The fast Illinois solver code (FISC) is a collaborative effort between the Center for Computational Electromagnetics and DEMACO to put together and industrial strength code that can solve for the radiation and scattering of electromagnetic field by and in the vicinity of complex structures.

At this point, it can calculate for the scattering solution (RCS) from complex targets like aircraft, tanks, cars, etc. It uses a multilevel fast multipole algorithm (MLFMA) developed at the University of Illinois.

The problem is formulated using the method of moments (MoM), where the RWG ( Raw, Wilton, and Glisson) basis functions are used. The resultant matrix equation is solved iteratively by the conjugate gradient (CG) method. The multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiplication in CG. Both complexities for the CPU time per iteration and memory requirements are of O(N log N), where N is the number of unknowns. A 2.4 million unknown problem can therefore be solved in a few hours on the SGI CRAY Origin 2000 at NCSA of the University of Illinois at Urbana-Champaign. Ordering information about the code can be found from DEMACO.

Complexity of FISC

To test the complexity of this algorithm, the electromagnetic scattering from a conducting sphere si computed using the combined field integral equations (CFIE) on SGI Power Challenge (single processor, 2GB of memory). The diameter of the sphere varies from 1.5 wavelength to 24 wavelength. The number of unknowns (N) ranges from 2,352 to 602,112, while the number of levels in MLFMA is from 3 to 7. The CPU time per iteration is close to 8.5x10-5 N log N and the memory requirement is close to 2.7x10-3 N.

CPU time and memory requirement as a function of N

Solving Large and Complex Structures on Supercomputers

The first simulation example is the computation of the current distribution on the VFY218 plane at 2 GHz. The plane wave is incident 30 degree from the nose, and is vertically polarized. AT 3 GHz, the VFY218 with inlet sealed is 155 wavelength long, and is refined to 2,032,518 unknowns. The problem can be solved on Origin 2000 with 8 processors, 6.6 GB of memory, and 13 hours of CPU time.

Current distribution on the VFY218 at 2 GHz.

The largest object that has been tested is a conducting sphere of 48 wavelength diameter at 7.2 GHz (2,408,448 unknowns, eight-level MLFMA). A total of 8 processors and 5GB of memory are used in an Origin 2000 at NCSA, University of Illinois. The problem takes 5 hours of CPU time to complete the computation. The current version of FISC is parallelized for SGI CRAY shared memory machines without changing the data structure. Our result show good agreement with the Mie-Series solution. The following Figure presents the Bistatic RCS computations for such a sphere.

Bistatic RCS of a 1-meter sphere

Capability of handling various kinds of boundary conditions

In the following example, a 1983 Chevrolet Camaro has been modeled. Most parts are modeled as PEC while the window glasses are modeled as thin dielectric sheets (TDS) and the tires are modeled with an IBC. The geometry is available in VRML (Virtual Reality Modeling Language) format. The incident field is generated by a Hertzain dipole shown in the following Figure.

1983 Chevrolet Camaro

Current distribution on the 1983 Camaro at 1GHz

The above work is a collaboration between Dr. Jiming Song, Dr. Cai-cheng Lu, Prof. Weng Cho Chew and Dr. Shung-wu Lee. Major funding comes from DOD MURI Program. Please send suggestions, comments, and inquiries to: song@sunchew.ece.uiuc.edu.