Research On Low Frequency Near Field Numerical Modeling And Algorithms

Due to its high accuracy and efficiency,the electric field integral equation solved by method of moment with the Rao-Wilton-Glisson basis function is widely used in the computational electromagnetics community,such as antennas,microwave circuits,scattering,and so on.For high and middles frequency problems,one can achieve the accurate solutions by solving the electric field integral equation.However,when the frequency is low,the solution of the electric field integral equation will broke down.This is because the coupling between the electric and magnetic field is vanishing and the singularity of the impedance matrix becomes severe when the frequency goes to zero.Several remedies have been proposed to address this low frequency break down problem in the recent years.In this dissertation,some work which focuses the low frequency problem has been done and several novel and stable low frequency numerical algorithms have been proposed.Firstly,some basic principles in the electromagnetic have been reviewed in the dissertation.According to the surface equivalence principle,the derivation process for the surface integral equation,such as the electric field integral equation and the magnetic field integral equation has also been presented.Then,the main process and key technique of the method of moments have been introduced and the efficiency and accuracy of the EFIE and MFIE have been compared in the numerical examples.Secondly,in the dissertation,the reason of the low frequency breakdown problem has been given and the process of the conventional augmented electric field integral equation(AEFIE)which has been proposed to remedy the low frequency breakdown problem has also been reviewed.Then,a new augmented combined field integral equation(ACFIE)formulation has been proposed to address the low frequency breakdown problem.The newly proposed ACFIE is developed by adding the magnetic field integral operator to the conventional augmented electric field integral equation(AEFIE).The proposed ACFIE method can not only improve the iteration property of the impedance matrix but also remedy the accuracy problem of solutions occurred in the conventional AEFIE method when the frequency is extremely low.In addition,a kind of saddle point constraint preconditioner has also been introduced to furtherly improve the iterative property of the system impedance matrix in the dissertation.Then,the dissertation reviewed the procedure of the conventional multiresolution preconditioner method which can also been used to remedy the low frequency breakdown problem.Based on the conventional multiresolution method,an improved multiresolution method has been proposed by choosing the loop-flower basis function instead of loop-tree basis function as the coarse level multiresolution basis function.The proposed improved multiresolution method can largely reduce the condition of the system matrix and thus improve the iterative property of the system matrix.Some numerical examples have been given to show the efficiency of the proposed improved multiresolution method.In addition,a novel kind of hierarchical loop-flower bases method is proposed to remedy the EFIE low frequency breakdown problem.By choosing the hierarchical loop-flower bases as the new multiresolution bases,the number of the total bases of the new multiresolution method can be reduced a third compared with the conventional multiresolution method.In addition,a new method by combing the conventional multiresolution method with the augmented electric field integral equation is also proposed in the dissertation.In the new method,the current vector in the augmented electric field integral equation is expanded with the multiresolution bases in stead of the traditional RWG bases.Then,a new multiresolution preconditioner can be achieved based on the above procedure.Next,the new multiresolution preconditioner is introduce to the augmented electric field integral equation.Some numerical examples have showed that for some very low frequency problem,both the augmented electric field integral equation method and the conventional multiresolution method can not achieve the accurate solution,while the new proposed method can still achieve accurate solution in the same example.Finally,the relationship between the skin depth of metal conductor which owns a limit conductivity and the frequency is studied in the dissertation.Based on the fact that when the frequency is low,the skin depth of metal conductor is not very small and can not be neglected,a new equivalent numerical model of non-perfect conductor has been proposed in the dissertation.