for Assessing the Accuracy of Solutions of Electromagnetic Scattering Problems
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We solved two classes of Helmholtz-type scattering problems; involving extremely-large perfectly-conducting (PEC) objects, and two-layered composite dielectric objects. The first class involves a conducting sphere and a NASA Almond geometries of various sizes, whereas the second class involves a two-layered dielectric sphere with various dielectric properties.
The PEC sphere has a radius of 0.3 m, and the NASA Almond has a length of 0.2523744 m. We solve the sphere at 20 GHz, 40 GHz, 80 GHz, 96 GHz, 120 GHz, 160 GHz, 180 GHz, 210 GHz, 260 GHz, 280 GHz, 340 GHz, 380 GHz, 440 GHz, 500 GHz, and NASA Almond at 112.5 GHz, 225 GHz, 450 GHz, 900 GHz, 1800 GHz, 2500 GHz frequencies.
All geometries are located at the origin and illuminated by a plane wave propagating in the -x direction with the electric field polarized in the y direction. Note that, NASA Almond lies on the x-y plane with its sharp end pointing in the +x direction. The case which NASA Almond is illuminated from its sharp edge, i.e., the planewave is propagating in the (θ,φ) = (π/2, 0) direction, is noted as head-on illumination. NASA Almond is also illuminated 30° from the x axis on the x-y plane. In that case, the planewave is propagating in the (θ, φ) = (π/2, π/6) and polarized in the φ direction in spherical coordinates.
We compute the far-zone co-polar electric field with its real and imaginary parts on the x-y plane with the resolution of 0.1°. Since geometries are symmetric with respect to the x-z plane, if they are illuminated from the +x direction, the results will be symmetric with respect to the x-z plane as well. Therefore, for the PEC and dielectric spheres as well as the NASA Almond which is head-on illuminated, the electric field is calculated at 1801 points on the x-y plane from φ = 0 (back-scattering direction) upto φ = π (forward-scattering direction). But for NASA Almond which is illuminated from (θ, φ) = (π/2, π/6), the electric field is calculated at 3601 points on the x-y plane from φ = 0 upto φ = 2π since the symmetry isn't exist. Specifically, we compute
The input file should be a plane text file which contains f[n] which is described above, with its real and imaginary parts. That is, for the spheres and head-on-illuminated NASA Almond, and input file should contains 1801 rows and two columns, and for NASA Almond 30° illuminated, it should contains 3601 rows and two columns. Each row corresponds to a sample with its real and imaginary parts.
Error CalculationWe calculate errors by the formula given below. Note that for sphere problems, input data is compared with their corresponding analytical Mie series results; but for NASA Almond, it is compared with ABAKUS's computational MLFMA results.
PlottingFor spheres, we calculate RCS by the formula which is given below. For NASA Almond, we multiply this value by π to prevent normalization. We also plot +-30° interval of back-scattering and forward scattering area. An example plot is shown below.
Extremely-Large Conducting Objects (Sphere & NASA Almond)
Composite Dielectric Objects (Two-layered Sphere)