A Study On Solution Of Electromagnetic Field Integral Equations Using The Adaptive Cross Approximation Algorithm

Computational techniques for solving electromagnetic wave scattering problems involving large complex bodies have been intensely studied by many researchers in the past. The phenomenal growth in computer technology, coupled with the development of fast algorithms with reduced computational complexity and memory requirements, have made a rigorous numerical solution of the problem of scattering from electrically large objects feasible.The electric field and equations derived from electromagnetic concepts used to solve radiation and scattering problems. The method of moments (MoM), a numerical technique used to convert the integral equation into dense matrix equation, which can be solved numerically using a computer. The fast methods for solving integral equations include but not limited to the CG-FFT, the AIM, and the FMM. These methods are called kernel-based fast methods, because their formulations, implementations, and performances depend on the specific integral kernels and an explicit decomposition of integral operators. Despite their remarkable power of solving large problems involving millions of unknowns, however, share one common drawback: their formulations and implementations change with the inherent kernels when applied to different problems.Besides the kernel-based fast methods, there is another class of fast methods, which are purely algebra based and kernel independent. The matrix generated by asymptotically smooth kernel is sparse in the sense that only few data are needed for their representation. Like many other fast solvers, the adaptive cross approximation (ACA) method takes advantage of the rank-deficient nature of off-diagonal sub blocks in the moment-method matrix. ACA uses only few of the original entries for the low-rank approximation of the whole matrix and is therefore well-suited to speed up existing computer codes. These methods work on the moment-method matrix directly and achieve their computational speed-up solely through linear-algebra manipulations.Our research is refined combination of H-matrix, present further recompresion techniques in ACA algorithm. The contribution is a new hybrid method that combines the ACA algorithm with the approximation the kernel function using Lagrange interpolation polynomial to deal with the dense matrices efficiently, avoid the quadratic cost for the assembly and storage. This algorithm also reduces the time for approximate matrix construction.