The use of Huygens´ equivalence principle for solving 3D volume integral equation of scattering

Presents an integral equation solver using the nested equivalence principle algorithm (NEPAL) which has been successfully applied previously to 2D problems. It is known that in solving an integral equation, one can first replace the volume scatterer by small subscatterers where the size of a subscatterer is much smaller than a wavelength. The unknown function to be sought is expanded in terms of basis functions which usually have their supports on the subscatterers. By matching the field on the subscatterers, a set of linear equations are formed. The number of unknowns is proportional to the number of subscatterers in this case. Physically, each subscatterer can be considered a scattering center. The interaction of a subscatterer with the other subscatterers can be described by interaction matrices. If there are N subscatterers, then there will be N/sup 2/ interaction matrices since each subscatterer will interact with all the other subscatterers including itself. The N/sup 2/ interaction matrices can be found with N/sup 3/ operations. The idea of NEPAL is to reduce the number of scattering centers, and hence to reduce the CPU time required for the solution, and essentially find the inverse of the integral operator with computational complexity less than O(N/sup 3/).