**Including CBFM for dielectric bodies and new RCS target models in Component Library**

Radar Cross Section (RCS) and scattering simulation is one of the key applications of Feko thanks to a complete solution from meshing and geometry tools, through general and specialist solvers, and to post-processing and reporting capabilities. Such simulation crucial to understand how visible an object is for radar systems, and being used across different industries, like Aerospace & Defense to develop stealth technology or Automotive in the context of Advanced Driver-Assistance Systems (ADAS).

The RCS of an object is influenced by several factors:

- Frequency, incident angle and polarization of the incident electromagnetic wave
- Size, shape, and material of the object

This can be illustrated with a simple generic (but typical) example. We first analyze the RCS of a metallic sphere. For reasons of symmetry, the RCS is independent of the direction of incidence. Now we add a cone to the sphere with tangent continuity along the connection curve.

On the back of the Cone-Sphere the RCS remains the same, but at the front it becomes 19 dB lower (blue curve vs. red curve). In addition, a dielectric coating can be applied to further minimize the RCS. The new result (green curve) is created using two dielectric layers on the metallic surface and is reducing the RCS in front direction by additional 20 dB.

The RCS-simulation of such dielectric coated materials is much more complex than for purely metallic structures. To improve RCS-simulation performance **Characteristic Basis Functions Method (CBFM) were introduced in Feko **2023 for metallic objects. Basically, CBFs are aggregated low-level basis functions with specific weights, computed from a plane wave spectrum to reduce the model size.

For more details about the principal idea, advantages and limitations of CBFM, please check the Altair Community article [1], which explains several examples including a model of an aircraft and a ship. Also, you may want to check this video on our Altair How-To Youtube Channel [2].

In the recent **Feko 2024 release** new features and several component library models have been added to reduce memory requirements for RCS-simulation and speed up model setup time. A bit more in detail, in Feko 2024 this feature is extended to dielectric bodies.

Let’s have a deeper look at the coated simulation model of the Cone-Sphere: The inner layer 1 with thickness t_{1} = 40 mm has dielectric material parameters e_{r} = 1.5 and tand = 0.067 and parameters of layer 2 are t_{2} = 5 mm, e_{r} = 4.0 and tand = 0.

Both layers are modeled with the surface equivalence principle (SEP) to use the full wave Methods of Moments (MoM) solver in Feko. For the simulation frequency is 1 GHz the object length is 14∙l (4.2 m) and the corresponding simulation model consists of 267.312 triangle elements to describe the metallic faces and the boundary surfaces of dielectric regions.

The model was simulated with the classical (default) RWG basis functions and the new characteristic basis functions (CBFM) for MoM.

Both solutions show excellent agreement for the RCS pattern. For the classical MoM-RWG solution the memory requirements are with 2.4 TB relatively high and require a large HPC cluster. With the MoM-CBFM the memory requirements can be reduced significantly **by factor 7.2** to 334 GB. That is much easier to handle on typical smaller size HPC clusters. In this example we pay a price for the large memory reduction with longer runtime.

Note, that the dielectric CBFM shows the same principal behavior as in the metallic case: In the first step of the simulation process the characteristic base functions are generated using a plane wave spectrum in order to approximate the current distribution over a subdomain on the structure. Because of this step, setting up the matrix elements takes longer with CBFM than with standard RWG basis functions. On the other hand the matrix size of the linear system is reduced and the more plane wave excitations are defined in the RCS simulation the better scales the runtime in the second solution step of CBFM.

**Standard Models for RCS evaluation **

In the Feko2024 release the Component Library is extended with standard RCS target objects, that can be used for method validation or to study principal RCS behavior for different frequencies or material parameters. Five types of objects **Almond**, **Ogive**, **Double-Ogive**, **Cone-Sphere**, and **Cone-Sphere with gap** are delivered in the updated **Component Library**.

The geometry of these objects is defined with analytical equations from [3]. The models come with frequency dependent dielectric material parameters, that have been used in the Austin RCS Benchmarks [4]. In this benchmark monostatic RCS measurements have been carried out using additively manufactured objects [5].

This measurement results have been published [4] and are available for validation purposes. With the already prepared RCS objects of the Component Library, it is very easy to set up such validation simulations.

In the two graphs the RCS pattern of the dielectric Almond at 7 GHz for vertical and horizontal polarization are plotted. The Feko result (blue curve) is compared with a reference solution and the measurement result, and an excellent correlation can be observed.

The complete Validation is documented in a white paper [6] available on the Altair website.

Finally, we use the dielectric Almond model from the library to compare MoM-CBFM with MoM-RWG at 10 GHz. Similar observation as in the first example: Nice memory reduction with longer computing time for the CBFM approach.

**More Resources about RCS, CBFM and radar target objects: **

- [1] Altair Community article about CBFM in Feko 2023:

- [2] Video in Altair How-To Youtube channel about CBFM: Characteristic Basis Functions Method in Feko (youtube.com)
- [3] A.C. Woo, H.T.G. Wang, M.J. Schuh, M.L. Sanders: Benchmark Radar Targets for the Validation of Computational Electromagnetics programs, IEEE Antennas and Propagation Magazine, Vol. 35, No. 1 February 1993.
- [4] https://github.com/UTAustinCEMGroup/AustinCEMBenchmarks/tree/master/Austin-RCS-Benchmarks
- [5] J. T. Kelly, D. A. Chamulak, C. C. Courtney, A. E. Yilmaz: Measurements of Non-Metallic Targets for the Austin RCS Benchmark Suite, AMTA 2019.
- [6] https://altair.com/resource/validation-of-austin-rcs-benchmarks-using-altair-feko?lang=en