NASA Almond
This is an EMCC benchmark target referenced in:
Alex C. Woo, Helen T. G. Wang, Michael J. Schuh, and Michael L. Sanders, "Benchmark Radar Targets for the
Validation of Computational Electromagnetic Programs" IEEE Antennas and Propagation Magazine Vol. 35,
No. 1 February 1993.
The Efield MLFMM was used to compute the RCS of the almond. Two different length of the almond was used in the
simulations. Two different material cases was studied, a PEC case and a coated case.
Definition of geometry
Two different geometrical configurations was used in the simulation of RCS. The definition of the
geometry is shown in Figure 2.
 Length: d = 9.936 inch
 Length: d = 2.5 m
Figure 1: The NASA almond

Figure 2: Definition of geometry of NASA almond

Simulation with efield
Four different cinfigurations was studied:
 9 inch PEC case
 9 inch coated case
 2.5m PEC case
 2.5m coated case
The 9 inch cases can be solved using Efield MoM solver but here we use the Efield MLFMM solver. The 2.5m cases
are electrically large and was solved using Efield MLFMM solver. The Efield MLFMM solver can handle both PEC cases
and mixed PEC, dielectric and magnetic materials such as in the coated case.
9inch PEC case
Model and simulation data:
 9 inch PEC case
 Monostatic RCS at 7 GHZ in azimuth plane (xyplane)
 CFIE is used with alpha = 0.5
 10020 elements
 15030 unknowns
In Figure 3 and Figure 4 the monostatic RCS are shown and compared with measurement results. In
Figure 5 the surface currents are shown.
Figure 3: Monostatic RCS of 9 inch PEC NASA almond at 7 GHz in azimuth plane.
Polarization VV. Computations (left) and results from Alex C. Woo, Helen T. G. Wang, Michael J. Schuh, and Michael L. Sanders (right).

Figure 4: Monostatic RCS of 9 inch PEC NASA almond at 7 GHz in azimuth plane.
Polarization HH. Computations (left) and results from Alex C. Woo, Helen T. G. Wang, Michael J. Schuh, and Michael L. Sanders (right).

Figure 5: Surface currents of 9 inch PEC NASA almond at 7 GHz

9inch coated case
Model and simulation data:
 9 inch coated case
 Monostatic RCS at 3 GHZ in upper xzplane
 0.1 λ coating (10 mm)
 Material parameters for the coating:
 Case 1: ε_{r} =1, μ_{r} =1
 Case 2: ε_{r} =32i, μ_{r} =2i
In Figure 6 the monostatic RCS is shown.
Figure 6: Monostatic RCS of 9 inch coated NASA almond at 3 GHz in upper xz plane.
In black pure PEC case, in red coated case with ε_{r} =1, μ_{r} =1 and CFIE,
in blue coated case with ε_{r} =1, μ_{r} =1 and EFIE,
in green coated case with ε_{r} =32i, μ_{r} =2i and CFIE and
in magenta coated case with ε_{r} =32i, μ_{r} =2i and EFIE.

2.5m PEC case
This case was a JINA 2006 test case. Model and simulation data:
 2.5 PEC case
 Plane wave excitation at φ=0 degrees and θ=90 degrees
 Bistatic RCS at 8 GHZ in xyplane and xzplane
 327612 elements
 419418 unknowns
 Efield MLFMM using CFIE with SPAI preconditioner
 Number of iterations in MLFMM:
 θpolarization: 27 iterations
 φpolarization: 29 iterations
 Total time: 3.5 hours
In Figure 7 the bistatic RCS is shown and in Figure 8 the surface currents is shown.
Figure 7: Bistatic RCS of 2.5m PEC NASA almond at 8 GHz in xyplane (left) and
xzplane (right).

Figure 8: Surface currents of 2.5m PEC NASA almond at 8 GHz

2.5m coated case
This case was a JINA 2006 test case. Model and simulation data:
 2.5m coated case
 30mm coating
 Material parameters for the coating:
ε_{r} =1.50.1i, μ_{r} =2.51.8i
 Plane wave excitation at φ=0 degrees and θ=90 degrees
 Bistatic RCS at 1 GHZ in xyplane
 77692 elements
 178464 unknowns
 Efield MLFMM using EFIE with SPAI preconditioner
 Number of iterations in MLFMM:
 θpolarization: 16 iterations
 φpolarization: 17 iterations
 Total time: 0.85 hours
In Figure 9 the bistatic RCS is shown.
Figure 9: Bistatic RCS of 2.5m coated NASA almond at 1 GHz in xyplane.
