Fast Electromagnetic Solvers for Large-Scale Naval Scattering Problems; Final rept. 1 Oct 2006-27 Sep 2008

摘要

Efficient modeling of electromagnetic scattering has always been an active topic in the field of computational electromagnetics. To reduce the memory and CPU time in the method of moments (MoM) solution, an efficient method based on pseudo skeleton approximation is presented in this report. The algorithm is purely algebraic, and therefore its performance is not associated with the kernel functions in the integral equations. The algorithm starts with a multilevel partitioning of the computational domain, which is very similar to the technique employed in multilevel fast multipole algorithm (MLFMA). Any of the impedance sub-matrices (with size of m x n) associated with the well- separated partitioning clusters (far interaction terms) is represented by the product of two much smaller matrices (with sizes of m x r and r x n), where r is the effective rank. Therefore, the memory requirement will be relieved and the total CPU time will be reduced significantly as well, since the rank is much smaller than the original matrix dimensions. It should be noted that we don't have to calculate all the impedance entries to implement the aforementioned decomposition. Instead, we only need to calculate a few randomly chosen rows and columns of those impedance entries. Further compressions based on singular value decomposition (SVD) are performed so that the rank reaches its optimal limit, which leads to the optimized final matrix compression. Numerical examples are provided to show the validity of the new algorithm. Future work directions are also discussed in this report.