This test case was one of the test cases in the JINA 2006 Workshop. The test case deals with the diffraction of a plane wave by a set of perfectly conducting half sphere and cylinder located over a perfectly conducting finite surface.

The radius of the half sphere is R; R=0.2 m. The length of the cylinder is L; L=1 m. The dimensions of the finite metallic surface is AxB; A=1.8 m, B=1.2 m. The gap between the cylinder and the perfectly conducting surface is H; H=0.02 m The centre of the cylinder is the origin of the coordinate system.

Figure 1: Geometry of the placyl test case |

Figure 2: Geometry of the placyl test case |

The RCS was computed using the EfieldFD MLFMM solver at frequencies 5GHz and 10GHz.

Bistatic RCS at 5GHz and 10GHz in two cuts:

- Bistatic RCS in the upper x-z plane for incident plane wave excitation at theta 50 degrees and phi 0 degrees (Bistatic RCS along cylinder)
- Bistatic RCS in the upper y-z plane for incident plane wave excitation at theta 50 degrees and phi 90 degrees (Bistatic RCS across cylinder)
- Polarizations: θθ and φφ

Monostatic RCS at 10 GHz for:

- Incident angles: theta 45 degrees and phi from 0 to 180 degrees with a 1 degree step
- Polarizations: θθ and φφ

In Figure 3 the bistatic RCS at 5GHz along the cylinder is shown, in Figure 4 the bistatic RCS at 5GHz across the cylinder is shown. In Figure 5 the bistatic RCS at 10GHz along the cylinder is shown and in Figure 6 the bistatic RCS at 10GHz across the cylinder is shown. In Figure 7 the surface currents for the bistatic simulation at 5GH with plane wave excitation with incident plane wave at theta 50 degrees and phi 0 degrees and theta polarisation is shown.

In Figure 8 the monostatic RCS at 10GHz is shownn.

The results obtained using efield agree very well with other results presented during the workshop.

The problem was solved using the EfieldFD Multi Level Fast Multipole Method. A Combined Field Integral Equation (CFIE) was used to speed up the convergence. The simulation was run on one processor for the bistatic cases and on four processors for the monostatic case on an AMD Dual Core Opteron 285 2.6 GHz with 16 Gb memory.

Simulation timing results are shown in Table 1 and Table 2.

Frequency |
Number of unknowns |
Number of elements |
Mesh resolution |
Memory |
CPU-time |

5 GHz | 525840 | 350560 | 10 edges per wavelength | 6.4 Gb | 1.4 hours |

10 GHz | 1167312 | 778208 | 7,5 edges per wavelength | 13 Gb | 5 hours |

Frequency |
Number of unknowns |
Number of elements |
Mesh resolution |
Memory |
CPU-time(total) |
CPU-time(assembly) |
CPU-time(solve) |

10 GHz | 1167312 | 778208 | 7,5 edges per wavelength | 13 Gb | 126 hours | 1.7 hours | 124 hours |

Figure 3: Bistatic RCS at 5GHz along cylinder |

Figure 4: Bistatic RCS at 5GHz across cylinder |

Figure 5: Bistatic RCS at 10GHz along cylinder |

Figure 6: Bistatic RCS at 10GHz across cylinder |

Figure 7: Surface currents at 5GHz |

Figure 8: Monostatic RCS at 10GHz |