and the Finite Difference Time Domain (FDTD, time domain) or Finite Integration Method (FIT, time domain). The asymptotic high frequency solvers Uniform Theory of Diffraction (UTD), Physical Optics (PO) and Geometrical Optics (GO) have been limited to very specific applications. The combination of these techniques (full wave solvers with asymptotic methods) under a single user interface or as hybrid solvers has been a major driving force in the development of CEM tools including FEKO [1].
solvers,
INTRODUCTION
It is a well-known fact that no single computational electromagnetics (CEM) solver is able to solve the whole spectrum of practical electromagnetic problems efficiently. Due to the underlying mathematical formulations their applicability to different problem types varies, see Fig. 1. Hybridisation of these techniques retains the best characteristics of each method but offers an improved efficiency for the solution of complex problems composed of different sub-problems (e.g. antenna mounted on a platform). Apart from hybridisation, fast solvers such as the multilevel fast multipole method (MLFMM), parallel processing and GPU algorithms play an important part in the solution of complex real-life electromagnetic problems.
B. Asymptotic High Frequency Techniques (PO, UTD, GO) The hybridisation of the Method of Moments (MoM) and the asymptotic high frequency Physical Optics (PO) technique was the first hybrid method in FEKO to expand the limits of what was possible on small computers at that time [2]. The hybrid MoM/UTD formulation [3], enables the efficient analysis of structures which can be represented by canonical objects. The ray-launching Geometrical Optics (GO) formulation (also sometimes referred to as SBR = shooting and bouncing rays) was added in 2008 to FEKO to allow for the solution of geometries where PO would be inefficient (e.g. transmission through dielectric lenses, multiple reflections). C. Finite Element Method (FEM) Where structures are separated by free space the integral equation technique MoM has shown to have an inherent advantage over those techniques which require discretisation of this space and truncation with an absorbing boundary condition. Despite this advantage the MoM on its own is not always sufficient. For example for highly inhomogeneous dielectric bodies a technique such as FEM is required. The hybrid MoM/FEM technique is an elegant solution and was introduced in FEKO in 2005 [4] and extended for electrically large problems to the hybrid MLFMM/FEM in 2010. D. Multi-Conductor Transmission Line (MTL) Despite the advances in 3D solvers, full wave solutions of large structures with a very high degree of geometrical complexity e.g. a shielded cable harness with multiple cable bundles, are theoretically possible but due to the number of un-
Figure 1 Graphical representation of the suitability of different numerical electromagnetics techniques.
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knowns impractical. However, also here a combination of different solvers in a hybrid formulation can be used. For example the body of a vehicle can be solved using the MoM or MLFMM and the cable harness inside the vehicle can be modelled using Multi-Conductor Transmission Line (MTL) theory [5] in a setup like in Fig. 2 (irradiation example).
V.
DESIGN, SYNTHESIS AND OPTIMISATION
With faster electromagnetic solvers it has become possible not only to analyse a specific fixed geometry but also to optimise a design for set goal functions like antenna performance. CEM codes are focused on the analysis of a given design and design software tools like Antenna Magus [7] are increasingly incorporated in the total design workflow which includes the technical specifications, the suggested design, fast synthesis of the basic design, accurate analysis and optimisation of the design and finally export of the design for manufacturing, see Fig. 4.
Figure 2. An equivalent distributed circuit is used to represent the multi-conductor transmission line for irradiation problems.
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SPECIAL EXTENSIONS AND APPROXIMATIONS
Where rigorous solutions cannot be obtained or where they would lead to drastic increases in the number of unknowns and solution times, approximations and their incorporation into solvers can be used to great effect. Examples of these include the handling of thin coatings, thin dielectric sheets (including windscreen antenna modelling). The effect of real ground, can also be taken into consideration through the Sommerfeld integrals in the MoM, see e.g. [6] for a summary. IV.
Figure 4. CEM software forms only part of the design cycle. Extensions and interfaces to other software packages are used to cover a larger part of the process.
FAST SOLUTIONS
Despite faster computers the fast solution of integral equations remains highly desirable. Here the MLFMM and the Adaptive Cross Approximation (ACA) methods have been used to great effect.
VI.
CONCLUSION
The hybridisation of different numerical techniques extends the range of electromagnetic problems that can be solved. Valid approximations can also be used to overcome limitations of rigorous full-wave solvers. Despite major advances in the speed, efficiency and capability of CEM solvers the requirements are ever demanding and challenging.
Distribution of the solver load by way of parallel processing is another technique which is utilised. Highly efficient shared memory or distributed memory systems using e.g. MPI/OpenMPI are supported (also in hybrid combination for clusters of multi-CPU nodes).
REFERENCES
Fast graphics cards (GPU processing) are used to solve different phases of the solution process such as the LU decomposition of the MoM matrix. See Fig. 3 for a performance comparison CPU versus GPU.
[1] [2]
[3]
[4]
[5]
[6] Figure 3. Performance of the LU decomposition of the MoM matrix comparing different CPUs with different GPUs (double precision accuracy). [7]
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FEKO, EM Software & Systems-S.A. (Pty) Ltd, www.feko.info. U. Jakobus and F. M. Landstorfer, "Improved PO-MM hybrid formulation for scattering from three-dimensional perfectly conducting bodies of arbitrary shape," IEEE Transactions on Antennas and Propagation, vol. 43, pp. 162-169, Feb. 1995. U. Jakobus and F.M. Landstorfer, “A combination of current- and raybased techniques for the efficient analysis of electrically large scattering problems,” Conference Proceedings of the 13th Annual Review of Progress in Applied Computational Electromagnetics, (Monterey), pp. 748-755, Mar. 1997. F. J. C. Meyer, D. B. Davidson, U. Jakobus, and M. Stuchly, "Human exposure assessment in the near field of GSM base station antennas using a hybrid finite element / method of moments technique," IEEE Transactions on Biomedical Engineering, vol. 50, pp. 224-233, Feb. 2003. M. Schoeman and U. Jakobus, “Numerical solution of complex EMC problems involving cables with combined field / transmission line approach,” Interference Technology ITEM, The International Journal of Electromagnetic Compatibility, pp. 78-88, April 2011. U. Jakobus, "Comparison of different techniques for the treatment of lossy dielectric/magnetic bodies within the method of moments formulation," AEÜ International Journal of Electronics and Communications, vol. 54, no. 3, pp. 163-173, 2000. Antenna Magus, MAGUS (Pty) Ltd, www.antennamagus.com.
