A Study On Hierarchical-matrix-based Fast Algorithm For Solving Partly Combined Field Integral Equation

Among the electromagnetic field numerical calculation methods, the method of moments whichuses combined field integral equation is an effective way to solve the closed structure. But in reality,electrically large platform wire antenna model has two parts, one is a closed structure, another is anopen structure. For this geometry of wire/surface combination, the combined field integral equationis not suitable. The convergence of the impedance matrix is bad when the electric field integralequation is used to solve antenna radiation problems, thus facing the defect that iterationconvergence is very slow.Partly combined field integral equation is a kind of improved integralequation, which uses the electric field integral equation for the wires and surfaces connected bywires, and the combined field integral equation for the remaining closed parts. Using this methodcan accelerate the speed of convergence of the iteration in the solution of the integral equation. It isan effective way of processing antenna platform radiation questions.This thesis reproduced partly combined field integral equation to solve wire/surface geometryantenna radiation and analyzed iterative convergence.The conventional method of moments facesbad efficiency to solve large objects. This thesis used Hierarchical matrix (H-matrix) which is basedon the degenerated kernel idea to reduce storage and computational time, using interpolationtechnology to separate the source and field coordinates. Since the main storage and calculation isdue to the matrix made by surface to surface operation, we only combined this part with H-matrix toreduce storage capacity and to improve the operation efficiency. These Matrix block elements usecombined field integral equation to calculate unless the junction elements. We first realized fastsolution in combined field integral equation which used permissible condition to discriminate nearblocks and blocks away. The block element which does not meet the condition is calculated by themethod of moments, while the rest can use Rk matrix to fill. On the basis of the fast algorithm ofcombined field integral equation, we found the common edges relevant to connected points andsubtracted the magnetic field integral equation part in iterative solution process, ultimatelyachieving rapid computation of the partly combined field integral equation.