A Study On H~2-Matrix-Based Algorithm For Solving The Electric Field Integral Equation

Solving large scale objects is one of the mainly research problems in ComputationalElectromagnetic. Hierarchical Basis H-Matrix (H2-matrix) method is an efficient way to handle thescattering problems. Using the Transfer Matrix, H2-matrix method can reduce much more storageand computational complexity than Hierarchical Matrix (H-matrix) method.This thesis is based on H2-matrix method, analyzing the scattering performance of conductors.Firstly, introduce the H2-matrix method and deduce the storage and computational complexity intheory and explain the advantages of H2-matrix method by comparing it with H-matrix method.Secondly, testify the property of Transfer Matrix, summarize the relationship between the numberof Lagrange interpolation points and accuracy. Reduce the storage of Coupling Matrix by usingmethod of its relative position. Finally, analyze the scatters’ property which includes to discrete thethree dimension objects and get the surface electronic current by MoM. The scatters aredecomposed in different layers to near and far fields and degenerate the kernel function by using theLagrange interpolation method in far field. Using the Transfer Matrix and relationship between thesons’ cluster basis of the trees to represent the relationship between the fathers’ cluster basis is anefficient way. Storing the elements in near field and solving the matrix by CG method. Verify theaccurate results by calculating the objects such as sphere, cylinder and so on. Comparing the resultswith those made by H-matrix method, good performance shows H2-matrix method can decrease thestorage and computational complexity for solving the scattering problems better than H-matrixmethod.