# Simulation for the RCS of the scattering by a dieletric sphere, compared with Mie theory

I follow the build-in Getting Started guide on Radar Cross Section to do a computation on the scattering by a dieletric sphere. The bistatic RCS result from HFSS (even after many refinement passes) still seems to be pretty off from the Mie theory solution.

The PEC cube in the guide is changed into a dielectric sphere of relative permittivity = 2.56. The simulation is done at 300MHz. The distance between PML and sphere is set to be 1 meter > λ/4. The incident wave is a plane wave towards +z, with E-field polarized along x-axis. After 16 adaptive passes, the solution has a delta energy ~ 0.001, and the sphere mesh has about 480k tetrahedrons. The normalized Bistatic RCS on E-plane looks closed to Mie theory, while on H-plane, it looks pretty off.

I check the Mie theory solution, for example in Figure 7.11 (Section 7.4.4) on page 356 from the text book *Theory and Computation of Electromagnetic Fields* amazon link: https://www.amazon.com/Theory-Computation-Electromagnetic-Fields-Wiley/dp/1119108047/

I would like to know why this discrepancy happens and how to mitigate it. Thanks in advance !

## Comments

PS : In the plots, Mie theory solution is shown in orange, HFSS in blue. The Mie theory solution look identical to the textbook plot, which can be found on page 356. You can find a book preview on google book: https://www.google.com/search?tbm=bks&q=Theory+and+Computation+of+Electromagnetic+Fields

I have exactly the same issue. Can anyone help?

HFSS is a FINITE element method. I.e. there is a space segmentation. It naturally leads to missing the target. The original feature of HFSS is adaptive meshing algorithm, which iteratively finds important areas for denser meshing, bringing you closer to truth, without requiring a supercomputer cluster and terabytes of RAM.

I would say, your plots are almost equal to your theoretical computation. The fit is really good in important areas. You would not get better in experiment.

You can get better result with denser meshing.

But the power of HFSS is in solving arbitrary geometry with arbitrary properties, which no analytic method can solve.

So you are just too picky to unimportant details, missing the main thing.

Hello,

The Analysis settings seem to be fine and what you could check about is the Boundary settings, like whether the boundary conditions are same in all the directions. You were saying like you got good results in one plane and other plane showing off results. So there are chances of the boundary condition discrepancies.

Otherwise, if every setup is intact then I would say the plot you got might be the correct one for the Model under simulation.

Regards,