Dielectric scatterer. Repeat Problem 12.6 above, but make the cylinder a dielectric material with r = 3. Use the average properties method to accurately model the cylindrical surface. Measure the scattering pattern with and without the average properties model and compare

Problem 12.6

Cylindrical scatterer.Repeat Problem 7.2, the cylindrical scatterer in 2D, including a TF/SF boundary and an absorbing boundary. This time, however, modify the updates on the surface of the cylinder to more accurately conform to the cylindrical surface, using the diagonal split-cell method described in this chapter. Compare the scattering pattern to that found in Problem 8.11.

Problem 7.2

Total-field/scattered-field in 2D. Consider implementing a 2D TM code similar to the example in Figure 7.4, except the scattering object will be a cylinder of radius 10 grid cells, rather than a square box. Make the space large enough so that fields do not reflect back into the space from the outer boundary.

(a) First, implement this scattering problem without the TF/SF method. In a separate simulation, compute the "incident" field by removing the scatterer. Calculate the scattered field by subtracting the incident field from the "total" field. Measure the scattering pattern by monitoring a number of points around the object at some distance.

(b) Now, implement this problem using the TF/SF method. You can use the same two simulations from part (a), and simply use the "incident" field at the boundary of the TF/SF interface. Measure the scattering pattern as you did in part (a). How do they compare? Comment on the relative merits of these two methods.